Similarity and Distance Metrics — dot

Metrics for measuring relationships between vector embeddings.

Usage

dot_prod(x, y)

cos_sim(x, y)

euc_dist(x, y)

minkowski_dist(x, y, p = 1)

anchored_sim(x, pos, neg)

Arguments

x: a numeric vector
y: a numeric vector the same length as x
p: p-norm used to compute the Minkowski distance
pos, neg: a pair of numeric vectors the same length as x; the positive and negative ends of the anchored vector

Details

dot_prod gives the dot product. cos_sim gives the cosine similarity (i.e. the dot product of two normalized vectors). euc_dist gives the Euclidean distance. anchored_sim gives the position of x on the spectrum between two anchor points, where vectors aligned with pos are given a score of 1 and those aligned with neg are given a score of 0. For more on anchored vectors, see Data Science for Psychology: Natural Language, Chapter 20. Note that, for a given set of values of x, anchored_sim(x, pos, neg) will be perfectly correlated with dot_prod(x, pos - neg).

Examples

vec1 <- c(1, 5, 2)
vec2 <- c(4, 2, 2)
vec3 <- c(1, -2, -13)

dot_prod(vec1, vec2)
#> [1] 18
cos_sim(vec1, vec2)
#> [1] 0.6708204
euc_dist(vec1, vec2)
#> [1] 4.242641
anchored_sim(vec1, vec2, vec3)
#> [1] 1.012