An R package to calculate distances. This provide a common framework to calculate distances.
73 | There are three main functions:
rdist computes the pairwise distances between observations in one matrix and returns a dist object,pdist computes the pairwise distances between observations in one matrix and returns a matrix, andcdist computes the distances between observations in two matrices and returns a matrix.All functions have an argument metric that can be used to specify the distance function. Available metrics are "euclidean", "minkowski", "manhattan", "maximum", "canberra", "angular", "correlation", "absolute_correlation", "hamming", and "jaccard". In addition the metric can be any function that takes two vectors as arguments and returns their distance. All predefined functions will return NA or NaN when one of the compared vectors contains NAs.
To install the latest released version from CRAN:
87 | 88 |To install the latest development version from github:
89 | 91 |If you find issues, please let me know. If you would like to contribute, please create a pull request.
96 |NEWS.md
99 | product_metric
108 | farthest_point_sampling
110 | is_distance_matrix and triangle_inequality checksAn R package to calculate distances. This provide a common framework to calculate distances.
129 | There are three main functions:
rdist computes the pairwise distances between observations in one matrix and returns a dist object,pdist computes the pairwise distances between observations in one matrix and returns a matrix, andcdist computes the distances between observations in two matrices and returns a matrix.All functions have an argument metric that can be used to specify the distance function. Available metrics are "euclidean", "minkowski", "manhattan", "maximum", "canberra", "angular", "correlation", "absolute_correlation", "hamming", and "jaccard". All functions will return NA or NaN when one of the compared vectors contains NAs.
To install the latest released version from CRAN:
143 | 144 |To install the latest development version from github:
145 | 147 |If you find issues, please let me know. If you would like to contribute, please create a pull request.
152 |R/farthest_point_sampling.R
104 | farthest_point_sampling.RdFarthest point sampling returns a reordering of the metric 110 | space P = p_1, ..., p_k, such that each p_i is the farthest 111 | point from the first i-1 points.
112 | 113 |farthest_point_sampling(mat, metric = "precomputed", k = nrow(mat), 116 | initial_point_index = 1L, return_clusters = FALSE)117 | 118 |
| mat | 123 |Original distance matrix |
124 |
|---|---|
| metric | 127 |Distance metric to use (either "precomputed" or a metric from |
128 |
| k | 131 |Number of points to sample |
132 |
| initial_point_index | 135 |Index of p_1 |
136 |
| return_clusters | 139 |Should the indices of the closest farthest points be returned? |
140 |
163 |146 | # generate data 147 | df <- matrix(runif(200), ncol = 2) 148 | dist_mat <- pdist(df) 149 | # farthest point sampling 150 | fps <- farthest_point_sampling(dist_mat) 151 | fps2 <- farthest_point_sampling(df, metric = "euclidean") 152 | all.equal(fps, fps2)#> [1] TRUE# have a look at the fps distance matrix 153 | rdist(df[fps[1:5], ])#> 1 2 3 4 154 | #> 2 1.0924360 155 | #> 3 0.9280582 0.8499785 156 | #> 4 0.8029144 0.8977409 1.3558406 157 | #> 5 0.5409166 0.5515509 0.7071422 0.6487099dist_mat[fps, fps][1:5, 1:5]#> [,1] [,2] [,3] [,4] [,5] 158 | #> [1,] 0.0000000 1.0924360 0.9280582 0.8029144 0.5409166 159 | #> [2,] 1.0924360 0.0000000 0.8499785 0.8977409 0.5515509 160 | #> [3,] 0.9280582 0.8499785 0.0000000 1.3558406 0.7071422 161 | #> [4,] 0.8029144 0.8977409 1.3558406 0.0000000 0.6487099 162 | #> [5,] 0.5409166 0.5515509 0.7071422 0.6487099 0.0000000
Does the distance matric come from a metric
108 | 109 |is_distance_matrix(mat, tolerance = .Machine$double.eps^0.5) 112 | 113 | triangle_inequality(mat, tolerance = .Machine$double.eps^0.5)114 | 115 |
| mat | 120 |The matrix to evaluate |
121 |
|---|---|
| tolerance | 124 |Differences smaller than tolerance are not reported. |
125 |
135 |#> [1] TRUEtriangle_inequality(dm)#> [1] TRUE133 | dm[1, 2] <- 1.1 * dm[1, 2] 134 | is_distance_matrix(dm)#> Matrix is not symmetric.#> [1] FALSE
Returns the p-product metric of two metric spaces. 109 | Works for output of `rdist`, `pdist` or `cdist`.
110 | 111 |product_metric(..., p = 2)114 | 115 |
| ... | 120 |Distance matrices or dist objects |
121 |
|---|---|
| p | 124 |The power of the Minkowski distance |
125 |
140 |# generate data 131 | df <- matrix(runif(200), ncol = 2) 132 | # distance matrices 133 | dist_mat <- pdist(df) 134 | dist_1 <- pdist(df[, 1]) 135 | dist_2 <- pdist(df[, 2]) 136 | # product distance matrix 137 | dist_prod <- product_metric(dist_1, dist_2) 138 | # check equality 139 | all.equal(dist_mat, dist_prod)#> [1] TRUE
R/distance_functions.r, R/rdist-package.r
107 | rdist.Rdrdist provide a common framework to calculate distances. There are three main functions:
rdist computes the pairwise distances between observations in one matrix and returns a dist object,
pdist computes the pairwise distances between observations in one matrix and returns a matrix, and
cdist computes the distances between observations in two matrices and returns a matrix.
In particular the cdist function is often missing in other distance functions. All
117 | calculations involving NA values will consistently return NA.
rdist(X, metric = "euclidean", p = 2L) 122 | 123 | pdist(X, metric = "euclidean", p = 2) 124 | 125 | cdist(X, Y, metric = "euclidean", p = 2)126 | 127 |
| X, Y | 132 |A matrix |
133 |
|---|---|
| metric | 136 |The distance metric to use |
137 |
| p | 140 |The power of the Minkowski distance |
141 |
Available distance measures are (written for two vectors v and w):
"euclidean": \(\sqrt{\sum_i(v_i - w_i)^2}\)
"minkowski": \((\sum_i|v_i - w_i|^p)^{1/p}\)
"manhattan": \(\sum_i(|v_i-w_i|)\)
"maximum" or "chebyshev": \(\max_i(|v_i-w_i|)\)
"canberra": \(\sum_i(\frac{|v_i-w_i|}{|v_i|+|w_i|})\)
"angular": \(\cos^{-1}(cor(v, w))\)
"correlation": \(\sqrt{\frac{1-cor(v, w)}{2}}\)
"absolute_correlation": \(\sqrt{1-|cor(v, w)|^2}\)
"hamming": \((\sum_i v_i \neq w_i) / \sum_i 1\)
"jaccard": \((\sum_i v_i \neq w_i) / \sum_i 1_{v_i \neq 0 \cup w_i \neq 0}\)
Any function that defines a distance between two vectors.