├── LICENSE
├── README.md
├── demo
├── demo_classif.m
├── demo_unmix.m
└── visu_classif.m
├── unmix
├── README.md
├── USGS_1995_Library.mat
├── demo1_sparse_TV.m
├── prune_library.m
├── soft.m
├── sort_library_by_angle.m
├── sunsal.m
└── sunsal_tv.m
└── utils
├── get_reg_prox.m
├── gist_chinge.m
├── gist_hinge2.m
├── gist_least.m
├── gist_logreg.m
├── gist_opt.m
├── initoptions.m
├── l2_unmix.m
├── l2_unmix_simplex.m
└── l2simplex.m
/LICENSE:
--------------------------------------------------------------------------------
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 | {one line to give the program's name and a brief idea of what it does.}
635 | Copyright (C) {year} {name of author}
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 | {project} Copyright (C) {year} {fullname}
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.md:
--------------------------------------------------------------------------------
1 | Non-convex optimization Toolbox
2 | ===============================
3 |
4 |
5 | This matlab toolbox propose a generic solver for proximal gradient descent in the convex or non-convex case. It is a complete reimplementation of the GIST algorithm proposed in [1] with new regularization terms such as the lp pseudo-norm with p=1/2.
6 |
7 | When using this toolbox in your research works please cite the paper [Non-convex regularization in remote sensing](http://remi.flamary.com/biblio/tuia2016nonconvex.pdf):
8 | ```
9 | D. Tuia, R. Flamary and M. Barlaud, "Non-convex regularization in remote sensing",
10 | IEEE transactions Transactions on Geoscience and Remote Sensing, (to appear) 2016.
11 | ```
12 |
13 | The code solve optimization problems of the form:
14 |
15 | min_x f(x)+lambda g(x)
16 |
17 | We provide solvers for solving the following data fitting terms f(x) problems:
18 | - Least square (linear regression)
19 | - Linear SVM with quadratic Hinge loss
20 | - Linear logistic regression
21 | - Calibrated Hinge loss
22 |
23 | The regularization terms g(x) that have been implemented include:
24 | - Lasso (l1)
25 | - Ridge (squared l2)
26 | - Log sum penalty (LSP) ([2],prox in [1])
27 | - lp regularization with p=1/2 (prox in [3])
28 | - Group lasso (l1-l2)
29 | - Minimax concave penalty (MCP)
30 | - Indicator function on convex (projection)
31 | - Indicator function on simplex (projection)
32 |
33 | New regularization terms can be easily implemented as discussed in section 3.
34 |
35 | # Start using the toolbox
36 |
37 | ## Installation
38 |
39 | All the functions in the toolbox a given in the folder /utils.
40 |
41 | The unmix folder contains code and data downloaded from the website of [ Jose M. Bioucas Dias](http://www.lx.it.pt/~bioucas/publications.html).
42 |
43 | In order to use the function we recommend to execute the following command
44 |
45 | ```Matlab
46 | addpath(genpath('.'))
47 | ```
48 |
49 | if you are not working in the root folder of the toolbox or replacing '.' by the location of the folder on your machine.
50 |
51 |
52 | ## Entry points
53 |
54 | We recommend to look at the following files to see how to use the toolbox:
55 | * demo/demo_classif.m : contains an example of 4 class linear classification problem and show how to learn different classifiers.
56 | * demo/demo_unmix.m : show an example of linear unmixing with positivity constraint and non-convex regularization.
57 | * demo/visu_classif.m : reproduce the example figure in the paper.
58 |
59 | # Solving your own optimization problem
60 |
61 | ## New regularization terms
62 |
63 | All the regularization terms (and theri proximal operators) are defined in the function [utils/get_reg_prox.m](utils/get_reg_prox.m).
64 |
65 | If you want to add a regularization term (or a projection), you only need to add a case to the switch beginning [line 37](utils/get_reg_prox.m#L37) and define two functions:
66 | - g(x) : R^d->R, loss function for the regularization term
67 | - prox_g(x,lambda) : R^d->R^d, proximal operator of lambda*g(x)
68 |
69 | For a simple example look at the implementations of the Lasso loss ([line 124](utils/get_reg_prox.m#L124)) soft thresholding ([Line 128](utils/get_reg_prox.m#L128)) and loss implementations.
70 |
71 | note that in order to limit the number of files, the loss and proximal operators functions are all implemented as subfunctions of file [utils/get_reg_prox.m](utils/get_reg_prox.m).
72 |
73 |
74 | ## Data fitting term
75 |
76 | You can easily change the data fitting term by providing a new loss and gradient functions to the optimization function [utils/gist_opt.m](utils/gist_opt.m).
77 |
78 | A good starting point is by looking at the least square implementation in [utils/gist_least.m](utils/gist_least.m). Changing the data fitting term correspond to only code the loss function at [Line 63](utils/gist_least.m#L63) and the corresponding gradient function at [Line 59](utils/gist_least.m#L59).
79 |
80 |
81 |
82 |
83 |
84 | # Contact and contributors
85 |
86 | * [Rémi Flamary](http://remi.flamary.com/)
87 | * [Devis Tuia](https://sites.google.com/site/devistuia/)
88 |
89 | ## Aknowledgements
90 |
91 | We want to thank [ Jose M. Bioucas Dias](http://www.lx.it.pt/~bioucas/publications.html) for providing the unmixing dataset and functions on his website.
92 |
93 | # References
94 |
95 | [1] Gong, P., Zhang, C., Lu, Z., Huang, J., & Ye, J. (2013, June). A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems. In ICML (2) (pp. 37-45).
96 |
97 | [2] Candes, E. J., Wakin, M. B., & Boyd, S. P. (2008). Enhancing sparsity by reweighted ? 1 minimization. Journal of Fourier analysis and applications, 14(5-6), 877-905.
98 |
99 | [3] Xu, Z., Chang, X., Xu, F., & Zhang, H. (2012). L1/2 regularization: A thresholding representation theory and a fast solver. IEEE Transactions on neural networks and learning systems, 23(7), 1013-1027.
100 |
101 |
102 |
103 | Copyright 2016
104 |
--------------------------------------------------------------------------------
/demo/demo_classif.m:
--------------------------------------------------------------------------------
1 | % This file show how to use the toolbox to estimate linear classifier with
2 | % different regularization scheme.
3 | % note that all classifiers naturally handle multiclass data
4 | %
5 | % The dataset contains only 2 discriminant dimensions and 8 noisy
6 | % dimension.
7 | % The timated classifier should select automatically the two first
8 | % dimension when sparsity is promoted.
9 |
10 | clear all
11 | close all
12 | addpath(genpath('.'))
13 |
14 |
15 | %% generate dataset
16 |
17 |
18 | mclass=[1 1; -1 1; 1 -1; -1 -1];
19 |
20 | nbperclass=1000;
21 |
22 |
23 | % generating good features and labels
24 | x=[];
25 | y=[];
26 | sigma=.5;
27 | for i=1:size(mclass,1);
28 |
29 | x=[x; ones(nbperclass,1)*mclass(i,:)+sigma*randn(nbperclass,size(mclass,2))];
30 | y=[y;i*ones(nbperclass,1)];
31 | end
32 |
33 |
34 | % adding random features
35 | nbnoise=8;
36 | x=[x sigma*randn(size(x,1),nbnoise)];
37 |
38 | % models should have only the two first components active
39 |
40 | %% visu data on 2 diuscriminant components
41 |
42 | figure(1)
43 |
44 | plot(x(y==1,1),x(y==1,2),'+')
45 | hold on
46 | plot(x(y==2,1),x(y==2,2),'x')
47 | plot(x(y==3,1),x(y==3,2),'o')
48 | plot(x(y==4,1),x(y==4,2),'s')
49 | hold off
50 |
51 | %% SVM with l2 regularization
52 |
53 | % options for solver
54 | options.verbose=1;
55 | options.lambda=1e-3 ;% regul parameter
56 | options.theta=.01; % parameter for lsp
57 | options.p=.5; % parameter for lp
58 | options.reg='l2'; % l2 l1 lp, lsp are possible options
59 |
60 | tic
61 | [svml2]=gist_hinge2(x,y,options); % hinge squared svn
62 | %[svm,LOG]=gist_chinge(x,y,options) % calibrated hinge
63 | %[svm,LOG]=gist_logreg(x,y,options) % logistic regression
64 | toc
65 |
66 | % classifier linear parameter
67 | wl2=svml2.w % normal vector to hyperlpaln
68 | w0l2=svml2.w0; % svm bias
69 |
70 | %% SVM with lp regularization
71 |
72 | % options for solver
73 | options.verbose=1;
74 | options.lambda=1e-2 ;% regul parameter
75 | options.theta=.01; % parameter for lsp
76 | options.p=.5; % parameter for lp
77 | options.reg='lp'; % l2 l1 lp, lsp are possible options
78 |
79 | tic
80 | [svmlp]=gist_hinge2(x,y,options); % hinge squared svn
81 | %[svm,LOG]=gist_chinge(x,y,options) % calibrated hinge
82 | %[svm,LOG]=gist_logreg(x,y,options) % logistic regression
83 | toc
84 |
85 | % classifier linear parameter
86 | wlp=svmlp.w % normal vector to hyperlpaln
87 | w0lp=svmlp.w0; % svm bias
88 |
89 |
90 |
91 | %% visu separation
92 | % plot classification regions in 2D (discriminant features)
93 |
94 | nbgrid=100;
95 | [Xgrid,Ygrid]=meshgrid(linspace(-3,3,nbgrid),linspace(-3,3,nbgrid));
96 |
97 | xtest=[Xgrid(:) Ygrid(:)];
98 |
99 | ypred=xtest*wlp(1:2,:)+ones(nbgrid*nbgrid,1)*w0lp;
100 |
101 | [temp,ypred_c]=min(ypred,[],2);
102 |
103 | Ypred=reshape(ypred_c,[nbgrid nbgrid]);
104 |
105 | figure(2)
106 |
107 | imagesc(linspace(-3,3,nbgrid),linspace(-3,3,nbgrid),Ypred)
108 |
109 | hold on
110 | plot(x(y==1,1),x(y==1,2),'+')
111 | plot(x(y==2,1),x(y==2,2),'x')
112 | plot(x(y==3,1),x(y==3,2),'o')
113 | plot(x(y==4,1),x(y==4,2),'s')
114 | hold off
115 |
116 |
117 |
--------------------------------------------------------------------------------
/demo/demo_unmix.m:
--------------------------------------------------------------------------------
1 | % This file show how to use the toolbox to estimate linear mixture with
2 | % different regularization scheme.
3 | %
4 | % The dataset contains only 3 active components
5 | % We compare l2 unmixing with positivity constraints, l1 and lp
6 | % regularization
7 |
8 | clear all
9 | close all
10 | addpath(genpath('.'))
11 |
12 |
13 | %% generate data
14 | seed=0
15 | rng(seed)
16 |
17 | load USGS_1995_Library.mat
18 |
19 | D=datalib(:,4:end);
20 |
21 | anglemin=20;
22 | D = prune_library(D,anglemin);
23 |
24 |
25 | wl=datalib(:,1);
26 |
27 |
28 | d=size(D,2);
29 | n=size(D,1);
30 |
31 |
32 | alpha_t=zeros(d,1);
33 |
34 |
35 | nbactive=3;
36 |
37 | perm=randperm(d);
38 | alpha_t(perm(1:nbactive))=rand(nbactive,1);
39 | %wtrue=wtrue./sum(wtrue)
40 |
41 | sigma=1e-1;
42 |
43 | y=D*alpha_t+sigma*randn(n,1);
44 | ytrue=D*alpha_t;
45 |
46 | %%
47 | figure(1)
48 | subplot(2,1,1)
49 |
50 | plot(wl,D)
51 |
52 | xlabel('Wavelength in microns')
53 |
54 | subplot(2,1,2)
55 |
56 | plot(wl,[ytrue y])
57 |
58 | xlabel('Wavelength in microns')
59 |
60 | %% l2 unmix
61 | lambda=1e-2;
62 |
63 | alpha_l2=l2_unmix(y,D,lambda)
64 | err_l2=sum(abs(alpha_l2-alpha_t).^2)
65 |
66 |
67 | %% l1 unmixing
68 |
69 | options.verbose=0; % do not print
70 | options.lambda=1e-3;% regul parameter
71 | options.reg='l1' % regularization
72 | options.bias=0; % forc no bias estimation
73 | options.pos=1; % fore positivity
74 | options.stopvarx=1e-6; % convergence conditions
75 | options.stopvarj=1e-6;% convergence conditions
76 | options.nbitermax=1e4;% convergence conditions
77 |
78 | tic
79 | [svm_l1,LOG]=gist_least(D,y,options);
80 | toc
81 |
82 | alpha_l1=svm_l1.w
83 |
84 |
85 |
86 | err_l2
87 | err_l1=sum(abs(alpha_l1-alpha_t).^2)/2
88 |
89 | %% lp unmixing
90 |
91 | options.verbose=0;
92 | options.lambda=5e-2% regul parameter
93 | options.p=.5; % value for p
94 | options.reg='lp'
95 | options.bias=0; % force no bias estimation
96 | options.pos=1; % force positivity
97 | options.stopvarx=1e-6; % convergence conditions
98 | options.stopvarj=1e-6;% convergence conditions
99 | options.nbitermax=1e4;% convergence conditions
100 |
101 | tic
102 | [svm_lp,LOG]=gist_least(D,y,options);
103 | toc
104 |
105 | alpha_lp=svm_lp.w
106 |
107 |
108 | % display errors
109 | err_l2
110 | err_l1
111 | err_lp=sum(abs(alpha_lp-alpha_t).^2)/2
112 |
113 |
114 | %% show reconsruction
115 |
116 |
117 | figure(2)
118 | imagesc([alpha_t alpha_l2 alpha_l1 alpha_lp]')
119 | set(gca,'Ytick',[1 2 3 4])
120 | set(gca,'YtickLabel',{'Ground truth','l2 unmix','l1 unmix','lp unmix'})
121 | colorbar()
122 |
123 |
124 |
125 |
--------------------------------------------------------------------------------
/demo/visu_classif.m:
--------------------------------------------------------------------------------
1 | % test gist
2 |
3 | clear all
4 | close all
5 | addpath(genpath('.'))
6 |
7 |
8 | %% generate dataset
9 |
10 |
11 | nbperclass=100;
12 |
13 |
14 | % generating good features and labels
15 | x=[];
16 | y=[];
17 | sigma=1;
18 | m1=[1, .5];
19 | m2=-m1;
20 | x=[ones(nbperclass,1)*m1+sigma*randn(nbperclass,2);ones(nbperclass,1)*m2+sigma*randn(nbperclass,2)];
21 | y=[ones(nbperclass,1);-ones(nbperclass,1)];
22 |
23 |
24 | % adding random features
25 | nbnoise=18;
26 | x=[x sigma*randn(size(x,1),nbnoise)];
27 |
28 | %% visu data
29 |
30 | figure(1)
31 |
32 | plot(x(y==1,1),x(y==1,2),'+')
33 | hold on
34 | plot(x(y==-1,1),x(y==-1,2),'xr')
35 | hold off
36 |
37 |
38 | %% bayes decision
39 |
40 | wb=(m1-m2)
41 |
42 | fb=@(x,y) x*wb(1)+y*wb(2);
43 |
44 |
45 | figure(1)
46 |
47 | plot(x(y==1,1),x(y==1,2),'+')
48 | hold on
49 | plot(x(y==-1,1),x(y==-1,2),'xr')
50 | h=ezplot(fb);
51 | set(h, 'Color','b')
52 | hold off
53 | %title('test')
54 | legend('Class 1','Class -1','Bayes decision')
55 |
56 |
57 |
58 | %% svm l1
59 |
60 | options.verbose=1;
61 | options.lambda=1e-1
62 | options.theta=.01;
63 | options.p=.5;
64 | options.reg='l1'
65 |
66 | tic
67 | [svml1,LOG]=gist_hinge2(x,y,options)
68 | %[svm,LOG]=gist_chinge(x,y,options)
69 | %[svml1,LOG]=gist_logreg(x,y,options)
70 | toc
71 |
72 | wl1=svml1.w(:,1);
73 |
74 | fl1=@(x,y) x*wl1(1)+y*wl1(2);
75 |
76 | figure(1)
77 |
78 | plot(x(y==1,1),x(y==1,2),'+')
79 | hold on
80 | plot(x(y==-1,1),x(y==-1,2),'xr')
81 | h=ezplot(fb);
82 | set(h, 'Color','b')
83 | h=ezplot(fl1);
84 | set(h, 'Color','r')
85 | hold off
86 | %title('test')
87 | legend('Class 1','Class -1','Bayes decision','l1 reg.')
88 |
89 | %% LSP
90 |
91 | options.verbose=1;
92 | options.lambda=2e-3
93 | options.theta=.001;
94 | options.p=.5;
95 | options.reg='lsp'
96 |
97 | tic
98 | [svmlsp,LOG]=gist_hinge2(x,y,options)
99 | %[svm,LOG]=gist_chinge(x,y,options)
100 | %[svmlsp,LOG]=gist_logreg(x,y,options)
101 | toc
102 |
103 | wlsp=svmlsp.w(:,1);
104 |
105 | flsp=@(x,y) x*wlsp(1)+y*wlsp(2);
106 | figure(1)
107 |
108 | plot(x(y==1,1),x(y==1,2),'+')
109 | hold on
110 | plot(x(y==-1,1),x(y==-1,2),'xr')
111 | h=ezplot(fb);
112 | set(h, 'Color','b')
113 | h=ezplot(fl1);
114 | set(h, 'Color','r')
115 | h=ezplot(flsp);
116 | set(h, 'Color',[0 .7 0])
117 | hold off
118 | %title('test')
119 | legend('Class 1','Class -1','Bayes decision','l1 reg.','lsp reg.')
120 |
121 |
122 | %% lp
123 |
124 | options.verbose=1;
125 | options.lambda=6e-2
126 | options.theta=.1;
127 | options.p=.5;
128 | options.reg='lp'
129 |
130 | tic
131 | [svmlp,LOG]=gist_hinge2(x,y,options)
132 | %[svm,LOG]=gist_chinge(x,y,options)
133 | %[svmlsp,LOG]=gist_logreg(x,y,options)
134 | toc
135 |
136 | limx=[-4,4]
137 |
138 | wlp=svmlp.w(:,1);
139 |
140 | flp=@(x,y) x*wlp(1)+y*wlp(2);
141 | figure(1)
142 |
143 | plot(x(y==1,1),x(y==1,2),'+')
144 | hold on
145 | plot(x(y==-1,1),x(y==-1,2),'xr')
146 | h=ezplot(fb,limx);
147 | set(h, 'Color','b')
148 | h=ezplot(fl1,limx);
149 | set(h, 'Color','r')
150 | h=ezplot(flsp,limx);
151 | set(h, 'Color',[0 .7 0],'LineStyle','-.')
152 | h=ezplot(flp,limx);
153 | set(h, 'Color',[0 .7 .7],'LineStyle','--')
154 | hold off
155 | title('')
156 | legend('Class 1','Class -1','Bayes decision','l1 reg.','lsp reg.','lp reg.')
157 |
158 | print('-depsc','toybias.eps')
--------------------------------------------------------------------------------
/unmix/README.md:
--------------------------------------------------------------------------------
1 |
2 | Source of this folder:
3 |
4 | This folder contains code and data downloaded from the website of [ Jose M. Bioucas Dias](http://www.lx.it.pt/~bioucas/publications.html).
5 |
--------------------------------------------------------------------------------
/unmix/USGS_1995_Library.mat:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/rflamary/nonconvex-optimization/4f09aa52f0147c6516c8d5a7d808c5faf14f85db/unmix/USGS_1995_Library.mat
--------------------------------------------------------------------------------
/unmix/demo1_sparse_TV.m:
--------------------------------------------------------------------------------
1 | %% demo_sunsal_TV
2 | %
3 | % This demo illustrates the sunsal_TV sparse regression algorithm
4 | % introduced in the paper
5 | %
6 | % M.-D. Iordache, J. Bioucas-Dias, and A. Plaza, "Total variation spatial
7 | % regularization for sparse hyperspectral unmixing", IEEE Transactions on
8 | % Geoscience and Remote Sensing, vol. PP, no. 99, pp. 1-19, 2012.
9 | %
10 | % which solves the optimization problem
11 | %
12 | % min 0.5*||AX-Y||^2_F + lambda_1 ||X||_{1,1} + lambda_tv TV(X)
13 | % X>=0
14 | %
15 | %
16 | % Demo parameters:
17 | % p = 5 % number of endmembers
18 | % SNR = 40 dB
19 | % size(A) = [220, 240] % size of the library
20 | % min angle(a_i, a_j) = 4.44 degs % minimum angle between any two
21 | % % elements of A
22 | %
23 | % Notes:
24 | %
25 | % You may change the demo parameters, namely SNR, the noise correlation,
26 | % the size of dictionary A by changing min_angle, and the true endmember
27 | % matrix M, which, in any case, must contain p=5 columns.
28 | %
29 | % Please keep in mind the following:
30 | %
31 | % a) sunsal adapts automatically the ADMM parameter for
32 | % convergence speed
33 | %
34 | % b) sunsal_tv deoes not adapts automatically the ADMM parameter.
35 | % So the inputted parameter mu has a critical impact on the
36 | % convergence speed
37 | %
38 | % c) the regularization parameters were hand tuned for optimal
39 | % performance.
40 | %
41 | % Author: Jose Bioucas Dias, August 2012
42 |
43 | close all
44 | clear all
45 |
46 | %%
47 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
48 | % Generate data
49 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
50 | % number of end members
51 | p = 5; % fixed for this demo
52 |
53 | %SNR in dB
54 | SNR = 40;
55 | % noise bandwidth in pixels of the noise low pass filter (Gaussian)
56 | bandwidth = 1000; % 10000 == iid noise
57 | %bandwidth = 5*pi/224; % colored noise
58 |
59 |
60 | % define random states
61 | rand('state',10);
62 | randn('state',10);
63 |
64 |
65 | %%
66 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
67 | % gererate fractional abundances
68 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
69 |
70 | % pure pixels
71 | x1 = eye(p);
72 |
73 | % mixtures with two materials
74 | x2 = x1 + circshift(eye(p),[1 0]);
75 |
76 | % mixtures with three materials
77 | x3 = x2 + circshift(eye(p),[2 0]);
78 |
79 | % mixtures with four materials
80 | x4 = x3 + circshift(eye(p),[3 0]);
81 |
82 | % mixtures with four materials
83 | x5 = x4 + circshift(eye(p),[4 0]);
84 |
85 |
86 | % normalize
87 | x2 = x2/2;
88 | x3 = x3/3;
89 | x4 = x4/4;
90 | x5 = x5/5;
91 |
92 |
93 | % background (random mixture)
94 | %x6 = dirichlet(ones(p,1),1)';
95 | x6 = [0.1149 0.0741 0.2003 0.2055, 0.4051]'; % as in the paper
96 |
97 | % build a matrix
98 | xt = [x1 x2 x3 x4 x5 x6];
99 |
100 |
101 | % build image of indices to xt
102 | imp = zeros(3);
103 | imp(2,2)=1;
104 |
105 | imind = [imp*1 imp*2 imp* 3 imp*4 imp*5;
106 | imp*6 imp*7 imp* 8 imp*9 imp*10;
107 | imp*11 imp*12 imp*13 imp*14 imp*15;
108 | imp*16 imp*17 imp* 18 imp*19 imp*20;
109 | imp*21 imp*22 imp* 23 imp*24 imp*25];
110 |
111 | imind = kron(imind,ones(5));
112 |
113 | % set backround index
114 | imind(imind == 0) = 26;
115 |
116 | % generare frectional abundances for all pixels
117 | [nl,nc] = size(imind);
118 | np = nl*nc; % number of pixels
119 | for i=1:np
120 | X(:,i) = xt(:,imind(i));
121 | end
122 |
123 | Xim = reshape(X',nl,nc,p);
124 |
125 | % image endmember 1
126 | figure(1)
127 | imagesc(Xim(:,:,5))
128 | title('Frational abundance of endmember 5')
129 |
130 | %%
131 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
132 | % buid the dictionary
133 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
134 | load USGS_1995_Library.mat
135 | % order bands by increasing wavelength
136 | [dummy index] = sort(datalib(:,1));
137 | A = datalib(index,4:end);
138 |
139 | % prune the library
140 | % min angle (in degres) between any two signatures
141 | % the larger min_angle the easier is the sparse regression problem
142 | min_angle = 4.44;
143 | A = prune_library(A,min_angle); % 240 signature
144 |
145 | % order the columns of A by decreasing angles
146 | [A, index, angles] = sort_library_by_angle(A);
147 |
148 |
149 | %% select p endmembers from A
150 | %
151 |
152 | % angles (a_1,a_j) \simeq min_angle)
153 | supp = 1:p;
154 | M = A(:,supp);
155 | [L,p] = size(M); % L = number of bands; p = number of material
156 |
157 |
158 | %%
159 | %---------------------------------
160 | % generate the observed data X
161 | %---------------------------------
162 |
163 | % set noise standard deviation
164 | sigma = sqrt(sum(sum((M*X).^2))/np/L/10^(SNR/10));
165 | % generate Gaussian iid noise
166 | noise = sigma*randn(L,np);
167 |
168 |
169 | % make noise correlated by low pass filtering
170 | % low pass filter (Gaussian)
171 | filter_coef = exp(-(0:L-1).^2/2/bandwidth.^2)';
172 | scale = sqrt(L/sum(filter_coef.^2));
173 | filter_coef = scale*filter_coef;
174 | noise = idct(dct(noise).*repmat(filter_coef,1,np));
175 |
176 | % observed spectral vector
177 | Y = M*X + noise;
178 |
179 |
180 | % create true X wrt the library A
181 | n = size(A,2);
182 | N = nl*nc;
183 | XT = zeros(n,N);
184 | XT(supp,:) = X;
185 |
186 |
187 | %% estimate noise and filter it out
188 | % [w,Rw] = estNoise(Y);
189 | %
190 | % % determine signal subspace
191 | % [kp,Ek] = hysime(Y,w,Rw);
192 | %
193 | % % remove noise
194 | % Y = Y-w;
195 | %
196 | % % project observed data on the signal subspace
197 | % Y = Ek*Ek'*Y;
198 | %
199 | % clear w;
200 |
201 |
202 | %%
203 | %--------------------------------------------------------------------------
204 | % SUNSAL and SUNSAL_TV solutions
205 | %--------------------------------------------------------------------------
206 |
207 | % constrained least squares CLS
208 | lambda = 0;
209 | [X_hat_cls] = sunsal(A,Y,'lambda',lambda,'ADDONE','no','POSITIVITY','yes', ...
210 | 'TOL',1e-4, 'AL_iters',2000,'verbose','yes');
211 |
212 | SRE_cls = 20*log10(norm(XT,'fro')/norm(X_hat_cls-XT,'fro'));
213 |
214 |
215 | % constrained least squares l2-l1
216 | lambda = 1e-2;
217 | [X_hat_l1] = sunsal(A,Y,'lambda',lambda,'ADDONE','no','POSITIVITY','yes', ...
218 | 'TOL',1e-4, 'AL_iters',2000,'verbose','yes');
219 |
220 | SRE_l1 = 20*log10(norm(XT,'fro')/norm(X_hat_l1-XT,'fro'));
221 |
222 |
223 | % constrained least squares l2-l1-TV (nonisotropic)
224 | lambda = 1e-3;
225 | lambda_TV = 3e-3;
226 | [X_hat_tv_ni,res,rmse_ni] = sunsal_tv(A,Y,'MU',0.05,'POSITIVITY','yes','ADDONE','no', ...
227 | 'LAMBDA_1',lambda,'LAMBDA_TV', lambda_TV, 'TV_TYPE','niso',...
228 | 'IM_SIZE',[75,75],'AL_ITERS',200, 'TRUE_X', XT, 'VERBOSE','yes');
229 |
230 | SRE_tv_ni = 20*log10(norm(XT,'fro')/norm(X_hat_tv_ni-XT,'fro'));
231 |
232 | % constrained least squares l2-l1-TV (isotropic)
233 | lambda = 1e-3;
234 | lambda_TV = 3e-3;
235 | [X_hat_tv_i,res,rmse_i] = sunsal_tv(A,Y,'MU',0.05,'POSITIVITY','yes','ADDONE','no', ...
236 | 'LAMBDA_1',lambda,'LAMBDA_TV', lambda_TV, 'TV_TYPE','iso',...
237 | 'IM_SIZE',[75,75],'AL_ITERS',200, 'TRUE_X', XT, 'VERBOSE','yes');
238 |
239 | SRE_tv_i = 20*log10(norm(XT,'fro')/norm(X_hat_tv_i-XT,'fro'));
240 |
241 |
242 | %%
243 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
244 | % print results
245 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
246 |
247 | fprintf('\n\n SIGNAL-TO-RECONSTRUCTION ERRORS (SRE)\n\n')
248 |
249 | fprintf('SRE-cls = %2.3f\nSRE-l1 = %2.3f\nSRE_tv-ni = %2.3f\nSRE-tv-i = %2.3f\n\n', ...
250 | SRE_cls, SRE_l1,SRE_tv_ni, SRE_tv_i)
251 |
252 |
253 | % endmember no. 1 (cls)
254 | X_hat_cls_im = reshape(X_hat_cls', nl,nc,n);
255 | figure(2)
256 | imagesc(X_hat_cls_im(:,:,supp(5)))
257 | title('CLS - Frational abundance of endmember 5')
258 |
259 |
260 | % endmember no. 1 (l2-l1)
261 | X_hat_l1_im = reshape(X_hat_l1', nl,nc,n);
262 | figure(3)
263 | imagesc(X_hat_l1_im(:,:,supp(5)))
264 | title('SUnSAL - Frational abundance of endmember 5')
265 |
266 |
267 | % endmember no. 1 (tv_ni)
268 | X_hat_tv_ni_im = reshape(X_hat_tv_ni', nl,nc,n);
269 | figure(4)
270 | imagesc(X_hat_tv_ni_im(:,:,supp(5)))
271 | title('SUnSAL-TV (NISO) - Frational abundance of endmember 5')
272 |
273 |
274 | % endmember no. 1 (tv_ni)
275 | X_hat_tv_i_im = reshape(X_hat_tv_i', nl,nc,n);
276 | figure(5)
277 | imagesc(X_hat_tv_i_im(:,:,supp(5)))
278 | title('SUnSAL-TV (ISO) - Frational abundance of endmember 5')
279 |
280 |
281 |
282 | scrsz = get(0,'ScreenSize');
283 | figure('Position',[1 1 scrsz(3)/2 scrsz(4)/2])
284 |
285 | subplot(151)
286 | imagesc(XT(:,1:100))
287 | title('spectral vectors (1;100)')
288 |
289 | subplot(152)
290 | imagesc(X_hat_cls(:,1:100))
291 | axis off
292 | title('CLS')
293 |
294 | subplot(153)
295 | imagesc(X_hat_l1(:,1:100))
296 | axis off
297 | title('SUnSAL')
298 |
299 | subplot(154)
300 | imagesc(X_hat_tv_ni(:,1:100))
301 | axis off
302 | title('SUnSAL-TV-NISO')
303 |
304 | subplot(155)
305 | imagesc(X_hat_tv_i(:,1:100))
306 | axis off
307 | title('SUnSAL-TV-ISO')
308 |
309 |
310 |
311 |
--------------------------------------------------------------------------------
/unmix/prune_library.m:
--------------------------------------------------------------------------------
1 | function B = prune_library(A,min_angle)
2 | % B = prune_library(A,min_angle)
3 | %
4 | % remove columns from A such that the minimum angle between the columns
5 | % of B in no smaller than max_angle
6 | %
7 | % Author: Jose Bioucas Dias. June, 2011
8 | %
9 |
10 | [L,m] = size(A); % L = number of bands; m = number of materilas
11 |
12 | %normalize A
13 | nA = sqrt(sum(A.^2));
14 | A_norm = A./repmat(nA,L,1);
15 |
16 | % compute angles
17 | angles = abs(acos(A_norm'*A_norm))*180/pi;
18 |
19 |
20 | % discard vectors with angles less than min_angle
21 | index = 1;
22 | for i=1:m
23 | if angles(i,i) ~= inf
24 | B(:,index) = A(:,i);
25 | angles(:,angles(i,:) < min_angle ) = inf;
26 | index = index + 1;
27 | end
28 |
29 | end
30 |
31 |
32 |
33 |
34 |
35 |
--------------------------------------------------------------------------------
/unmix/soft.m:
--------------------------------------------------------------------------------
1 | function y = soft(x,T)
2 |
3 | T = T + eps;
4 | y = max(abs(x) - T, 0);
5 | y = y./(y+T) .* x;
6 |
7 |
--------------------------------------------------------------------------------
/unmix/sort_library_by_angle.m:
--------------------------------------------------------------------------------
1 | function [B,index,angles] = sort_library_by_angle(A)
2 | % [B,index,angles] = sort_library_by_angle(A)
3 | %
4 | % B = A(index,:) where index in the column index of A ordered by inreasing
5 | % minimum angle with every other colum
6 | %
7 | %
8 | % % Author: Jose Bioucas Dias. June, 2011
9 |
10 | BIG = 1e10;
11 |
12 | [L,m] = size(A); % L = number of bands; m = number of materilas
13 |
14 | %normalize A
15 | nA = sqrt(sum(A.^2));
16 | A_norm = A./repmat(nA,L,1);
17 |
18 | % compute angles
19 | angles = abs(acos(A_norm'*A_norm))*180/pi;
20 | angles = angles + BIG*diag(ones(1,m));
21 |
22 | % compute min angles between a given column and every other column
23 | [min_angles index_rows] = min(angles);
24 | % sort columns by increasing angles
25 | [angles, index] = sort(min_angles);
26 |
27 | B = A(:,index);
28 |
29 |
30 |
31 |
32 |
33 |
--------------------------------------------------------------------------------
/unmix/sunsal.m:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/rflamary/nonconvex-optimization/4f09aa52f0147c6516c8d5a7d808c5faf14f85db/unmix/sunsal.m
--------------------------------------------------------------------------------
/unmix/sunsal_tv.m:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/rflamary/nonconvex-optimization/4f09aa52f0147c6516c8d5a7d808c5faf14f85db/unmix/sunsal_tv.m
--------------------------------------------------------------------------------
/utils/get_reg_prox.m:
--------------------------------------------------------------------------------
1 | function [g,prox_g]=get_reg_prox(reg,params)
2 | % return reg function and corresponding proximal operator
3 | %
4 | % the regularization functions are of the form:
5 | % g(x)=\sum_k h(x_k)
6 | %
7 | % reg: regularization term
8 | % - 'l2' : squared l2 ,orme (ridge regularization)
9 | % h(u)=u^2
10 | % - '0' : no reglarization
11 | % h(u)=0
12 | % - 'set' : indicator function of a set C=[C(1) C(2)]
13 | % h(u)= 0 if C(1)<= u <= C(2), Inf otherwise
14 | % params.C : 1D set (default=[0 1])
15 | % - 'l1' : lasso l1 regularization
16 | % h(u)=|u|
17 | % - 'l1l2' : group lasso on the columns of x
18 | % h(u)=||u||_2
19 | % - 'lsp' : log sum penalty
20 | % h(u)=log(1+|u|/theta)
21 | % params.theta: lsp param (default=1)
22 | % - 'mcp' : minimax concave penalty
23 | % Zhang, C. H. (2010). Nearly unbiased variable selection under minimax concave penalty. The Annals of statistics, 894-942.
24 | % - 'lp' : lp pseudo-norm (implemented only for p=1/2)
25 | % h(u)=|u|^p
26 | % params.p: (default=1/2)
27 | % - 'l0' : l0 pseudo norm
28 | % h(u)=0 if u=0 1 otherwise
29 | % - 'simplex' : simplex indicator function (for projected gradient)
30 |
31 | if nargin<2
32 | param=struct;
33 | end
34 |
35 | params=initoptions(mfilename,params,'params');
36 |
37 | switch reg
38 |
39 | case 'l2'
40 |
41 | g=@reg_l2;
42 | prox_g=@prox_l2;
43 |
44 | case '0'
45 |
46 | g=@(x) 0;
47 | prox_g=@(x,lambda) x;
48 |
49 |
50 | case 'set'
51 |
52 | g=@(x) reg_set(x,params.C);
53 | prox_g=@(x,lambda) prox_set(x,lambda,params.C);
54 |
55 | case 'l1'
56 |
57 | g=@reg_l1;
58 | prox_g=@prox_l1;
59 |
60 | case 'l1l2'
61 |
62 | g=@reg_l1l2;
63 | prox_g=@prox_l1l2;
64 |
65 |
66 | case 'lsp'
67 |
68 | g=@(x) reg_lsp(x,params.theta);
69 | prox_g=@(x,lambda) prox_lsp(x,lambda,params.theta);
70 |
71 | case 'mcp'
72 |
73 | g=@(x) reg_mcp(x,1,params.theta);
74 | prox_g=@(x,lambda) prox_mcp(x,lambda,params.theta);
75 |
76 | case 'lp'
77 |
78 | g=@(x) reg_lp(x,params.p);
79 | prox_g=@(x,lambda) prox_lp(x,lambda,params.p);
80 |
81 | case 'l0'
82 |
83 | g=@(x) reg_l0(x);
84 | prox_g=@(x,lambda) prox_l0(x,lambda);
85 |
86 | case 'simplex'
87 |
88 | g=@(x) reg_simplex(x);
89 | prox_g=@(x,lambda) prox_simplex(x,lambda);
90 |
91 |
92 | otherwise
93 |
94 | error('unknown reg term')
95 |
96 | end
97 |
98 |
99 |
100 | end
101 |
102 |
103 | function res=reg_set(x,C)
104 | res=sum((xC(2)));
105 | if res>0
106 | res=1e3;
107 | end
108 | end
109 |
110 | function res=prox_set(x,lambda,C)
111 | res=max(min(x,C(2)),C(1));
112 | end
113 |
114 |
115 |
116 | function res=reg_l2(x)
117 | res=norm(x(1:end,:),'fro')^2/2;
118 | end
119 |
120 | function res=prox_l2(x,lambda)
121 | res=x/(1+lambda);
122 | end
123 |
124 | function res=reg_l1(x)
125 | res=sum(sum(abs(x(1:end,:))));
126 | end
127 |
128 | function res=prox_l1(x,lambda)
129 | res=sign(x).*max(abs(x)-lambda,0);
130 | end
131 |
132 | function res=reg_l1l2(x)
133 | res=sum(sqrt(sum(abs(x(1:end-1,:)).^2,2)));
134 | end
135 |
136 | function res=prox_l1l2(x,lambda)
137 | res=x;
138 | for i=1:size(x,1)
139 | res(i,:)=x(i,:).*max(0,1-lambda/norm(x(i,:)));
140 | end
141 | end
142 |
143 | function res=reg_lsp(x,theta)
144 | res=sum(sum(log(1+abs(x(1:end,:))/theta)));
145 | end
146 |
147 | function res=prox_lsp(x,lambda,theta)
148 | z = abs(x) - theta;
149 | v = z.*z - 4.0*(lambda - abs(x)*theta);
150 |
151 |
152 | sqrtv = sqrt(v);
153 | xtemp1 = max(0,0.5*(z + sqrtv));
154 | xtemp2 = max(0,0.5*(z - sqrtv));
155 |
156 | ytemp0 = 0.5*x.*x;
157 | ytemp1= 0.5*(xtemp1 - abs(x)).*(xtemp1 - abs(x)) + lambda*log(1.0 + xtemp1/theta);
158 | ytemp2 = 0.5*(xtemp2 - abs(x)).*(xtemp2 - abs(x)) + lambda*log(1.0 + xtemp2/theta);
159 |
160 | sel1=(ytemp10).*xtemp;
166 | end
167 |
168 | function res=reg_mcp(x,lambda,theta)
169 | indUnb = (abs(x(1:end-1,:))>theta*lambda) ;
170 | indBia = (abs(x(1:end-1,:))<=theta*lambda).*(abs(x(1:end-1,:))>0) ;
171 | res=sum(sum((x(1:end,:)-x(1:end,:).^2/(2*theta*lambda)).*indBia + theta*lambda/2*indUnb));
172 | end
173 |
174 | function res=prox_mcp(x,lambda,theta)
175 | res=zeros(size(x));
176 | indUnb = (abs(x(1:end,:))>theta*lambda) ;
177 | indBia = (abs(x(1:end,:))<=theta*lambda).*(abs(x(1:end,:))>0) ;
178 | res(1:end,:)=x(1:end,:).*indUnb + theta/(theta-1)*(x(1:end,:)-lambda*sign(x(1:end-1,:))).*indBia;
179 | end
180 |
181 | function res=reg_lp(x,p)
182 | res=sum(sum(abs(x(1:end,:)).^p));
183 | end
184 |
185 | function res=prox_lp(x,lambda,p)
186 | res=zeros(size(x));
187 | switch p
188 | case .5
189 | ind = (abs(x)>(.75*lambda^(2/3))) ;
190 | res(ind) = 2/3*x(ind).*(1+cos(2*pi/3-2/3*acos(lambda/8*(abs(x(ind))/3).^(-3/2)))) ;
191 | end
192 | end
193 |
194 | function res=reg_l0(x)
195 | res=sum(sum(abs(x(1:end,:)))>0);
196 | end
197 |
198 | function res=prox_l0(x,lambda)
199 | thr=sqrt(2*lambda);
200 | res=x.*(abs(x)>thr);
201 | end
202 |
203 |
204 | function res=reg_simplex(x)
205 | res=0;
206 | end
207 |
208 | function res=prox_simplex(x,lambda)
209 | res=projectSimplex(x(1:end-1));
210 | res(end+1)=0;
211 | end
212 |
213 |
214 | function [w] = projectSimplex(v)
215 | % Computest the minimum L2-distance projection of vector v onto the probability simplex
216 | nVars = length(v);
217 | mu = sort(v,'descend');
218 | sm = 0;
219 | for j = 1:nVars
220 | sm = sm+mu(j);
221 | if mu(j) - (1/j)*(sm-1) > 0
222 | row = j;
223 | sm_row = sm;
224 | end
225 | end
226 | theta = (1/row)*(sm_row-1);
227 | w = max(v-theta,0);
228 | end
229 |
--------------------------------------------------------------------------------
/utils/gist_chinge.m:
--------------------------------------------------------------------------------
1 | function [svm,LOG]=gist_chinge(X,y,options)
2 | % GIST solver for the problem
3 | %
4 | % min_x |y-Xw|^2/n+\lambda*g(x)
5 | %
6 | % options:
7 | % options.lambda : reg term (default=1)
8 | % options.eps : l2 reg term for bounded fun (default=1e-8)
9 | % options.reg: reg term (l1,lsp,l2) (default='l2')
10 | % options.bias: learn bias (default=1)
11 |
12 | options=initoptions(mfilename,options);
13 |
14 | [g,prox_g]=get_reg_prox(options.reg,options);
15 |
16 | if options.bias
17 | X0=[X ones(size(X,1),1)];
18 | g=@(x) g(x(1:end-1,:));
19 | prox_g=@(x,lambda) prox_bias(x,lambda,prox_g);
20 | else
21 | X0=X;
22 | end
23 |
24 | vals=unique(y);
25 | nbclass=length(vals);
26 |
27 | y0=-ones(size(X,1),nbclass);
28 |
29 | for i=1:nbclass
30 | y0(y==vals(i),i)=1;
31 | end
32 |
33 |
34 | f=@(x) cost(x,X0,y0);
35 | df=@(x) grad(x,X0,y0);
36 |
37 | W0=zeros(size(X0,2),nbclass);
38 |
39 |
40 | [W,LOG]=gist_opt(f,df,g,prox_g,W0,options);
41 |
42 | if options.bias
43 | svm.w=W(1:end-1,:);
44 | svm.w0=W(end,:);
45 | else
46 | svm.w=W;
47 | svm.w0=0;
48 | end
49 |
50 | svm.W=W;
51 |
52 | svm.multiclass=1;
53 | svm.nbclass=length(vals);
54 | svm.vals=vals;
55 |
56 |
57 | end
58 |
59 | function df=grad(w,X,y)
60 | yp=y.*(X*w);
61 | P=1-(1+max(0,yp))./(2+abs(yp));
62 | df=-(X)'*(y.*P)/size(X,1);
63 | end
64 |
65 | function f=cost(w,X,y)
66 | yp=y.*(X*w);
67 | f=sum(sum(max(0,-yp)-log(2+abs(yp))))/size(X,1);
68 | end
69 |
70 | function res=prox_bias(x,lambda,prox)
71 | res=prox(x,lambda);
72 | res(end,:)=x(end,1);
73 | end
--------------------------------------------------------------------------------
/utils/gist_hinge2.m:
--------------------------------------------------------------------------------
1 | function [svm,LOG]=gist_hinge2(X,y,options)
2 | % GIST solver for the problem
3 | %
4 | % min_x |y-Xw|^2/n+\lambda*g(x)
5 | %
6 | % options:
7 | % options.lambda : reg term (default=1)
8 | % options.eps : l2 reg term for bounded fun (default=1e-8)
9 | % options.reg: reg term (l1,lsp,l2) (default='l2')
10 | % options.bias: learn bias (default=1)
11 |
12 | options=initoptions(mfilename,options);
13 |
14 | [g,prox_g]=get_reg_prox(options.reg,options);
15 |
16 | if options.bias
17 | X0=[X ones(size(X,1),1)];
18 | g=@(x) g(x(1:end-1,:));
19 | prox_g=@(x,lambda) prox_bias(x,lambda,prox_g);
20 | else
21 | X0=X;
22 | end
23 |
24 | vals=unique(y);
25 | nbclass=length(vals);
26 |
27 | y0=-ones(size(X,1),nbclass);
28 |
29 | for i=1:nbclass
30 | y0(y==vals(i),i)=1;
31 | end
32 |
33 |
34 | f=@(x) cost(x,X0,y0);
35 | df=@(x) grad(x,X0,y0);
36 |
37 | W0=zeros(size(X0,2),nbclass);
38 |
39 |
40 | [W,LOG]=gist_opt(f,df,g,prox_g,W0,options);
41 |
42 | if options.bias
43 | svm.w=W(1:end-1,:);
44 | svm.w0=W(end,:);
45 | else
46 | svm.w=W;
47 | svm.w0=0;
48 | end
49 |
50 | svm.W=W;
51 |
52 | svm.multiclass=1;
53 | svm.nbclass=length(vals);
54 | svm.vals=vals;
55 |
56 |
57 | end
58 |
59 | function df=grad(w,X,y)
60 | T=max(1-y.*(X*w),0);
61 | df=-X'*(T.*y)/size(X,1);
62 | end
63 |
64 | function f=cost(w,X,y)
65 | T=max(1-y.*(X*w),0);
66 | f=sum(sum(T.^2))/size(X,1)/2;
67 | end
68 |
69 | function res=prox_bias(x,lambda,prox)
70 | res=prox(x,lambda);
71 | res(end,:)=x(end,1);
72 | end
73 |
--------------------------------------------------------------------------------
/utils/gist_least.m:
--------------------------------------------------------------------------------
1 | % function [w,w0,LOG]=gist_least(X,y,options)
2 | function [svm,LOG]=gist_least(X,y,options)
3 | % GIST solver for the problem
4 | %
5 | % min_x |y-Xw|^2/n+\lambda*g(x)
6 | %
7 | % options:
8 | % options.lambda : reg term (default=1)
9 | % options.reg: reg term (l1,lsp,l2) (default='l2')
10 | % options.bias : estimate a bias (default=1)
11 | % options.pos : force positive 0 (default=0)
12 | % options.W0 : force positive 0 (default=[])
13 |
14 | options=initoptions(mfilename,options);
15 |
16 |
17 | % get proximal operator and reg function
18 | [g,prox_g]=get_reg_prox(options.reg,options);
19 |
20 | % generate matrix with without bias
21 | if options.bias
22 | X0=[X ones(size(X,1),1)];
23 | g=@(x) g(x(1:end-1,:));
24 | prox_g=@(x,lambda) prox_bias(x,lambda,prox_g);
25 | else
26 | X0=X;
27 | end
28 |
29 | % add positivity constraints
30 | if options.pos
31 | prox_g=@(x,lambda) prox_g(max(x,0),lambda);
32 | end
33 |
34 | if isempty(options.W0)
35 | W0=zeros(size(X0,2),size(y,2)); % Starting point a parametrer ?
36 | W0(end)=0;
37 | else
38 | W0=options.W0;
39 | end
40 |
41 | f=@(x) cost(x,X0,y);
42 | df=@(x) grad(x,X0,y);
43 |
44 | [W,LOG]=gist_opt(f,df,g,prox_g,W0,options);
45 |
46 | if options.bias
47 | svm.w=W(1:end-1,:);
48 | svm.w0=W(end,:);
49 | else
50 | svm.w=W;
51 | svm.w0=0;
52 | end
53 |
54 | svm.W=W;
55 |
56 |
57 | end
58 |
59 | function df=grad(w,X,y)
60 | df=-X'*(y-X*w);%/size(X,1);
61 | end
62 |
63 | function f=cost(w,X,y)
64 | f=norm(y-X*w,'fro')^2/2;%/size(X,1)/2;
65 | end
66 |
67 | function res=prox_bias(x,lambda,prox)
68 | res=prox(x,lambda);
69 | res(end,:)=x(end,1);
70 | end
--------------------------------------------------------------------------------
/utils/gist_logreg.m:
--------------------------------------------------------------------------------
1 | function [svm,LOG]=gist_logreg(X,y,options)
2 | % GIST solver for the problem
3 | %
4 | % min_x |y-Xw|^2/n+\lambda*g(x)
5 | %
6 | % options:
7 | % options.lambda : reg term (default=1)
8 | % options.eps : l2 reg term for bounded fun (default=1e-8)
9 | % options.reg: reg term (l1,lsp,l2) (default='l2')
10 | % options.bias: learn bias (default=1)
11 |
12 | options=initoptions(mfilename,options);
13 |
14 | [g,prox_g]=get_reg_prox(options.reg,options);
15 |
16 | if options.bias
17 | X0=[X ones(size(X,1),1)];
18 | g=@(x) g(x(1:end-1,:));
19 | prox_g=@(x,lambda) prox_bias(x,lambda,prox_g);
20 | else
21 | X0=X;
22 | end
23 |
24 | vals=unique(y);
25 | nbclass=length(vals);
26 |
27 | y0=zeros(size(X,1),nbclass);
28 |
29 | for i=1:nbclass
30 | y0(y==vals(i),i)=1;
31 | end
32 |
33 | y0=logical(y0);
34 |
35 | f=@(x) cost(x,X0,y0);
36 | df=@(x) grad(x,X0,y0);
37 |
38 | W0=zeros(size(X0,2),nbclass);
39 |
40 |
41 | [W,LOG]=gist_opt(f,df,g,prox_g,W0,options);
42 |
43 | if options.bias
44 | svm.w=W(1:end-1,:);
45 | svm.w0=W(end,:);
46 | else
47 | svm.w=W;
48 | svm.w0=0;
49 | end
50 |
51 | svm.W=W;
52 |
53 | svm.multiclass=1;
54 | svm.nbclass=length(vals);
55 | svm.vals=vals;
56 |
57 |
58 | end
59 |
60 | function df=grad(w,X,y)
61 | [R]=lr_mc_residue(w,X,y);
62 | df=X'*R/size(X,1);
63 | end
64 |
65 | function f=cost(w,X,y)
66 | t=size(y,2);
67 | M=X*w;
68 | py=M(y);
69 | E=exp(M-py*ones(1,t));
70 | f=sum(log(sum(E,2)))/size(X,1);
71 | end
72 |
73 | function [R]=lr_mc_residue(w,X,y)
74 | t=size(y,2);
75 | M=X*w;
76 | py=M(y);
77 |
78 | E=exp(M-py*ones(1,t));
79 |
80 | SE=sum(E,2)*ones(1,t);
81 |
82 | R=(E-y.*SE)./SE;
83 | end
84 |
85 | function res=prox_bias(x,lambda,prox)
86 | res=prox(x,lambda);
87 | res(end,:)=x(end,1);
88 | end
89 |
--------------------------------------------------------------------------------
/utils/gist_opt.m:
--------------------------------------------------------------------------------
1 | function [x,LOG]=gist_opt(f,df,g,prox_g,x0,options)
2 | % GIST solver for the problem
3 | %
4 | % min_x f(x)+\lambda g(x)
5 | %
6 | % f : cost function
7 | % df : gradien of the cost function
8 | % g : reg function
9 | % prox_g: proximal function
10 | % x0 : starting point
11 | %
12 | % options:
13 | % options.lambda : reg term (default=1e0)
14 | % options.eta: backward param for linesearch (default=2)
15 | % options.t0 : initial step (default=1)
16 | % options.sigma : line search param (default=1e-5)
17 | % options.m : line serarch param 2 (default=5)
18 | % options.nbitermax: max number iterations (default=1000)
19 | % options.stopvarx: stop threshold variation w (default=1e-5)
20 | % options.stopvarj: stop threshold variation cost (default=1e-5)
21 | % options.nbinneritermax: max number iterations (default=20)
22 | % options.verbose: print infos (default=0)
23 |
24 |
25 | options=initoptions(mfilename,options);
26 |
27 | x=x0;
28 |
29 | grad=df(x);
30 |
31 | loss=f(x)+options.lambda*g(x);
32 |
33 | t=options.t0;
34 |
35 |
36 | if options.verbose
37 | fprintf('|%5s|%13s|%13s|%13s|\n-------------------------------------------------\n','Iter','Loss','Dloss','Step')
38 | fprintf('|%5d|%+8e|%+8e|%+8e|\n',0,loss(end),0,1/t)
39 | end
40 |
41 | loop=1;
42 | it=1;
43 | test = 0 ;
44 |
45 | while loop
46 |
47 | x_1=x;
48 | grad_1=grad;
49 |
50 | grad=df(x);
51 |
52 | x=prox_g(x_1-grad/t,options.lambda/t);
53 |
54 | loss=[loss;f(x)+options.lambda*g(x)];
55 |
56 | it2=1;
57 | ifin = length(loss) ;
58 | thr_back=max(loss(max(ifin-options.m,1):ifin-1)-options.sigma/2*t*norm(x-x_1,'fro')^2);
59 | while loss(end)>thr_back && it2 < options.nbinneritermax
60 | t=t*options.eta;
61 | x=prox_g(x_1-grad/t,options.lambda/t);
62 | loss(end)=f(x)+options.lambda*g(x);
63 | ifin = length(loss) ;
64 | thr_back=max(loss(max(ifin-options.m,1):ifin-1)-options.sigma/2*t*norm(x-x_1,'fro')^2);
65 | it2=it2+1;
66 | end
67 |
68 | xbb=x-x_1;
69 | ybb=grad-grad_1;
70 | % if it>=1 && norm(xbb,'fro')>1e-12 && norm(ybb,'fro')>1e-12
71 | if it>=1 && norm(xbb,'fro')/size(xbb,1)>1e-12 && norm(ybb,'fro')/size(ybb,1)>1e-12
72 | t=abs(sum(sum((xbb.*ybb)))/sum(sum(xbb.*xbb)));
73 | t = min(max(t,1e-20),1e20);
74 | end
75 |
76 | if options.verbose
77 | if mod(it,20)==0
78 | fprintf('|%5s|%13s|%13s|%13s|\n-------------------------------------------------\n','Iter','Loss','Dloss','Step')
79 | end
80 | fprintf('|%5d|%+8e|%+8e|%+8e|\n',it,loss(end),(loss(end)-loss(end-1))/abs(loss(end-1)),1/t)
81 | end
82 |
83 | % if norm(x-x_1)/norm(x)=options.nbitermax
101 | loop=0;
102 | if options.verbose
103 | disp('max number iteration reached')
104 | end
105 | end
106 |
107 | if test>=3
108 | loop=0;
109 | if options.verbose
110 | disp('3 criteres de cv atteints')
111 | end
112 | end
113 |
114 | it=it+1;
115 |
116 |
117 |
118 | end
119 |
120 |
121 | LOG.loss=loss ;
--------------------------------------------------------------------------------
/utils/initoptions.m:
--------------------------------------------------------------------------------
1 | function options=initoptions(fname,options,optname)
2 | % options=initoptions(fname,options)
3 | % function that automatically load default options from comments
4 | % in a matlab function
5 | % example of options parameters
6 | %
7 | % options parameters:
8 | % options.test1 Crappy value to set (default=10)
9 | % options.test2 Crappy value to also set (default='testdestring')
10 |
11 | if nargin<2
12 | options=struct();
13 | end
14 |
15 |
16 | if nargin<3
17 | optname='options';
18 | end
19 |
20 |
21 | pattern_opt=[optname '\.(\w+)' ];
22 | pattern_val=['\(default=(.+)\)' ];
23 |
24 | fileID = fopen([fname '.m'],'r');
25 |
26 | tline = fgetl(fileID);
27 | while ischar(tline)
28 | if ~isempty(tline)
29 | if tline(1)=='%'
30 | opt=regexp(tline,pattern_opt,'tokens');
31 | if ~isempty(opt)
32 | val=regexp(tline,pattern_val,'tokens');
33 | if ~isempty(val)
34 | tsk=['temp=' val{1}{1} ';'];
35 | eval(tsk);
36 | if ~isfield(options,opt{1}{1})
37 | options.(opt{1}{1}) =temp;
38 | end
39 | end
40 | end
41 |
42 | end
43 | end
44 | tline = fgetl(fileID);
45 | end
46 |
47 | fclose(fileID);
48 |
--------------------------------------------------------------------------------
/utils/l2_unmix.m:
--------------------------------------------------------------------------------
1 | function x=l2_unmix(y,D,lambda)
2 |
3 | H=D'*D+lambda*eye(size(D,2));
4 | f=-y'*D;
5 | opts1= optimset('display','off');
6 |
7 | x = quadprog(H,f,[],[],[],[],zeros(size(D,2),1),[],[],opts1);
--------------------------------------------------------------------------------
/utils/l2_unmix_simplex.m:
--------------------------------------------------------------------------------
1 | function x=l2_unmix(y,D,lambda)
2 |
3 | H=D'*D+lambda*eye(size(D,2));
4 | f=-y'*D;
5 | A=ones(1,size(D,2));
6 | b=1;
7 | x = quadprog(H,f,[],[],A,b,zeros(size(D,2),1));
--------------------------------------------------------------------------------
/utils/l2simplex.m:
--------------------------------------------------------------------------------
1 | function res=l2simplex(x,lambda)
2 | if lambda>=1
3 | res=zeros(size(x));
4 | ind=find(x==max(x));
5 | res(ind(1))=1;
6 | else
7 | res=projectSimplex(x/(1-lambda));
8 | end
9 | end
--------------------------------------------------------------------------------