├── COPYING ├── README ├── adapt_gmm.m ├── convert_hmm_to_gaussian_emissions.m ├── decode_hmm.m ├── eval_gmm.m ├── eval_hmm.m ├── is_valid_gmm.m ├── is_valid_hmm.m ├── kmeans.m ├── lmvnpdf.m ├── logsum.m ├── merge_states.m ├── reorder_states.m ├── sample_gaussian.m ├── sample_gmm.m ├── sample_hmm.m └── train_gmm.m /COPYING: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. By contrast, 15 | the GNU General Public License is intended to guarantee your freedom to 16 | share and change all versions of a program--to make sure it remains free 17 | software for all its users. We, the Free Software Foundation, use the 18 | GNU General Public License for most of our software; it applies also to 19 | any other work released this way by its authors. You can apply it to 20 | your programs, too. 21 | 22 | When we speak of free software, we are referring to freedom, not 23 | price. Our General Public Licenses are designed to make sure that you 24 | have the freedom to distribute copies of free software (and charge for 25 | them if you wish), that you receive source code or can get it if you 26 | want it, that you can change the software or use pieces of it in new 27 | free programs, and that you know you can do these things. 28 | 29 | To protect your rights, we need to prevent others from denying you 30 | these rights or asking you to surrender the rights. Therefore, you have 31 | certain responsibilities if you distribute copies of the software, or if 32 | you modify it: responsibilities to respect the freedom of others. 33 | 34 | For example, if you distribute copies of such a program, whether 35 | gratis or for a fee, you must pass on to the recipients the same 36 | freedoms that you received. You must make sure that they, too, receive 37 | or can get the source code. And you must show them these terms so they 38 | know their rights. 39 | 40 | Developers that use the GNU GPL protect your rights with two steps: 41 | (1) assert copyright on the software, and (2) offer you this License 42 | giving you legal permission to copy, distribute and/or modify it. 43 | 44 | For the developers' and authors' protection, the GPL clearly explains 45 | that there is no warranty for this free software. For both users' and 46 | authors' sake, the GPL requires that modified versions be marked as 47 | changed, so that their problems will not be attributed erroneously to 48 | authors of previous versions. 49 | 50 | Some devices are designed to deny users access to install or run 51 | modified versions of the software inside them, although the manufacturer 52 | can do so. This is fundamentally incompatible with the aim of 53 | protecting users' freedom to change the software. The systematic 54 | pattern of such abuse occurs in the area of products for individuals to 55 | use, which is precisely where it is most unacceptable. Therefore, we 56 | have designed this version of the GPL to prohibit the practice for those 57 | products. If such problems arise substantially in other domains, we 58 | stand ready to extend this provision to those domains in future versions 59 | of the GPL, as needed to protect the freedom of users. 60 | 61 | Finally, every program is threatened constantly by software patents. 62 | States should not allow patents to restrict development and use of 63 | software on general-purpose computers, but in those that do, we wish to 64 | avoid the special danger that patents applied to a free program could 65 | make it effectively proprietary. To prevent this, the GPL assures that 66 | patents cannot be used to render the program non-free. 67 | 68 | The precise terms and conditions for copying, distribution and 69 | modification follow. 70 | 71 | TERMS AND CONDITIONS 72 | 73 | 0. Definitions. 74 | 75 | "This License" refers to version 3 of the GNU General Public License. 76 | 77 | "Copyright" also means copyright-like laws that apply to other kinds of 78 | works, such as semiconductor masks. 79 | 80 | "The Program" refers to any copyrightable work licensed under this 81 | License. Each licensee is addressed as "you". "Licensees" and 82 | "recipients" may be individuals or organizations. 83 | 84 | To "modify" a work means to copy from or adapt all or part of the work 85 | in a fashion requiring copyright permission, other than the making of an 86 | exact copy. The resulting work is called a "modified version" of the 87 | earlier work or a work "based on" the earlier work. 88 | 89 | A "covered work" means either the unmodified Program or a work based 90 | on the Program. 91 | 92 | To "propagate" a work means to do anything with it that, without 93 | permission, would make you directly or secondarily liable for 94 | infringement under applicable copyright law, except executing it on a 95 | computer or modifying a private copy. Propagation includes copying, 96 | distribution (with or without modification), making available to the 97 | public, and in some countries other activities as well. 98 | 99 | To "convey" a work means any kind of propagation that enables other 100 | parties to make or receive copies. Mere interaction with a user through 101 | a computer network, with no transfer of a copy, is not conveying. 102 | 103 | An interactive user interface displays "Appropriate Legal Notices" 104 | to the extent that it includes a convenient and prominently visible 105 | feature that (1) displays an appropriate copyright notice, and (2) 106 | tells the user that there is no warranty for the work (except to the 107 | extent that warranties are provided), that licensees may convey the 108 | work under this License, and how to view a copy of this License. If 109 | the interface presents a list of user commands or options, such as a 110 | menu, a prominent item in the list meets this criterion. 111 | 112 | 1. Source Code. 113 | 114 | The "source code" for a work means the preferred form of the work 115 | for making modifications to it. "Object code" means any non-source 116 | form of a work. 117 | 118 | A "Standard Interface" means an interface that either is an official 119 | standard defined by a recognized standards body, or, in the case of 120 | interfaces specified for a particular programming language, one that 121 | is widely used among developers working in that language. 122 | 123 | The "System Libraries" of an executable work include anything, other 124 | than the work as a whole, that (a) is included in the normal form of 125 | packaging a Major Component, but which is not part of that Major 126 | Component, and (b) serves only to enable use of the work with that 127 | Major Component, or to implement a Standard Interface for which an 128 | implementation is available to the public in source code form. A 129 | "Major Component", in this context, means a major essential component 130 | (kernel, window system, and so on) of the specific operating system 131 | (if any) on which the executable work runs, or a compiler used to 132 | produce the work, or an object code interpreter used to run it. 133 | 134 | The "Corresponding Source" for a work in object code form means all 135 | the source code needed to generate, install, and (for an executable 136 | work) run the object code and to modify the work, including scripts to 137 | control those activities. However, it does not include the work's 138 | System Libraries, or general-purpose tools or generally available free 139 | programs which are used unmodified in performing those activities but 140 | which are not part of the work. For example, Corresponding Source 141 | includes interface definition files associated with source files for 142 | the work, and the source code for shared libraries and dynamically 143 | linked subprograms that the work is specifically designed to require, 144 | such as by intimate data communication or control flow between those 145 | subprograms and other parts of the work. 146 | 147 | The Corresponding Source need not include anything that users 148 | can regenerate automatically from other parts of the Corresponding 149 | Source. 150 | 151 | The Corresponding Source for a work in source code form is that 152 | same work. 153 | 154 | 2. Basic Permissions. 155 | 156 | All rights granted under this License are granted for the term of 157 | copyright on the Program, and are irrevocable provided the stated 158 | conditions are met. This License explicitly affirms your unlimited 159 | permission to run the unmodified Program. The output from running a 160 | covered work is covered by this License only if the output, given its 161 | content, constitutes a covered work. This License acknowledges your 162 | rights of fair use or other equivalent, as provided by copyright law. 163 | 164 | You may make, run and propagate covered works that you do not 165 | convey, without conditions so long as your license otherwise remains 166 | in force. You may convey covered works to others for the sole purpose 167 | of having them make modifications exclusively for you, or provide you 168 | with facilities for running those works, provided that you comply with 169 | the terms of this License in conveying all material for which you do 170 | not control copyright. Those thus making or running the covered works 171 | for you must do so exclusively on your behalf, under your direction 172 | and control, on terms that prohibit them from making any copies of 173 | your copyrighted material outside their relationship with you. 174 | 175 | Conveying under any other circumstances is permitted solely under 176 | the conditions stated below. Sublicensing is not allowed; section 10 177 | makes it unnecessary. 178 | 179 | 3. Protecting Users' Legal Rights From Anti-Circumvention Law. 180 | 181 | No covered work shall be deemed part of an effective technological 182 | measure under any applicable law fulfilling obligations under article 183 | 11 of the WIPO copyright treaty adopted on 20 December 1996, or 184 | similar laws prohibiting or restricting circumvention of such 185 | measures. 186 | 187 | When you convey a covered work, you waive any legal power to forbid 188 | circumvention of technological measures to the extent such circumvention 189 | is effected by exercising rights under this License with respect to 190 | the covered work, and you disclaim any intention to limit operation or 191 | modification of the work as a means of enforcing, against the work's 192 | users, your or third parties' legal rights to forbid circumvention of 193 | technological measures. 194 | 195 | 4. Conveying Verbatim Copies. 196 | 197 | You may convey verbatim copies of the Program's source code as you 198 | receive it, in any medium, provided that you conspicuously and 199 | appropriately publish on each copy an appropriate copyright notice; 200 | keep intact all notices stating that this License and any 201 | non-permissive terms added in accord with section 7 apply to the code; 202 | keep intact all notices of the absence of any warranty; and give all 203 | recipients a copy of this License along with the Program. 204 | 205 | You may charge any price or no price for each copy that you convey, 206 | and you may offer support or warranty protection for a fee. 207 | 208 | 5. Conveying Modified Source Versions. 209 | 210 | You may convey a work based on the Program, or the modifications to 211 | produce it from the Program, in the form of source code under the 212 | terms of section 4, provided that you also meet all of these conditions: 213 | 214 | a) The work must carry prominent notices stating that you modified 215 | it, and giving a relevant date. 216 | 217 | b) The work must carry prominent notices stating that it is 218 | released under this License and any conditions added under section 219 | 7. This requirement modifies the requirement in section 4 to 220 | "keep intact all notices". 221 | 222 | c) You must license the entire work, as a whole, under this 223 | License to anyone who comes into possession of a copy. This 224 | License will therefore apply, along with any applicable section 7 225 | additional terms, to the whole of the work, and all its parts, 226 | regardless of how they are packaged. This License gives no 227 | permission to license the work in any other way, but it does not 228 | invalidate such permission if you have separately received it. 229 | 230 | d) If the work has interactive user interfaces, each must display 231 | Appropriate Legal Notices; however, if the Program has interactive 232 | interfaces that do not display Appropriate Legal Notices, your 233 | work need not make them do so. 234 | 235 | A compilation of a covered work with other separate and independent 236 | works, which are not by their nature extensions of the covered work, 237 | and which are not combined with it such as to form a larger program, 238 | in or on a volume of a storage or distribution medium, is called an 239 | "aggregate" if the compilation and its resulting copyright are not 240 | used to limit the access or legal rights of the compilation's users 241 | beyond what the individual works permit. Inclusion of a covered work 242 | in an aggregate does not cause this License to apply to the other 243 | parts of the aggregate. 244 | 245 | 6. Conveying Non-Source Forms. 246 | 247 | You may convey a covered work in object code form under the terms 248 | of sections 4 and 5, provided that you also convey the 249 | machine-readable Corresponding Source under the terms of this License, 250 | in one of these ways: 251 | 252 | a) Convey the object code in, or embodied in, a physical product 253 | (including a physical distribution medium), accompanied by the 254 | Corresponding Source fixed on a durable physical medium 255 | customarily used for software interchange. 256 | 257 | b) Convey the object code in, or embodied in, a physical product 258 | (including a physical distribution medium), accompanied by a 259 | written offer, valid for at least three years and valid for as 260 | long as you offer spare parts or customer support for that product 261 | model, to give anyone who possesses the object code either (1) a 262 | copy of the Corresponding Source for all the software in the 263 | product that is covered by this License, on a durable physical 264 | medium customarily used for software interchange, for a price no 265 | more than your reasonable cost of physically performing this 266 | conveying of source, or (2) access to copy the 267 | Corresponding Source from a network server at no charge. 268 | 269 | c) Convey individual copies of the object code with a copy of the 270 | written offer to provide the Corresponding Source. This 271 | alternative is allowed only occasionally and noncommercially, and 272 | only if you received the object code with such an offer, in accord 273 | with subsection 6b. 274 | 275 | d) Convey the object code by offering access from a designated 276 | place (gratis or for a charge), and offer equivalent access to the 277 | Corresponding Source in the same way through the same place at no 278 | further charge. You need not require recipients to copy the 279 | Corresponding Source along with the object code. If the place to 280 | copy the object code is a network server, the Corresponding Source 281 | may be on a different server (operated by you or a third party) 282 | that supports equivalent copying facilities, provided you maintain 283 | clear directions next to the object code saying where to find the 284 | Corresponding Source. Regardless of what server hosts the 285 | Corresponding Source, you remain obligated to ensure that it is 286 | available for as long as needed to satisfy these requirements. 287 | 288 | e) Convey the object code using peer-to-peer transmission, provided 289 | you inform other peers where the object code and Corresponding 290 | Source of the work are being offered to the general public at no 291 | charge under subsection 6d. 292 | 293 | A separable portion of the object code, whose source code is excluded 294 | from the Corresponding Source as a System Library, need not be 295 | included in conveying the object code work. 296 | 297 | A "User Product" is either (1) a "consumer product", which means any 298 | tangible personal property which is normally used for personal, family, 299 | or household purposes, or (2) anything designed or sold for incorporation 300 | into a dwelling. In determining whether a product is a consumer product, 301 | doubtful cases shall be resolved in favor of coverage. For a particular 302 | product received by a particular user, "normally used" refers to a 303 | typical or common use of that class of product, regardless of the status 304 | of the particular user or of the way in which the particular user 305 | actually uses, or expects or is expected to use, the product. A product 306 | is a consumer product regardless of whether the product has substantial 307 | commercial, industrial or non-consumer uses, unless such uses represent 308 | the only significant mode of use of the product. 309 | 310 | "Installation Information" for a User Product means any methods, 311 | procedures, authorization keys, or other information required to install 312 | and execute modified versions of a covered work in that User Product from 313 | a modified version of its Corresponding Source. The information must 314 | suffice to ensure that the continued functioning of the modified object 315 | code is in no case prevented or interfered with solely because 316 | modification has been made. 317 | 318 | If you convey an object code work under this section in, or with, or 319 | specifically for use in, a User Product, and the conveying occurs as 320 | part of a transaction in which the right of possession and use of the 321 | User Product is transferred to the recipient in perpetuity or for a 322 | fixed term (regardless of how the transaction is characterized), the 323 | Corresponding Source conveyed under this section must be accompanied 324 | by the Installation Information. But this requirement does not apply 325 | if neither you nor any third party retains the ability to install 326 | modified object code on the User Product (for example, the work has 327 | been installed in ROM). 328 | 329 | The requirement to provide Installation Information does not include a 330 | requirement to continue to provide support service, warranty, or updates 331 | for a work that has been modified or installed by the recipient, or for 332 | the User Product in which it has been modified or installed. Access to a 333 | network may be denied when the modification itself materially and 334 | adversely affects the operation of the network or violates the rules and 335 | protocols for communication across the network. 336 | 337 | Corresponding Source conveyed, and Installation Information provided, 338 | in accord with this section must be in a format that is publicly 339 | documented (and with an implementation available to the public in 340 | source code form), and must require no special password or key for 341 | unpacking, reading or copying. 342 | 343 | 7. Additional Terms. 344 | 345 | "Additional permissions" are terms that supplement the terms of this 346 | License by making exceptions from one or more of its conditions. 347 | Additional permissions that are applicable to the entire Program shall 348 | be treated as though they were included in this License, to the extent 349 | that they are valid under applicable law. If additional permissions 350 | apply only to part of the Program, that part may be used separately 351 | under those permissions, but the entire Program remains governed by 352 | this License without regard to the additional permissions. 353 | 354 | When you convey a copy of a covered work, you may at your option 355 | remove any additional permissions from that copy, or from any part of 356 | it. (Additional permissions may be written to require their own 357 | removal in certain cases when you modify the work.) You may place 358 | additional permissions on material, added by you to a covered work, 359 | for which you have or can give appropriate copyright permission. 360 | 361 | Notwithstanding any other provision of this License, for material you 362 | add to a covered work, you may (if authorized by the copyright holders of 363 | that material) supplement the terms of this License with terms: 364 | 365 | a) Disclaiming warranty or limiting liability differently from the 366 | terms of sections 15 and 16 of this License; or 367 | 368 | b) Requiring preservation of specified reasonable legal notices or 369 | author attributions in that material or in the Appropriate Legal 370 | Notices displayed by works containing it; or 371 | 372 | c) Prohibiting misrepresentation of the origin of that material, or 373 | requiring that modified versions of such material be marked in 374 | reasonable ways as different from the original version; or 375 | 376 | d) Limiting the use for publicity purposes of names of licensors or 377 | authors of the material; or 378 | 379 | e) Declining to grant rights under trademark law for use of some 380 | trade names, trademarks, or service marks; or 381 | 382 | f) Requiring indemnification of licensors and authors of that 383 | material by anyone who conveys the material (or modified versions of 384 | it) with contractual assumptions of liability to the recipient, for 385 | any liability that these contractual assumptions directly impose on 386 | those licensors and authors. 387 | 388 | All other non-permissive additional terms are considered "further 389 | restrictions" within the meaning of section 10. If the Program as you 390 | received it, or any part of it, contains a notice stating that it is 391 | governed by this License along with a term that is a further 392 | restriction, you may remove that term. If a license document contains 393 | a further restriction but permits relicensing or conveying under this 394 | License, you may add to a covered work material governed by the terms 395 | of that license document, provided that the further restriction does 396 | not survive such relicensing or conveying. 397 | 398 | If you add terms to a covered work in accord with this section, you 399 | must place, in the relevant source files, a statement of the 400 | additional terms that apply to those files, or a notice indicating 401 | where to find the applicable terms. 402 | 403 | Additional terms, permissive or non-permissive, may be stated in the 404 | form of a separately written license, or stated as exceptions; 405 | the above requirements apply either way. 406 | 407 | 8. Termination. 408 | 409 | You may not propagate or modify a covered work except as expressly 410 | provided under this License. Any attempt otherwise to propagate or 411 | modify it is void, and will automatically terminate your rights under 412 | this License (including any patent licenses granted under the third 413 | paragraph of section 11). 414 | 415 | However, if you cease all violation of this License, then your 416 | license from a particular copyright holder is reinstated (a) 417 | provisionally, unless and until the copyright holder explicitly and 418 | finally terminates your license, and (b) permanently, if the copyright 419 | holder fails to notify you of the violation by some reasonable means 420 | prior to 60 days after the cessation. 421 | 422 | Moreover, your license from a particular copyright holder is 423 | reinstated permanently if the copyright holder notifies you of the 424 | violation by some reasonable means, this is the first time you have 425 | received notice of violation of this License (for any work) from that 426 | copyright holder, and you cure the violation prior to 30 days after 427 | your receipt of the notice. 428 | 429 | Termination of your rights under this section does not terminate the 430 | licenses of parties who have received copies or rights from you under 431 | this License. If your rights have been terminated and not permanently 432 | reinstated, you do not qualify to receive new licenses for the same 433 | material under section 10. 434 | 435 | 9. Acceptance Not Required for Having Copies. 436 | 437 | You are not required to accept this License in order to receive or 438 | run a copy of the Program. Ancillary propagation of a covered work 439 | occurring solely as a consequence of using peer-to-peer transmission 440 | to receive a copy likewise does not require acceptance. However, 441 | nothing other than this License grants you permission to propagate or 442 | modify any covered work. These actions infringe copyright if you do 443 | not accept this License. Therefore, by modifying or propagating a 444 | covered work, you indicate your acceptance of this License to do so. 445 | 446 | 10. Automatic Licensing of Downstream Recipients. 447 | 448 | Each time you convey a covered work, the recipient automatically 449 | receives a license from the original licensors, to run, modify and 450 | propagate that work, subject to this License. You are not responsible 451 | for enforcing compliance by third parties with this License. 452 | 453 | An "entity transaction" is a transaction transferring control of an 454 | organization, or substantially all assets of one, or subdividing an 455 | organization, or merging organizations. If propagation of a covered 456 | work results from an entity transaction, each party to that 457 | transaction who receives a copy of the work also receives whatever 458 | licenses to the work the party's predecessor in interest had or could 459 | give under the previous paragraph, plus a right to possession of the 460 | Corresponding Source of the work from the predecessor in interest, if 461 | the predecessor has it or can get it with reasonable efforts. 462 | 463 | You may not impose any further restrictions on the exercise of the 464 | rights granted or affirmed under this License. For example, you may 465 | not impose a license fee, royalty, or other charge for exercise of 466 | rights granted under this License, and you may not initiate litigation 467 | (including a cross-claim or counterclaim in a lawsuit) alleging that 468 | any patent claim is infringed by making, using, selling, offering for 469 | sale, or importing the Program or any portion of it. 470 | 471 | 11. Patents. 472 | 473 | A "contributor" is a copyright holder who authorizes use under this 474 | License of the Program or a work on which the Program is based. The 475 | work thus licensed is called the contributor's "contributor version". 476 | 477 | A contributor's "essential patent claims" are all patent claims 478 | owned or controlled by the contributor, whether already acquired or 479 | hereafter acquired, that would be infringed by some manner, permitted 480 | by this License, of making, using, or selling its contributor version, 481 | but do not include claims that would be infringed only as a 482 | consequence of further modification of the contributor version. For 483 | purposes of this definition, "control" includes the right to grant 484 | patent sublicenses in a manner consistent with the requirements of 485 | this License. 486 | 487 | Each contributor grants you a non-exclusive, worldwide, royalty-free 488 | patent license under the contributor's essential patent claims, to 489 | make, use, sell, offer for sale, import and otherwise run, modify and 490 | propagate the contents of its contributor version. 491 | 492 | In the following three paragraphs, a "patent license" is any express 493 | agreement or commitment, however denominated, not to enforce a patent 494 | (such as an express permission to practice a patent or covenant not to 495 | sue for patent infringement). To "grant" such a patent license to a 496 | party means to make such an agreement or commitment not to enforce a 497 | patent against the party. 498 | 499 | If you convey a covered work, knowingly relying on a patent license, 500 | and the Corresponding Source of the work is not available for anyone 501 | to copy, free of charge and under the terms of this License, through a 502 | publicly available network server or other readily accessible means, 503 | then you must either (1) cause the Corresponding Source to be so 504 | available, or (2) arrange to deprive yourself of the benefit of the 505 | patent license for this particular work, or (3) arrange, in a manner 506 | consistent with the requirements of this License, to extend the patent 507 | license to downstream recipients. "Knowingly relying" means you have 508 | actual knowledge that, but for the patent license, your conveying the 509 | covered work in a country, or your recipient's use of the covered work 510 | in a country, would infringe one or more identifiable patents in that 511 | country that you have reason to believe are valid. 512 | 513 | If, pursuant to or in connection with a single transaction or 514 | arrangement, you convey, or propagate by procuring conveyance of, a 515 | covered work, and grant a patent license to some of the parties 516 | receiving the covered work authorizing them to use, propagate, modify 517 | or convey a specific copy of the covered work, then the patent license 518 | you grant is automatically extended to all recipients of the covered 519 | work and works based on it. 520 | 521 | A patent license is "discriminatory" if it does not include within 522 | the scope of its coverage, prohibits the exercise of, or is 523 | conditioned on the non-exercise of one or more of the rights that are 524 | specifically granted under this License. You may not convey a covered 525 | work if you are a party to an arrangement with a third party that is 526 | in the business of distributing software, under which you make payment 527 | to the third party based on the extent of your activity of conveying 528 | the work, and under which the third party grants, to any of the 529 | parties who would receive the covered work from you, a discriminatory 530 | patent license (a) in connection with copies of the covered work 531 | conveyed by you (or copies made from those copies), or (b) primarily 532 | for and in connection with specific products or compilations that 533 | contain the covered work, unless you entered into that arrangement, 534 | or that patent license was granted, prior to 28 March 2007. 535 | 536 | Nothing in this License shall be construed as excluding or limiting 537 | any implied license or other defenses to infringement that may 538 | otherwise be available to you under applicable patent law. 539 | 540 | 12. No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README: -------------------------------------------------------------------------------- 1 | This package contains a set of functions for evaluating HMMs and GMMs. 2 | 3 | The portions written by me are distributed under the terms of the GNU 4 | General Public License. See the file COPYING for details. 5 | 6 | * Functions 7 | 8 | - The important ones: 9 | - train_gmm - train a GMM from data 10 | - eval_gmm - compute the posterior probability of a GMM given data 11 | - eval_hmm - compute the posterior probabilities of all possible HMM 12 | state sequences given data 13 | - decode_hmm - find the most likely state sequence through the HMM 14 | given data 15 | 16 | - Utility functions: 17 | - logsum - takes the sum of a matrix of log likelihoods 18 | - lmvnpdf - compute the log probability of data under a 19 | multivariate Gaussian distribution 20 | 21 | * Data Structures 22 | 23 | The functions in this toolbox pass around the following structures: 24 | Note: all probabilities are stored as log probabilities 25 | 26 | ** GMM 27 | - gmm.nmix - number of components in the mixture 28 | - gmm.priors - array of prior log probabilities over each state 29 | - gmm.means - matrix of means (column x is mean of component x) 30 | - gmm.covars - matrix of covariances (column x is the diagonal of the 31 | covariance matrix of component x) 32 | 33 | ** HMM with GMM observations (does not work with all functions) 34 | - hmm.name - 35 | - hmm.nstates - number of states in the HMM 36 | - hmm.emission_type - 'GMM' 37 | - hmm.start_prob - array of log probs P(first observation is state x) 38 | - hmm.end_prob - array of log probs P(last observation is state x) 39 | - hmm.transmat - matrix of transition log probs (transmat(x,y) 40 | = log(P(transition from state x to state y))) 41 | - hmm.labels - optional cell array of labels for each state in the HMM 42 | (for use in composing HMMs) 43 | - hmm.gmms - array of GMM structures 44 | 45 | ** HMM with Gaussian observations 46 | - hmm.nstates - number of states in the HMM 47 | - hmm.emission_type - 'gaussian' 48 | - hmm.start_prob - array of log probs P(first observation is state x) 49 | - hmm.end_prob - array of log probs P(last observation is state x) 50 | - hmm.transmat - matrix of transition log probs (transmat(x,y) 51 | = log(P(transition from state x to state y))) 52 | - hmm.labels - optional cell array of labels for each state in the HMM 53 | (for use in composing HMMs) 54 | - hmm.means - matrix of means (column x is mean of state x) 55 | - hmm.covars - matrix of means (column x is the diagonal of the 56 | covariance matrix of component x) 57 | 58 | Note that each row of exp(hmm.transmat) does not necessarily sum to 1 59 | because for each state x there is some probability 60 | (exp(hmm.end_prob(x))) that the next transition will be to a 61 | non-emitting exit state (i.e. the current observation is the last 62 | observation in the sequence). The correct invariant is: 63 | sum(exp(hmm.transmat), 2)' + exp(hmm.end_prob) == ones(hmm.nstates, 1) 64 | 65 | 2007-11-06 Ron Weiss 66 | -------------------------------------------------------------------------------- /adapt_gmm.m: -------------------------------------------------------------------------------- 1 | function gmm = adapt_gmm(pgmm, trdata, niter, adapt_weight, verb, MINCV) 2 | % gmmparams = adapt_gmm(prior_gmm, trdata, nmix, niter, 3 | % adapt_weight, verb, min_cv) 4 | % 5 | % Adapt the given prior_gmm to the given training data using MAP 6 | % adaptation. 7 | % 8 | % Inputs: 9 | % prior_gmm - initial GMM parameters to adapt. 10 | % trdata - training data (cell array of training sequences, each 11 | % column of the sequences arrays contains an observation) 12 | % niter - number of EM iterations to perform. Defaults to 10. 13 | % adapt_weight - weight of initial GMM in update equations (see HTK 14 | % book section 9.3). If adapt_weight is a vector, the 15 | % first element corresponds to the adaptation weight 16 | % for the Gaussian means (tau), and the second 17 | % correponse to the weight for the covariances (alpha). 18 | % Defaults to 10 (i.e. do not update covar parameters). 19 | % verb - set to 1 to output loglik at each iteration 20 | % min_cv - minimum covariance to avoid overfitting. Defaults to 1. 21 | % 22 | % Outputs: 23 | % gmmparams - structure containing hmm parameters learned from training 24 | % data (gmm.priors, gmm.means(:,1:nmix), gmm.covars(:,1:nmix)) 25 | % 26 | % 2009-06-15 ronw@ee.columbia.edu 27 | 28 | DEBUG = false; 29 | 30 | if nargin < 3 31 | niter = 10; 32 | end 33 | if nargin < 4 34 | adapt_weight = 10; 35 | end 36 | if nargin < 5 37 | verb = 0; 38 | end 39 | if nargin < 6 40 | MINCV = 1; 41 | end 42 | 43 | if ~iscell(trdata) 44 | trdata = {trdata}; 45 | end 46 | 47 | ndata = length(trdata); 48 | 49 | T = adapt_weight(1); 50 | adapt_covars = false; 51 | if length(adapt_weight) == 2 52 | adapt_covars = true; 53 | A = adapt_weight(2); 54 | end 55 | 56 | % Initialization 57 | gmm = pgmm; 58 | ppriors = exp(pgmm.priors); 59 | nmix = pgmm.nmix; 60 | 61 | if size(trdata{1}, 1) ~= size(gmm.means, 1) 62 | error(['Dimensionality of initial GMM not compatible with given ' ... 63 | 'training data']); 64 | end 65 | ndim = size(trdata{1}, 1); 66 | 67 | % sufficient statistics 68 | norm = zeros(size(gmm.priors)); 69 | means = zeros(size(gmm.means)); 70 | covars = zeros(size(gmm.covars)); 71 | 72 | last_loglik = -Inf; 73 | for iter = 1:niter 74 | % E-step 75 | loglik = 0; 76 | norm(:) = 0; 77 | means(:) = 0; 78 | covars(:) = 0; 79 | for n = 1:ndata 80 | curr_data = trdata{n}; 81 | [ll, posteriors] = eval_gmm(gmm, curr_data); 82 | 83 | loglik = loglik + sum(ll); 84 | 85 | norm = norm + sum(posteriors, 2)'; 86 | means = means + curr_data * posteriors'; 87 | covars = covars + curr_data.^2 * posteriors'; 88 | end 89 | 90 | if verb, 91 | fprintf('Iteration %d: log likelihood = %f\n', iter, loglik) 92 | 93 | if DEBUG 94 | figure(1) 95 | plot_on_same_axes(pgmm.priors, gmm.priors) 96 | figure(2) 97 | cax = [-80 -10]; 98 | subplot(211); imagesc(pgmm.means); axis xy; colorbar; caxis(cax); 99 | subplot(212); imagesc(gmm.means); axis xy; colorbar; caxis(cax); 100 | figure(3) 101 | cax = [0 100]; 102 | subplot(211); imagesc(pgmm.covars); axis xy; colorbar; caxis(cax); 103 | subplot(212); imagesc(gmm.covars); axis xy; colorbar; caxis(cax); 104 | drawnow 105 | end 106 | end 107 | 108 | % Check for convergence 109 | if abs(loglik - last_loglik) < 1e-5 110 | fprintf('Converged at iteration %d\n', iter) 111 | break 112 | end 113 | last_loglik = loglik; 114 | 115 | % M-step 116 | % based on Huang, Acero, Hon, "Spoken Language Processing", p. 443 - 445 117 | npriors = (ppriors - 1 + norm) ./ sum(ppriors - 1 + norm); 118 | npriors(npriors < 0) = 0; 119 | gmm.priors = log(npriors); 120 | nrm = repmat(norm, [ndim 1]); 121 | gmm.means = (T * pgmm.means + means) ./ (T + nrm); 122 | if adapt_covars 123 | gmm.covars = ((A - 1) * pgmm.covars ... 124 | + T * (gmm.means - pgmm.means).^2 ... 125 | + (covars - 2*gmm.means.*means) .* nrm + gmm.means.^2) ... 126 | ./ (A - 1 + nrm); 127 | gmm.covars(gmm.covars < MINCV) = MINCV; 128 | end 129 | end 130 | -------------------------------------------------------------------------------- /convert_hmm_to_gaussian_emissions.m: -------------------------------------------------------------------------------- 1 | function new_hmms = convert_hmm_to_gaussian_emissions(hmms) 2 | % new_hmms = convert_hmm_to_gaussian_emissions(hmms) 3 | % 4 | % Convert HMMs with GMM emissions in hmms to new_hmms with gaussian 5 | % emissions. hmms can be an array of hmm structures. 6 | % 7 | % 2007-01-18 ronw@ee.columbia.edu 8 | 9 | % Copyright (C) 2007 Ron J. Weiss 10 | % 11 | % This program is free software: you can redistribute it and/or modify 12 | % it under the terms of the GNU General Public License as published by 13 | % the Free Software Foundation, either version 3 of the License, or 14 | % (at your option) any later version. 15 | % 16 | % This program is distributed in the hope that it will be useful, 17 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 18 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 19 | % GNU General Public License for more details. 20 | % 21 | % You should have received a copy of the GNU General Public License 22 | % along with this program. If not, see . 23 | 24 | for n = 1:length(hmms) 25 | if strcmp(hmms(n).emission_type, 'gaussian') 26 | new_hmms(n) = hmms(n); 27 | continue; 28 | end 29 | 30 | new_hmms(n).name = hmms(n).name; 31 | new_hmms(n).emission_type = 'gaussian'; 32 | 33 | nmix = [hmms(n).gmms(:).nmix]; 34 | state_offset = cumsum([0, nmix(1:end-1)]); 35 | 36 | new_hmms(n).nstates = sum(nmix); 37 | new_hmms(n).transmat = repmat(-Inf, [new_hmms(n).nstates, new_hmms(n).nstates]); 38 | 39 | curr_state = 0; 40 | for s = 1:hmms(n).nstates 41 | ns = state_offset(s) + [1:nmix(s)]; 42 | 43 | new_hmms(n).start_prob(ns) = hmms(n).start_prob(s); 44 | new_hmms(n).end_prob(ns) = hmms(n).end_prob(s); 45 | 46 | if(isfield(hmms(n), 'labels')) 47 | new_hmms(n).labels(ns) = hmms(n).labels(s); 48 | end 49 | 50 | new_hmms(n).means(:,ns) = hmms(n).gmms(s).means; 51 | new_hmms(n).covars(:,ns) = hmms(n).gmms(s).covars; 52 | 53 | for ss = 1:hmms(n).nstates 54 | nss = state_offset(ss) + [1:nmix(ss)]; 55 | new_hmms(n).transmat(ns, nss) = hmms(n).transmat(s,ss); 56 | end 57 | end 58 | 59 | priors = [hmms(n).gmms(:).priors]; 60 | % make sure priors is a column vector 61 | priors = priors(:); 62 | for r = 1:new_hmms(n).nstates 63 | new_hmms(n).transmat(r,:) = new_hmms(n).transmat(r,:) + priors'; 64 | end 65 | 66 | new_hmms(n).start_prob = new_hmms(n).start_prob + priors'; 67 | end 68 | -------------------------------------------------------------------------------- /decode_hmm.m: -------------------------------------------------------------------------------- 1 | function [loglik, stateseq, recon, lattice, tb, mllattice] = decode_hmm(hmm, frameLogLike, maxRank, beamLogProb, normalize_lattice, verb) 2 | % [loglik, stateseq, recon, lattice, tb] = decode_hmm(hmm, seq, rank, beam) 3 | % 4 | % Performs Viterbi decode of seq. Does rank and beam pruning. 5 | % Assumes all hmm params are logprobs. 6 | % 7 | % 2007-02-26 ronw@ee.columbia.edu 8 | 9 | % Copyright (C) 2007 Ron J. Weiss 10 | % 11 | % This program is free software: you can redistribute it and/or modify 12 | % it under the terms of the GNU General Public License as published by 13 | % the Free Software Foundation, either version 3 of the License, or 14 | % (at your option) any later version. 15 | % 16 | % This program is distributed in the hope that it will be useful, 17 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 18 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 19 | % GNU General Public License for more details. 20 | % 21 | % You should have received a copy of the GNU General Public License 22 | % along with this program. If not, see . 23 | 24 | zeroLogProb = -1e200; 25 | 26 | % no rank pruning by default 27 | if nargin < 3 28 | maxRank = 0; 29 | end 30 | 31 | % no beam pruning by default 32 | if nargin < 4 33 | beamLogProb = -Inf; 34 | end 35 | 36 | if nargin < 5 37 | normalize_lattice = 0; 38 | end 39 | 40 | if nargin < 6 41 | verb = 0; 42 | end 43 | 44 | [nstates, nobs] = size(frameLogLike); 45 | if nstates ~= hmm.nstates && nstates == size(hmm.means, 1) 46 | seq = frameLogLike; 47 | ndim = nstates; 48 | nstates = hmm.nstates; 49 | if strcmp(hmm.emission_type, 'gaussian') 50 | frameLogLike = lmvnpdf(seq, hmm.means, hmm.covars); 51 | elseif strcmp(hmm.emission_type, 'GMM') 52 | for s = 1:hmm.nstates 53 | frameLogLike(s,:) = eval_gmm(hmm.gmms(s), seq); 54 | end 55 | else 56 | error('Unknown HMM emission distribution.'); 57 | end 58 | end 59 | 60 | 61 | % how big should our rank pruning histogram be? 62 | histSize = 1000; 63 | 64 | stateseq = zeros(1, nobs); 65 | tb = zeros(hmm.nstates, nobs); 66 | 67 | if nargout > 3 68 | lattice = repmat(zeroLogProb, [hmm.nstates, nobs]); 69 | end 70 | % FIXME - there is a bug here in how the first frame is handled - 71 | % an extra transition probability from the non-existant 0th frame 72 | % to the 1st frame is added into lattice... 73 | prevLatticeFrame = hmm.start_prob(:); 74 | %prevLatticeFrame = hmm.start_prob(:) + frameLogLike(:,1); 75 | tb = zeros(hmm.nstates, nobs); 76 | 77 | % fill in the lattice... 78 | avg_nactive = 0; 79 | prevFrameMaxLogProb = 0; 80 | for obs = 1:nobs 81 | if verb >= 2 82 | tic 83 | end 84 | 85 | % beam pruning 86 | threshLogProb = prevFrameMaxLogProb + beamLogProb; 87 | 88 | % rank pruning 89 | if maxRank > 0 90 | tmp = prevLatticeFrame(:); 91 | min_tmp = 2*min(tmp(tmp > zeroLogProb)); 92 | tmp(tmp < zeroLogProb) = min_tmp; 93 | 94 | [hst cdf] = hist(tmp, histSize); 95 | 96 | % want to look at the high ranks of the last frame 97 | hst = hst(end:-1:1); 98 | cdf = cdf(end:-1:1); 99 | 100 | hst = cumsum(hst); 101 | idx = min(find(hst >= maxRank)); 102 | rankThresh = cdf(idx); 103 | 104 | % only change the threshold if it is stricter than the beam 105 | % threshold 106 | threshLogProb = max(threshLogProb, rankThresh); 107 | 108 | if verb >= 3 109 | %imgsc(prevLatticeFrame), colorbar, title(num2str(obs)), drawnow 110 | 111 | disp(['beam thresh = ' num2str(prevFrameMaxLogProb+beamLogProb) ... 112 | ', rank thresh = ' num2str(rankThresh) ... 113 | ', final thresh = ' num2str(threshLogProb)]); 114 | end 115 | end 116 | 117 | % which states are active? 118 | s_idx = find(prevLatticeFrame >= threshLogProb); 119 | nactive = numel(s_idx); 120 | avg_nactive = avg_nactive + nactive/nobs; 121 | 122 | vitPr = hmm.transmat(s_idx, :)' + repmat(prevLatticeFrame(s_idx), [1, hmm.nstates])'; 123 | 124 | currllik = frameLogLike(:,obs); 125 | 126 | % v_idx = find(max(vitPr,[], 2) > zeroLogProb); 127 | % nv = length(v_idx); 128 | % currllik = repmat(zeroLogProb, [hmm.nstates, 1]); 129 | % if strcmp(hmm.emission_type, 'gaussian') 130 | % currllik(v_idx) = lmvnpdf(seq(:,obs), hmm.means(:, v_idx), ... 131 | % hmm.covars(:, v_idx)); 132 | % else 133 | % for s = 1:nv 134 | % currllik(v_idx(s)) = eval_gmm(hmm.gmms(v_idx(s)), seq(:,obs)); 135 | % end 136 | % end 137 | 138 | [prevLatticeFrame tb_tmp] = max(vitPr + repmat(currllik, [1, nactive]), [], 2); 139 | % This is equivalent to the above? 140 | %[prevLatticeFrame tb_tmp] = max(vitPr, [], 2); 141 | %prevLatticeFrame = prevLatticeFrame + currllik; 142 | tb(:,obs) = s_idx(tb_tmp); 143 | 144 | if nargout > 3 145 | lattice(:,obs) = prevLatticeFrame; 146 | end 147 | 148 | prevFrameMaxLogProb = max(prevLatticeFrame); 149 | 150 | if verb >= 2 151 | T = toc; 152 | disp(['frame ' num2str(obs), ' (' num2str(T) ' sec)' ... 153 | ': total active states: ' num2str(nactive)]); 154 | end 155 | end 156 | 157 | % include end_prob in lattice: 158 | ptmp = prevLatticeFrame; 159 | prevLatticeFrame = prevLatticeFrame + hmm.end_prob(:); 160 | 161 | %%% 162 | % do the traceback: 163 | [loglik s] = max(prevLatticeFrame(:)); 164 | 165 | % we might have pruned too much, don't want to give up if end_prob 166 | % restrictions are too strong - so just ignore them in this case 167 | if loglik <= zeroLogProb 168 | warning(['decode_hmm: overpruned during decode,' ... 169 | ' ignoring probabilities that the hmms end in a' ... 170 | ' particular state']); 171 | prevLatticeFrame = ptmp; 172 | [loglik s] = max(prevLatticeFrame); 173 | end 174 | 175 | if nargout > 3 176 | lattice(:,end) = prevLatticeFrame; 177 | end 178 | 179 | for obs = nobs:-1:1 180 | stateseq(obs) = s; 181 | s = tb(s, obs); 182 | end 183 | 184 | 185 | % need to keep track of which gmm component was used in the 186 | % traceback for reconstruction - since this code doesn't do that, 187 | % can only guess as to the right reconstruction for GMM emissions - 188 | % should use convert_hmm_to_gaussian_emissions before calling this 189 | % function to get the full traceback 190 | if strcmp(hmm.emission_type, 'gaussian') 191 | recon = hmm.means(:,stateseq); 192 | else 193 | for s = 1:hmm.nstates 194 | means(:,s) = hmm.gmms(s).means * exp(hmm.gmms(s).priors)'; 195 | end 196 | 197 | recon = means(:,stateseq); 198 | end 199 | 200 | if nargout > 3 & normalize_lattice 201 | nrm = logsum(lattice, 1); 202 | lattice = exp(lattice - repmat(nrm, [hmm.nstates, 1])); 203 | lattice(lattice < 1e-5) = 0; 204 | end 205 | 206 | if nargout > 4 207 | mllattice = sparse(hmm.nstates, nobs); 208 | for o = 1:nobs 209 | mllattice(stateseq(o),o) = 1; 210 | end 211 | end 212 | 213 | 214 | if verb 215 | disp(['decode_hmm: log likelihood: ' num2str(loglik) ... 216 | ', average number of active states per frame: ' ... 217 | num2str(avg_nactive)]); 218 | end 219 | -------------------------------------------------------------------------------- /eval_gmm.m: -------------------------------------------------------------------------------- 1 | function [ll, post, mlg, mmserecon] = eval_gmm(gmm, data, norm) 2 | % [loglik, posteriors, mlseq, recon] = eval_gmm(gmm, data) 3 | % 4 | % Evaluate the log probability of each column of data given GMM gmm. 5 | % 6 | % Outputs: 7 | % loglik - log likelihood of each colimn of data 8 | % posteriors - posterior probability of each GMM component for each 9 | % column of data 10 | % mlseq - index of the most likely GMM component for each 11 | % column of data 12 | % recon - MMSE reconstruction of data given the GMM 13 | % 14 | % 2005-11-20 ronw@ee.columbia.edu 15 | 16 | % Copyright (C) 2005-2007 Ron J. Weiss 17 | % 18 | % This program is free software: you can redistribute it and/or modify 19 | % it under the terms of the GNU General Public License as published by 20 | % the Free Software Foundation, either version 3 of the License, or 21 | % (at your option) any later version. 22 | % 23 | % This program is distributed in the hope that it will be useful, 24 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 25 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 26 | % GNU General Public License for more details. 27 | % 28 | % You should have received a copy of the GNU General Public License 29 | % along with this program. If not, see . 30 | 31 | if nargin < 3, norm = 1; end 32 | 33 | [ndim, ndat] = size(data); 34 | 35 | post = lmvnpdf(data, gmm.means, gmm.covars) + repmat(gmm.priors(:), [1, ndat]); 36 | ll = logsum(post, 1); 37 | 38 | if nargout > 1 && norm 39 | post = exp(post - repmat(logsum(post,1), gmm.nmix, 1)); 40 | end 41 | 42 | if nargout > 2 43 | [mlg tmp] = ind2sub(size(post), find(post == repmat(max(post),gmm.nmix,1))); 44 | end 45 | 46 | if nargout > 3 47 | if norm 48 | mmserecon = gmm.means*post; 49 | else 50 | postnorm = exp(post - repmat(logsum(post,1), gmm.nmix, 1)); 51 | mmserecon = gmm.means*postnorm; 52 | end 53 | end 54 | 55 | -------------------------------------------------------------------------------- /eval_hmm.m: -------------------------------------------------------------------------------- 1 | function [loglik, lattice, alpha, beta, gamma] = eval_hmm(hmm, frameLogLike, maxRank, beamLogProb, do_backward, verb) 2 | % [loglik, lattice] = eval_hmm(hmm, seq, rank, beam) 3 | % 4 | % Performs forward-backward inference on seq. Does rank and beam 5 | % pruning. Assumes all hmm params are logprobs. 6 | % 7 | % 2008-08-11 ronw@ee.columbia.edu 8 | 9 | % Copyright (C) 2006-2008 Ron J. Weiss 10 | % 11 | % This program is free software: you can redistribute it and/or modify 12 | % it under the terms of the GNU General Public License as published by 13 | % the Free Software Foundation, either version 3 of the License, or 14 | % (at your option) any later version. 15 | % 16 | % This program is distributed in the hope that it will be useful, 17 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 18 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 19 | % GNU General Public License for more details. 20 | % 21 | % You should have received a copy of the GNU General Public License 22 | % along with this program. If not, see . 23 | 24 | 25 | % no rank pruning by default 26 | if nargin < 3 27 | maxRank = 0; 28 | end 29 | 30 | % No beam pruning by default. 31 | if nargin < 4 32 | beamLogProb = -Inf; 33 | end 34 | 35 | if nargin < 5 36 | do_backward = true; 37 | end 38 | 39 | if nargin < 6 40 | verb = 0; 41 | end 42 | 43 | % Don't bother doing backward calculation if all we want is log 44 | % likelihood. 45 | if nargout < 2 46 | do_backward = false; 47 | else 48 | do_backward = true; 49 | end 50 | 51 | zeroLogProb = -1e200; 52 | hmm.transmat(hmm.transmat < zeroLogProb) = zeroLogProb; 53 | 54 | % Verify type of observations. Can be observed sequence or 55 | % precomputed log likelihoods (i.e. for variational inference). 56 | [nstates, nobs] = size(frameLogLike); 57 | if nstates ~= hmm.nstates && nstates == size(hmm.means, 1) 58 | seq = frameLogLike; 59 | ndim = nstates; 60 | nstates = hmm.nstates; 61 | if strcmp(hmm.emission_type, 'gaussian') 62 | frameLogLike = lmvnpdf(seq, hmm.means, hmm.covars); 63 | elseif strcmp(hmm.emission_type, 'GMM') 64 | for s = 1:hmm.nstates 65 | frameLogLike(s,:) = eval_gmm(hmm.gmms(s), seq); 66 | end 67 | else 68 | error('Unknown HMM emission distribution.'); 69 | end 70 | end 71 | 72 | 73 | %%%%% 74 | % Forward 75 | %%%%% 76 | alpha = zeros(nstates, nobs) - Inf; 77 | prevLatticeFrame = hmm.start_prob(:) + frameLogLike(:,1); 78 | alpha(:,1) = prevLatticeFrame; 79 | if verb >= 2 80 | fprintf('Starting forward pass...\n frame 1: ll = %f\n', ... 81 | logsum(prevLatticeFrame)) 82 | end 83 | 84 | for obs = 2:nobs 85 | if verb >= 2; tic; end 86 | 87 | idx = prune_states(prevLatticeFrame, maxRank, beamLogProb, verb); 88 | pr = hmm.transmat(idx,:)' + repmat(prevLatticeFrame(idx), [1, hmm.nstates])'; 89 | prevLatticeFrame = logsum(pr, 2) + frameLogLike(:, obs); 90 | alpha(:,obs) = prevLatticeFrame; 91 | 92 | if verb >= 2 93 | T = toc; 94 | fprintf(' frame %d: ll = %f (%f sec, %d active states)\n', obs, ... 95 | logsum(prevLatticeFrame), T, length(idx)); 96 | end 97 | end 98 | alpha(alpha <= zeroLogProb) = -Inf; 99 | 100 | % Don't forget hmm.end_prob 101 | % This double counts frameLogLike(:,end)!! 102 | %nextLatticeFrame = hmm.end_prob(:) + frameLogLike(:,end); 103 | nextLatticeFrame = hmm.end_prob(:); 104 | loglik = logsum(prevLatticeFrame + nextLatticeFrame); 105 | if isinf(loglik) || isnan(loglik) 106 | nextLatticeFrame = frameLogLike(:,end); 107 | loglik = logsum(prevLatticeFrame + nextLatticeFrame); 108 | end 109 | 110 | if verb 111 | fprintf('eval_hmm: log likelihood = %f\n', loglik) 112 | end 113 | 114 | 115 | if ~do_backward 116 | return 117 | end 118 | 119 | %%%%% 120 | % Backward 121 | %%%%% 122 | beta = zeros(nstates, nobs) - Inf; 123 | beta(:,nobs) = nextLatticeFrame; 124 | if verb >= 2 125 | fprintf('Starting backward pass...\n frame %d: ll = %f\n', nobs, ... 126 | logsum(nextLatticeFrame)); 127 | end 128 | 129 | for obs = nobs-1:-1:1 130 | if verb >= 2; tic; end 131 | 132 | % Do HTK style pruning (p. 137 of HTK Book version 3.4). Don't 133 | % bother computing backward probability if alpha*beta is more than a 134 | % certain distance from the total log likelihood. 135 | idx = prune_states(nextLatticeFrame + alpha(:,obs+1), 0, -20, verb); 136 | %idx = prune_states(nextLatticeFrame + alpha(:,obs+1), 10, -Inf, verb); 137 | 138 | pr = hmm.transmat(:,idx) + repmat(nextLatticeFrame(idx) ... 139 | + frameLogLike(idx,obs+1), [1, hmm.nstates])'; 140 | nextLatticeFrame = logsum(pr, 2); 141 | beta(:,obs) = nextLatticeFrame; 142 | 143 | if verb >= 2 144 | T = toc; 145 | fprintf(' frame %d: ll = %f (%f sec, %d active states)\n', obs, ... 146 | logsum(nextLatticeFrame), T, length(idx)); 147 | end 148 | end 149 | beta(beta <= zeroLogProb) = -Inf; 150 | 151 | gamma = alpha + beta; 152 | lattice = exp(gamma - repmat(logsum(gamma, 1), [hmm.nstates 1])); 153 | 154 | 155 | 156 | function [state_idx thresh] = prune_states(latticeFrame, ... 157 | maxRank, beamLogProb, verb) 158 | zeroLogProb = -1e200; 159 | frameLogProb = logsum(latticeFrame); 160 | 161 | % Beam pruning 162 | threshLogProb = frameLogProb + beamLogProb; 163 | 164 | % Rank pruning 165 | if maxRank > 0 166 | % How big should our rank pruning histogram be? 167 | histSize = 3*length(latticeFrame); 168 | 169 | tmp = latticeFrame(:); 170 | min_tmp = min(tmp(tmp > zeroLogProb)) - 1; 171 | tmp(tmp <= zeroLogProb) = min_tmp; 172 | 173 | [hst cdf] = hist(tmp, histSize); 174 | 175 | % Want to look at the high ranks of the last frame. 176 | hst = hst(end:-1:1); 177 | cdf = cdf(end:-1:1); 178 | 179 | hst = cumsum(hst); 180 | idx = min(find(hst >= maxRank)); 181 | rankThresh = cdf(idx); 182 | 183 | % Only change the threshold if it is stricter than the beam 184 | % threshold. 185 | threshLogProb = max(threshLogProb, rankThresh); 186 | 187 | if verb >= 3 188 | fprintf('beam thresh = %f, rank thresh = %f, final thresh = %f\n', ... 189 | frameLogProb+beamLogProb, rankThresh, threshLogProb); 190 | end 191 | end 192 | 193 | % Which states are active? 194 | state_idx = find(latticeFrame >= threshLogProb); 195 | 196 | -------------------------------------------------------------------------------- /is_valid_gmm.m: -------------------------------------------------------------------------------- 1 | function out = is_valid_gmm(gmm, verb) 2 | % y = is_valid_gmm(gmm) 3 | % 4 | % Returns 1 if and only if gmm is a valid GMM structure 5 | % 6 | % 2008-06-03 ronw@ee.columbia.edu 7 | 8 | % Copyright (C) 2008 Ron J. Weiss 9 | % 10 | % This program is free software: you can redistribute it and/or modify 11 | % it under the terms of the GNU General Public License as published by 12 | % the Free Software Foundation, either version 3 of the License, or 13 | % (at your option) any later version. 14 | % 15 | % This program is distributed in the hope that it will be useful, 16 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 17 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 18 | % GNU General Public License for more details. 19 | % 20 | % You should have received a copy of the GNU General Public License 21 | % along with this program. If not, see . 22 | 23 | if nargin < 2; verb = 0; end 24 | 25 | out = true; 26 | if ~isstruct(gmm) 27 | out = false; 28 | if verb; fprintf('is_valid_gmm: not a structure\n'); end 29 | return 30 | end 31 | 32 | if ~isfield(gmm, 'nmix') 33 | out = false; 34 | if verb; fprintf('is_valid_gmm: missing nmix field\n'); end 35 | return 36 | end 37 | 38 | if ~isfield(gmm, 'priors') 39 | out = false; 40 | if verb; fprintf('is_valid_gmm: missing priors field\n'); end 41 | else 42 | if length(gmm.priors) ~= gmm.nmix 43 | out = false; 44 | if verb; fprintf('is_valid_gmm: priors field is wrong length\n'); end 45 | end 46 | if abs(logsum(gmm.priors)) > 1e-3 47 | out = false; 48 | if verb; fprintf('is_valid_gmm: priors don''t sum to 1\n'); end 49 | end 50 | end 51 | 52 | if ~isfield(gmm, 'means') 53 | out = false; 54 | if verb; fprintf('is_valid_gmm: missing means field\n'); end 55 | else 56 | if size(gmm.means, 2) ~= gmm.nmix 57 | out = false; 58 | if verb; fprintf('is_valid_gmm: means field is wrong length\n'); end 59 | end 60 | end 61 | 62 | if ~isfield(gmm, 'covars') 63 | out = false; 64 | if verb; fprintf('is_valid_gmm: missing covars field\n'); end 65 | else 66 | if size(gmm.covars, 2) ~= gmm.nmix 67 | out = false; 68 | if verb; fprintf('is_valid_gmm: covars field is wrong length\n'); end 69 | end 70 | if isfield(gmm, 'means') && size(gmm.means, 1) ~= size(gmm.covars,1) 71 | out = false; 72 | if verb 73 | fprintf('is_valid_gmm: means and covars have inconsistent dimensions\n'); 74 | end 75 | end 76 | if ~all(all(gmm.covars > 0)) 77 | out = false; 78 | if verb; fprintf('is_valid_gmm: 0 or negative covars\n'); end 79 | end 80 | end 81 | 82 | 83 | -------------------------------------------------------------------------------- /is_valid_hmm.m: -------------------------------------------------------------------------------- 1 | function out = is_valid_hmm(hmm, verb) 2 | % y = is_valid_hmm(hmm) 3 | % 4 | % Returns 1 if and only if hmm is a valid HMM structure 5 | % 6 | % 2008-06-03 ronw@ee.columbia.edu 7 | 8 | % Copyright (C) 2008 Ron J. Weiss 9 | % 10 | % This program is free software: you can redistribute it and/or modify 11 | % it under the terms of the GNU General Public License as published by 12 | % the Free Software Foundation, either version 3 of the License, or 13 | % (at your option) any later version. 14 | % 15 | % This program is distributed in the hope that it will be useful, 16 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 17 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 18 | % GNU General Public License for more details. 19 | % 20 | % You should have received a copy of the GNU General Public License 21 | % along with this program. If not, see . 22 | 23 | if nargin < 2; verb = 0; end 24 | 25 | out = true; 26 | if ~isstruct(hmm) 27 | out = false; 28 | if verb; fprintf('is_valid_hmm: not a structure\n'); end 29 | return 30 | end 31 | 32 | if ~isfield(hmm, 'nstates') 33 | out = false; 34 | if verb; fprintf('is_valid_hmm: missing nstates field\n'); end 35 | return 36 | end 37 | if ~isfield(hmm, 'emission_type') 38 | out = false; 39 | if verb; fprintf('is_valid_hmm: missing emissionn type field\n'); end 40 | end 41 | 42 | 43 | if ~isfield(hmm, 'start_prob') 44 | out = false; 45 | if verb; fprintf('is_valid_hmm: missing start_prob field\n'); end 46 | else 47 | if length(hmm.start_prob) ~= hmm.nstates 48 | out = false; 49 | if verb; fprintf('is_valid_hmm: start_prob field is wrong length\n'); end 50 | end 51 | if abs(logsum(hmm.start_prob)) > 1e-3 52 | out = false; 53 | if verb; fprintf('is_valid_hmm: start_prob doesn''t sum to 1\n'); end 54 | end 55 | end 56 | 57 | if ~isfield(hmm, 'end_prob') 58 | out = false; 59 | if verb; fprintf('is_valid_hmm: missing end_prob field\n'); end 60 | else 61 | if length(hmm.end_prob) ~= hmm.nstates 62 | out = false; 63 | if verb; fprintf('is_valid_hmm: end_prob field is wrong length\n'); end 64 | end 65 | if ~isfield(hmm, 'transmat') 66 | out = false; 67 | if verb; fprintf('is_valid_hmm: missing transmat field\n'); end 68 | else 69 | if ~all(size(hmm.transmat) == [hmm.nstates hmm.nstates]) 70 | out = false; 71 | if verb; fprintf('is_valid_hmm: transmat is wrong size\n'); end 72 | end 73 | if ~all(abs(sum(exp(hmm.transmat), 2) + exp(hmm.end_prob(:)) - 1) < 1e-3) 74 | out = false; 75 | if verb; 76 | fprintf('is_valid_hmm: transmat is not normalized properly\n'); 77 | end 78 | end 79 | end 80 | end 81 | 82 | 83 | if strcmp(hmm.emission_type, 'GMM') 84 | if ~isfield(hmm, 'gmms') 85 | out = false; 86 | if verb; fprintf('is_valid_hmm: missing gmms field\n'); end 87 | else 88 | for s = 1:length(hmm.gmms) 89 | tmp = is_valid_gmm(hmm.gmms(s)); 90 | if ~tmp 91 | out = false; 92 | if verb 93 | fprintf('is_valid_hmm: Error in state %d:\n ', s); 94 | is_valid_gmm(hmm.gmms(s), verb); 95 | end 96 | break 97 | end 98 | end 99 | end 100 | end 101 | if strcmp(hmm.emission_type, 'gaussian') 102 | if ~isfield(hmm, 'means') 103 | out = false; 104 | if verb; fprintf('is_valid_hmm: missing means field\n'); end 105 | else 106 | if size(hmm.means, 2) ~= hmm.nstates 107 | out = false; 108 | if verb; fprintf('is_valid_hmm: means field is wrong length\n'); end 109 | end 110 | end 111 | 112 | if ~isfield(hmm, 'covars') 113 | out = false; 114 | if verb; fprintf('is_valid_hmm: missing covars field\n'); end 115 | else 116 | if size(hmm.covars, 2) ~= hmm.nstates 117 | out = false; 118 | if verb; fprintf('is_valid_hmm: covars field is wrong length\n'); end 119 | end 120 | if isfield(hmm, 'means') && size(hmm.means, 1) ~= size(hmm.covars,1) 121 | out = false; 122 | if verb 123 | fprintf(['is_valid_hmm: means and covars have inconsistent ' ... 124 | 'dimensions\n']); 125 | end 126 | end 127 | if ~all(all(hmm.covars > 0)) 128 | out = false; 129 | if verb; fprintf('is_valid_hmm: 0 or negative covars\n'); end 130 | end 131 | end 132 | end 133 | 134 | -------------------------------------------------------------------------------- /kmeans.m: -------------------------------------------------------------------------------- 1 | function codebook = kmeans(trdata, nclust, niter) 2 | % codebook = kmeans(data, nclust, niter) 3 | % 4 | % Learns a k-means codebook from data with nclust codewords. 5 | % 6 | % 2006-12-07 ronw@ee.columbia.edu 7 | 8 | % Copyright (C) 2006 Ron J. Weiss 9 | % 10 | % This program is free software: you can redistribute it and/or modify 11 | % it under the terms of the GNU General Public License as published by 12 | % the Free Software Foundation, either version 3 of the License, or 13 | % (at your option) any later version. 14 | % 15 | % This program is distributed in the hope that it will be useful, 16 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 17 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 18 | % GNU General Public License for more details. 19 | % 20 | % You should have received a copy of the GNU General Public License 21 | % along with this program. If not, see . 22 | 23 | if nargin < 2 24 | nclust = 10; 25 | end 26 | if nargin < 3 27 | niter = 5; 28 | end 29 | 30 | [ndim, nobs] = size(trdata); 31 | 32 | % init using k-means: 33 | rp = randperm(nobs); 34 | % in case there aren't enough observations... 35 | rp = repmat(rp,1,ceil(nclust/nobs)); 36 | codebook = trdata(:,rp(1:nclust)); 37 | for i = 1:niter 38 | % ||x-y || = x^Tx -2x^Ty + y^Ty 39 | % x^Tx = repmat(sum(x.^2),xc,1); 40 | % y^Ty = repmat(sum(y.^2),yc,1); 41 | D = repmat(sum(trdata.^2,1)',1,nclust) - 2*trdata'*codebook ... 42 | + repmat(sum(codebook.^2,1),nobs,1); 43 | 44 | %assign each data point to one of the clusters 45 | [tmp idx] = min(D,[],2); 46 | 47 | for k = 1:nclust 48 | if sum(idx == k) > 0 49 | codebook(:,k) = mean(trdata(:,idx == k),2); 50 | end 51 | end 52 | end 53 | -------------------------------------------------------------------------------- /lmvnpdf.m: -------------------------------------------------------------------------------- 1 | function lpr = lmvnpdf(obs, mu, cv); 2 | % lpr = lmvnpdf(obs, mu, cv) 3 | % 4 | % Return the log probability of obs under the Gaussian distribution 5 | % parameterized by mu and cv. 6 | % 7 | % obs is an array of column vectors (DxO). mu and cv are also arrays 8 | % of column vectors (this only supports diagonal covariance matrices, 9 | % so mu and cv must both be DxC where C is the number of Gaussians). 10 | % lpr will be a CxO matrix where each row contains the log probability 11 | % of each observation given one of the C Gaussians. 12 | % 13 | % 2006-06-19 ronw@ee.columbia.edu 14 | 15 | % Copyright (C) 2006-2007 Ron J. Weiss 16 | % 17 | % This program is free software: you can redistribute it and/or modify 18 | % it under the terms of the GNU General Public License as published by 19 | % the Free Software Foundation, either version 3 of the License, or 20 | % (at your option) any later version. 21 | % 22 | % This program is distributed in the hope that it will be useful, 23 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 24 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 25 | % GNU General Public License for more details. 26 | % 27 | % You should have received a copy of the GNU General Public License 28 | % along with this program. If not, see . 29 | 30 | if nargin < 3 31 | cv = 1; 32 | end 33 | 34 | [ndim, nobs] = size(obs); 35 | [ndim_mu, nmu] = size(mu); 36 | [ndim_cv, ncv] = size(cv); 37 | 38 | % make sure all the arguments are consistent 39 | if ndim ~= ndim_mu 40 | error('lmvnpdf: obs and mu must have the same number of dimensions.'); 41 | end 42 | if nmu ~= ncv 43 | if ncv == 1 44 | % use the same diagonal covariance for each distribution 45 | cv = repmat(cv, 1, nmu); 46 | else 47 | error('lmvnpdf: mu and cv must have the same number of components.'); 48 | end 49 | end 50 | ngauss = nmu; 51 | 52 | % are covariances scalar? 53 | if ndim_cv == 1 54 | cv = repmat(cv, ndim, 1); 55 | end 56 | 57 | 58 | % vectorized like there is no tomorrow: 59 | % ||x-y|| = x'x - 2*x'y + y'y 60 | % x'x = repmat(sum(x.^2),xc,1); 61 | % y'y = repmat(sum(y.^2),yc,1); 62 | % 63 | % but here, its ||(x-y)/cv||: 64 | % where cv has the same size as x (mu), but not the same as y (obs)... 65 | 66 | lpr = -0.5*(repmat(sum((mu.^2)./cv, 1)' + sum(log(cv))', [1 nobs]) ... 67 | - 2*(mu./cv)'*obs + (1./cv)'*(obs.^2) + ndim*log(2*pi)); 68 | -------------------------------------------------------------------------------- /logsum.m: -------------------------------------------------------------------------------- 1 | function s = logsum(array, dim) 2 | % s = logsum(array, dim) 3 | % 4 | % returns log(sum(exp(array), dim)) minimizing possibility of over/underflow 5 | 6 | 7 | if nargin < 2 8 | amax = max(array(:)); 9 | s = log(sum(exp(array - amax))) + amax; 10 | else 11 | amax = max(array,[],dim); 12 | rep = ones(1, length(size(array))); 13 | rep(dim) = size(array,dim); 14 | s = log(sum(exp(array - repmat(amax, rep)), dim)) + amax; 15 | end 16 | -------------------------------------------------------------------------------- /merge_states.m: -------------------------------------------------------------------------------- 1 | function new_hmm = merge_states(hmm, idx) 2 | % new_hmm = merge_states(hmm, idx) 3 | % 4 | % Merge states of the given HMM. idx is a list of state indices to 5 | % merge. If idx is a matrix, the indices in each column will be 6 | % merged into a single state. Also works on GMM structures. 7 | % 8 | % Examples: 9 | % - Merge states 1, 3, and 5: merge_states(hmm, [1 3 5]) 10 | % - Merge states 1:5 and 10:20: merge_states(hmm, [1:5; 10:20]') 11 | % - Merge succesive pairs of states: 12 | % merge_states(hmm, reshape(1:hmm.nstates, [2, hmm.nstates/2])) 13 | % 14 | % Note that the merging isn't at all correct - it just dumbly takes 15 | % the weighted average of the given states. 16 | % 17 | % 2008-06-03 ronw@ee.columbia.edu 18 | 19 | % Copyright (C) 2008 Ron J. Weiss 20 | % 21 | % This program is free software: you can redistribute it and/or modify 22 | % it under the terms of the GNU General Public License as published by 23 | % the Free Software Foundation, either version 3 of the License, or 24 | % (at your option) any later version. 25 | % 26 | % This program is distributed in the hope that it will be useful, 27 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 28 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 29 | % GNU General Public License for more details. 30 | % 31 | % You should have received a copy of the GNU General Public License 32 | % along with this program. If not, see . 33 | 34 | [nr nc] = size(idx); 35 | if nr == 1 || nc == 1 36 | % Turn into a column vector 37 | idx = idx(:); 38 | end 39 | 40 | if is_valid_gmm(hmm) 41 | new_hmm = merge_states_gmm(hmm, idx); 42 | else 43 | new_hmm = merge_states_hmm(hmm, idx); 44 | end 45 | 46 | 47 | 48 | function new_gmm = merge_states_gmm(gmm, idx) 49 | [nr nc] = size(idx); 50 | new_gmm = gmm; 51 | states_to_delete = zeros(gmm.nmix, 1); 52 | for c = 1:nc 53 | i = idx(:,c); 54 | states_to_delete(i(2:end)) = 1; 55 | 56 | lp = gmm.priors(i); 57 | new_gmm.priors(i(1)) = logsum(lp); 58 | 59 | p = exp(lp(:) - logsum(lp)); 60 | new_gmm.means(:,i(1)) = gmm.means(:,i) * p; 61 | new_gmm.covars(:,i(1)) = gmm.covars(:,i) * p; 62 | end 63 | 64 | i = find(~states_to_delete); 65 | new_gmm.nmix = length(i); 66 | new_gmm.priors = new_gmm.priors(i); 67 | new_gmm.means = new_gmm.means(:,i); 68 | new_gmm.covars = new_gmm.covars(:,i); 69 | 70 | 71 | 72 | function new_hmm = merge_states_hmm(hmm, idx) 73 | if strcmp(hmm.emission_type, 'GMM') 74 | error('HMMs with GMM emissions are not supported.'); 75 | end 76 | [nr nc] = size(idx); 77 | new_hmm = hmm; 78 | states_to_delete = zeros(hmm.nstates, 1); 79 | for c = 1:nc 80 | i = idx(:,c); 81 | states_to_delete(i(2:end)) = 1; 82 | 83 | lp = logsum(hmm.transmat(:,i), 1); 84 | p = exp(lp(:) - logsum(lp)); 85 | 86 | new_hmm.start_prob(i(1)) = logsum(hmm.start_prob(i)); 87 | new_hmm.transmat(i(1),i(1)) = logsum(logsum(hmm.transmat(i,i), 2) + p); 88 | for s = 1:hmm.nstates 89 | new_hmm.transmat(s,i(1)) = logsum(hmm.transmat(s,i)); 90 | end 91 | new_hmm.end_prob(i(1)) = logsum(hmm.end_prob(i)); 92 | 93 | new_hmm.means(:,i(1)) = hmm.means(:,i) * p; 94 | new_hmm.covars(:,i(1)) = hmm.covars(:,i) * p; 95 | end 96 | 97 | i = find(~states_to_delete); 98 | new_hmm.nstates = length(i); 99 | new_hmm.start_prob = new_hmm.start_prob(i); 100 | new_hmm.transmat = new_hmm.transmat(i,i); 101 | new_hmm.end_prob = new_hmm.end_prob(i); 102 | new_hmm.means = new_hmm.means(:,i); 103 | new_hmm.covars = new_hmm.covars(:,i); 104 | 105 | % Get rid of NaNs introduced by logsum(-Inf) 106 | new_hmm.start_prob(isnan(new_hmm.start_prob)) = -Inf; 107 | new_hmm.end_prob(isnan(new_hmm.end_prob)) = -Inf; 108 | new_hmm.transmat(isnan(new_hmm.transmat)) = -Inf; 109 | 110 | % make sure transmat and end_prob are normalized properly 111 | norm = logsum(cat(2, logsum(new_hmm.transmat, 2), new_hmm.end_prob'), 2); 112 | new_hmm.transmat = new_hmm.transmat - repmat(norm, [1 new_hmm.nstates]); 113 | new_hmm.end_prob = new_hmm.end_prob - norm'; 114 | -------------------------------------------------------------------------------- /reorder_states.m: -------------------------------------------------------------------------------- 1 | function new_hmm = reorder_states(hmm, idx) 2 | % new_hmm = reorder_states(hmm, idx) 3 | % 4 | % Rearrange the states of hmm using the given indices. 5 | % 6 | % 2008-09-12 ronw@ee.columbia.edu 7 | 8 | % Copyright (C) 2008 Ron J. Weiss 9 | % 10 | % This program is free software: you can redistribute it and/or modify 11 | % it under the terms of the GNU General Public License as published by 12 | % the Free Software Foundation, either version 3 of the License, or 13 | % (at your option) any later version. 14 | % 15 | % This program is distributed in the hope that it will be useful, 16 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 17 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 18 | % GNU General Public License for more details. 19 | % 20 | % You should have received a copy of the GNU General Public License 21 | % along with this program. If not, see . 22 | 23 | if is_valid_gmm(hmm) 24 | new_hmm = reorder_states_gmm(hmm, idx); 25 | else 26 | new_hmm = reorder_states_hmm(hmm, idx); 27 | end 28 | 29 | function new_gmm = reorder_states_gmm(gmm, idx) 30 | new_gmm = gmm; 31 | new_gmm.nmix = length(idx); 32 | new_gmm.means = gmm.means(:,idx); 33 | new_gmm.covars = gmm.covars(:,idx); 34 | % Ensure priors are normalized (if components are deleted and not 35 | % just rearranged). 36 | new_gmm.priors = gmm.priors(idx) - logsum(gmm.priors(idx)); 37 | 38 | 39 | function new_hmm = reorder_states_hmm(hmm, idx) 40 | new_hmm = hmm; 41 | new_hmm.nstates = length(idx); 42 | if strcmp(hmm.emission_type, 'GMM') 43 | new_hmm.gmms = hmm.gmms(idx); 44 | else 45 | new_hmm.means = hmm.means(:,idx); 46 | new_hmm.covars = hmm.covars(:,idx); 47 | end 48 | new_hmm.start_prob = hmm.start_prob(idx); 49 | new_hmm.transmat = hmm.transmat(idx,idx); 50 | new_hmm.end_prob = hmm.end_prob(idx); 51 | 52 | % Make sure everything is normalized properly. 53 | new_hmm.start_prob = new_hmm.start_prob - logsum(new_hmm.start_prob); 54 | norm = logsum(cat(2, logsum(new_hmm.transmat, 2), new_hmm.end_prob'), 2); 55 | new_hmm.transmat = new_hmm.transmat - repmat(norm, [1 new_hmm.nstates]); 56 | new_hmm.end_prob = new_hmm.end_prob - norm'; 57 | -------------------------------------------------------------------------------- /sample_gaussian.m: -------------------------------------------------------------------------------- 1 | function y = sample_gaussian(mu, cv) 2 | % sample = sample_gaussian(mu, cv) 3 | % 4 | % Generate a random sample from a Gaussian distribution with the given 5 | % parameters. 6 | % 7 | % 2008-06-04 ronw@ee.columbia.edu 8 | 9 | % Copyright (C) 2008 Ron J. Weiss 10 | % 11 | % This program is free software: you can redistribute it and/or modify 12 | % it under the terms of the GNU General Public License as published by 13 | % the Free Software Foundation, either version 3 of the License, or 14 | % (at your option) any later version. 15 | % 16 | % This program is distributed in the hope that it will be useful, 17 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 18 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 19 | % GNU General Public License for more details. 20 | % 21 | % You should have received a copy of the GNU General Public License 22 | % along with this program. If not, see . 23 | 24 | y = randn(size(mu)).*sqrt(cv) + mu; 25 | -------------------------------------------------------------------------------- /sample_gmm.m: -------------------------------------------------------------------------------- 1 | function samples = sample_gmm(gmm, nsamp) 2 | % samples = sample_gmm(gmm, N) 3 | % 4 | % Generate N random samples from the given GMM. 5 | % 6 | % 2008-06-04 ronw@ee.columbia.edu 7 | 8 | % Copyright (C) 2008 Ron J. Weiss 9 | % 10 | % This program is free software: you can redistribute it and/or modify 11 | % it under the terms of the GNU General Public License as published by 12 | % the Free Software Foundation, either version 3 of the License, or 13 | % (at your option) any later version. 14 | % 15 | % This program is distributed in the hope that it will be useful, 16 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 17 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 18 | % GNU General Public License for more details. 19 | % 20 | % You should have received a copy of the GNU General Public License 21 | % along with this program. If not, see . 22 | 23 | prior_pdf = exp(gmm.priors); 24 | prior_cdf = cumsum(prior_pdf); 25 | 26 | ndim = size(gmm.means, 1); 27 | 28 | samples = zeros(ndim, nsamp); 29 | for n = 1:nsamp 30 | p = rand(1); 31 | c = min(find(prior_cdf >= p)); 32 | samples(:,n) = sample_gaussian(gmm.means(:,c), gmm.covars(:,c)); 33 | end 34 | 35 | -------------------------------------------------------------------------------- /sample_hmm.m: -------------------------------------------------------------------------------- 1 | function [samples state_seq] = sample_hmm(hmm) 2 | % [samples state_seq] = sample_hmm(hmm) 3 | % 4 | % Generate a random sample from the given HMM. 5 | % 6 | % 2008-06-04 ronw@ee.columbia.edu 7 | 8 | % Copyright (C) 2008 Ron J. Weiss 9 | % 10 | % This program is free software: you can redistribute it and/or modify 11 | % it under the terms of the GNU General Public License as published by 12 | % the Free Software Foundation, either version 3 of the License, or 13 | % (at your option) any later version. 14 | % 15 | % This program is distributed in the hope that it will be useful, 16 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 17 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 18 | % GNU General Public License for more details. 19 | % 20 | % You should have received a copy of the GNU General Public License 21 | % along with this program. If not, see . 22 | 23 | sp_pdf = exp(hmm.start_prob); 24 | sp_cdf = cumsum(sp_pdf); 25 | trans_pdf = exp([hmm.transmat hmm.end_prob']); 26 | trans_cdf = cumsum(trans_pdf, 2); 27 | 28 | % Initial state 29 | p = rand(1); 30 | s = min(find(sp_cdf >= p)); 31 | state_seq = s; 32 | samples = sample_from_state(hmm, s); 33 | 34 | i = 1; 35 | while true 36 | % Select next component or exit. 37 | p = rand(1); 38 | os = s; 39 | s = min(find(trans_cdf(os,:) >= p)); 40 | if isempty(s) 41 | s = length(trans_cdf(os,:)); 42 | end 43 | 44 | if s > hmm.nstates 45 | break 46 | else 47 | i = i + 1; 48 | samples(:,i) = sample_from_state(hmm, s); 49 | state_seq(i) = s; 50 | end 51 | end 52 | 53 | 54 | function y = sample_from_state(hmm, s) 55 | if strcmp(hmm.emission_type, 'GMM') 56 | y = sample_gmm(hmm.gmms(s), 1); 57 | elseif strcmp(hmm.emission_type, 'gaussian') 58 | y = sample_gaussian(hmm.means(:,s), hmm.covars(:,s)); 59 | else 60 | error(['Invalid HMM emission type: ' hmm.emission_type]); 61 | end 62 | -------------------------------------------------------------------------------- /train_gmm.m: -------------------------------------------------------------------------------- 1 | function gmm = train_gmm(trdata, nmix, niter, verb, CVPRIOR, mu0); 2 | % gmmparams = train_gmm(trdata, nmix, niter, verb, cvprior, mu0); 3 | % 4 | % Train a GMM with diagonal covariance. 5 | % 6 | % Inputs: 7 | % trdata - training data (cell array of training sequences, each 8 | % column of the sequences arrays contains an 9 | % observation) 10 | % nmix - number of mixture components. Defaults to 3. 11 | % niter - number of EM iterations to perform. Defaults to 10. 12 | % verb - set to 1 to output loglik at each iteration 13 | % cvprior - 14 | % 15 | % Outputs: 16 | % gmmparams - structure containing hmm parameters learned from training 17 | % data (gmm.priors, gmm.means(:,1:nmix), gmm.covars(:,1:nmix)) 18 | % 19 | % 2007-11-06 ronw@ee.columbia.edu 20 | 21 | if nargin < 2 22 | nmix = 3; 23 | end 24 | if nargin < 3 25 | niter = 10; 26 | end 27 | 28 | if nargin < 4 29 | verb = 0; 30 | end 31 | 32 | % prior on observation covariances to avoid overfitting: 33 | if nargin < 5 34 | CVPRIOR = 1; 35 | end 36 | 37 | if ~iscell(trdata) 38 | trdata = {trdata}; 39 | end 40 | 41 | ndata = length(trdata); 42 | 43 | 44 | % Initialization 45 | gmm.priors = log(ones(1, nmix)/nmix); 46 | gmm.nmix = nmix; 47 | 48 | if nargin < 6 | numel(mu0) == 1 & mu0 == 1 49 | gmm.means = kmeans(cat(2, trdata{:}), nmix, niter/2); 50 | else 51 | if size(mu0, 2) == nmix 52 | gmm.means = mu0; 53 | end 54 | end 55 | 56 | ndim = size(trdata{1}, 1); 57 | %gmm.covars = ones(ndim, nmix); 58 | gmm.covars(:,1:nmix) = repmat(var(trdata{1}')', [1 nmix]); 59 | 60 | 61 | % sufficient statistics 62 | norm = zeros(size(gmm.priors)); 63 | means = zeros(size(gmm.means)); 64 | covars = zeros(size(gmm.covars)); 65 | 66 | last_loglik = 0; 67 | for iter = 1:niter 68 | % E-step 69 | loglik = 0; 70 | norm(:) = 0; 71 | means(:) = 0; 72 | covars(:) = 0; 73 | for n = 1:ndata 74 | curr_data = trdata{n}; 75 | [ll, posteriors] = eval_gmm(gmm, curr_data); 76 | 77 | loglik = loglik + sum(ll); 78 | 79 | norm = norm + sum(posteriors, 2)'; 80 | means = means + curr_data * posteriors'; 81 | covars = covars + curr_data.^2 * posteriors'; 82 | end 83 | 84 | if verb, 85 | fprintf('Iteration %d: log likelihood = %f\n', iter, loglik); 86 | end 87 | 88 | % Check for convergence 89 | if abs(loglik - last_loglik) < 1e-5 90 | break 91 | end 92 | last_loglik = loglik; 93 | 94 | % M-step 95 | gmm.priors = log(norm/sum(norm)); 96 | 97 | nrm = repmat(1./norm, [ndim 1]); 98 | gmm.means = means .* nrm; 99 | gmm.covars = (covars - 2*gmm.means.*means) .* nrm + gmm.means.^2; 100 | gmm.covars(gmm.covars < CVPRIOR) = CVPRIOR; 101 | end 102 | --------------------------------------------------------------------------------