Calculates the cosine similarity and angular similarity on two vectors or a matrix
A vector or matrix object
If x is a vector, then a vector object
If x is a matrix, a list object with: similarity and angular.similarity matrices
If x and y are vectors, a vector of similarity and angular.similarity
The cosine similarity index is a measure of similarity between two vectors of an inner product space. This index is bested suited for high-dimensional positive variable space. One useful application of the index is to measure separability of clusters derived from algorithmic approaches (e.g., k-means). It is a good common practice to centre the data before calculating the index. It should be noted that the cosine similarity index is mathematically, and often numerically, equivalent to the Pearson's correlation coefficient
cosine similarity index is derived:
s(xy) = x * y / ||x|| * ||y||
expected 1.0 (perfect similarity) to -1.0 (perfect dissimilarity)
A normalised angle between the vectors can be used as a bounded similarity function within [0,1]
angular similarity = 1 - (cos(s)^-1/pi)
Jeffrey S. Evans <[email protected]>
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# Compare two vectors (centred using scale) x=runif(100) y=runif(100)^2 csi(as.vector(scale(x)),as.vector(scale(y))) #' # Compare columns (vectors) in a matrix (centred using scale) x <- matrix(round(runif(100),0),nrow=20,ncol=5) ( s <- csi(scale(x)) ) # Compare vector (x) to each column in a matrix (y) y <- matrix(round(runif(500),3),nrow=100,ncol=5) x=runif(100) csi(as.vector(scale(x)),scale(y))
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