Farthest point sampling

Description

Farthest point sampling returns a reordering of the metric space P = p_1, ..., p_k, such that each p_i is the farthest point from the first i-1 points.

Usage

farthest_point_sampling(
  mat,
  metric = "precomputed",
  k = nrow(mat),
  initial_point_index = 1L,
  return_clusters = FALSE
)

Arguments

Examples

# generate data
df <- matrix(runif(200), ncol = 2)
dist_mat <- pdist(df)
# farthest point sampling
fps <- farthest_point_sampling(dist_mat)
fps2 <- farthest_point_sampling(df, metric = "euclidean")
all.equal(fps, fps2)
# have a look at the fps distance matrix
rdist(df[fps[1:5], ])
dist_mat[fps, fps][1:5, 1:5]

Metric and triangle inequality

Description

Does the distance matric come from a metric

Usage

is_distance_matrix(mat, tolerance = .Machine$double.eps^0.5)

triangle_inequality(mat, tolerance = .Machine$double.eps^0.5)

Arguments

Examples

data <- matrix(rnorm(20), ncol = 2)
dm <- pdist(data)
is_distance_matrix(dm)
triangle_inequality(dm)

dm[1, 2] <- 1.1 * dm[1, 2]
is_distance_matrix(dm)

Product metric

Description

Returns the p-product metric of two metric spaces. Works for output of 'rdist', 'pdist' or 'cdist'.

Usage

product_metric(..., p = 2)

Arguments

Examples

# generate data
df <- matrix(runif(200), ncol = 2)
# distance matrices
dist_mat <- pdist(df)
dist_1 <- pdist(df[, 1])
dist_2 <- pdist(df[, 2])
# product distance matrix
dist_prod <- product_metric(dist_1, dist_2)
# check equality
all.equal(dist_mat, dist_prod)

rdist: an R package for distances

Description

rdist 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 calculations involving NA values will consistently return NA.

Usage

rdist(X, metric = "euclidean", p = 2L)

pdist(X, metric = "euclidean", p = 2)

cdist(X, Y, metric = "euclidean", p = 2)

Arguments

Details

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.