R/similarity.R
In CAMCOS/camcos2017: CAMCOS Spring 2017: Efficient and Scalable Spectral Clustering for Document Clustering.
Defines functions
similarity
Documented in
similarity
#' Calculate similarity matrices
#'
#' Note: this function sets the self-similarity diagonal = 0. For certain
#' applications, diagonal = 1 may be more appropriate.
#'
#' @param data Matrix.
#' @param method One of the following: "correlation", "cosine", "dotproduct", "Gaussian".
#' @param rowscaling One of the following: "L2", "L1".
#' @param colscaling Single option: "standardize" (center and divide by variance).
#' @param sigma Variance for Gaussian Kernel method.
#' @param centers Proportion of columns to be sampled, if desired (e.g. centers = .25).
#' @param seed For sampling reproducibility.
#' @param distance For use with Gaussian Kernel; options = "JSdivergence", "L1", "L2"
#' @param sparse Logical. Is the data sparse or not.
#'
#' @return Similarity matrix.
#' @seealso \code{\link{colweights}}, \code{\link{clustering}}
#' @import Matrix
#' @export
similarity <- function(data, method, rowscaling = NULL, colscaling = NULL,
sigma = NULL, centers = NULL, seed = NULL, distance = NULL, sparse = T) {
a <- Sys.time()
# require(Matrix)
##### Column scaling #####
if (!(is.null(colscaling))) {
if (colscaling == "standardize") {
data <- apply(data, 2, scale) }
else {stop("Pick a valid column scaling.")}
}
#####
#####
##### Row scaling #####
if (!(is.null(rowscaling))) {
if (rowscaling == "L2") {
data <- data/sqrt(rowSums(data^2)) }
else if (rowscaling == "L1") {
data <- data/rowSums(data) }
else {stop("Pick a valid row scaling.")}
}
#####
#####
##### Distance -> Gaussian similarity #####
if (method == "Gaussian") {
# Calculate a distance metric.
if (distance == "JSdivergence") {
jsdiv <- function(P){
nrows <- length(P[,1])
ncols <- length(P[1,])
D <- matrix(rep.int(0, nrows ** 2), nrow = nrows)
P[is.nan(P)] <- 0
for(i in 2:nrows){
p.row <- P[i,]
for(j in 1:i-1){
q.row <- P[j,]
m.row <- 1/2 * (p.row + q.row)
D[i,j] <- D[j,i] <- (1/2 * sum(p.row * log(p.row/m.row), na.rm =TRUE) + 1/2 * sum(q.row * log(q.row/m.row), na.rm = TRUE))
}
}
return(D)
}
dist <- jsdiv(data) }
else if (distance == "L2") {
dist <- as.matrix(dist(data)) }
else if (distance == "L1") {
dist <- as.matrix(dist(data, method = "manhattan")) }
else {stop("Pick a valid distance.")}
# Convert distance to similarity
if (is.null(sigma)) {stop("Choose a sigma value.")}
else { Similarity <- exp(-1 * dist^2 / (2*sigma)) }
}
#####
#####
##### Compute the NxN similarity matrix #####
###
### dense matrix:
###
if (sparse == F) {
if (is.null(centers)) {
if (method == "correlation") {
centeredcolumns <- t(t(data)-colMeans(data)) # center the data by column
rowvar <- rowSums(centeredcolumns^2) # store the variances for each row (where colMeans=0)
Cov.matrix <- tcrossprod(centeredcolumns) # calculate the covariance matrix (dot product all rows)
# corr = cov(x,y) / sqrt(var(x)var(y)
Corr.true <- Cov.matrix/sqrt(rowvar)
Similarity <- t(t(Corr.true)/sqrt(rowvar))
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(0, nrow(Similarity))
}
else if (method == "corr.hack") {
# center the data by column
centeredcolumns <- t(t(data)-colMeans(data))
# # store the variances for each row (where colMeans=0)
# rowvar <- rowSums(centeredcolumns^2)
# calculate the covariance matrix (dot product all rows)
Cov.matrix <- tcrossprod(centeredcolumns)
# calculate the length of each row (eventually scale by row&col)
cov.rowsums <- rowSums(Cov.matrix^2)
Corr.hack <- Cov.matrix/sqrt(cov.rowsums)
Similarity <- t(t(Corr.hack)/sqrt(cov.rowsums))
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(0, nrow(Similarity))
}
else if (method == "cosine") {
rowlength <- rowSums(data^2)
Dot.prods <- tcrossprod(data)
Cosines <- Dot.prods/sqrt(rowlength)
Similarity <- t(t(Cosines)/sqrt(rowlength))
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(0, nrow(Similarity))
}
else if (method == "dotproduct") {
Similarity <- tcrossprod(data)
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(0, nrow(Similarity))
}
}
#####
#####
##### Random centers similarity matrix #####
else {
if (is.numeric(seed)) { set.seed(seed) }
if (method == "correlation") {
centeredcolumns <- data-colMeans(data) # center the data by column
rowvar.full <- rowSums(centeredcolumns^2) # store the variances for each row (where colMeans=0)
# rcenters is rxN matrix, r = kcenters % of rows, sampled randomly
kcenters <- centers*nrow(data)
rcenters <- as.matrix(centeredcolumns[sample(nrow(data),kcenters,replace = FALSE), ])
rowvar.centers <- rowSums(rcenters^2)
dotprod.centers <- tcrossprod(centeredcolumns,rcenters)
# corr = cov(x,y) / sqrt(var(x)var(y)
Corr.true <- dotprod.centers/sqrt(rowvar.full)
Corr.centers <- t(t(Corr.true)/sqrt(rowvar.centers))
Similarity <- tcrossprod(Corr.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
else if (method == "corr.hack") {
centeredcolumns <- data-colMeans(data) # center the data by column
# rcenters is rxN matrix, r = kcenters % of rows, sampled randomly
kcenters <- centers*nrow(data)
rcenters <- as.matrix(centeredcolumns[sample(nrow(data),kcenters,replace = FALSE), ])
dotprod.centers <- tcrossprod(centeredcolumns,rcenters)
rowlengths <- rowSums(dotprod.centers)
collengths <- colSums(dotprod.centers)
# hack = cov(x,y) / sqrt(length(x)length(y))
Corr.hack <- dotprod.centers/sqrt(rowlengths)
Corrhack.centers <- t(t(Corr.hack)/sqrt(collengths))
Similarity <- tcrossprod(Corrhack.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
else if (method == "cosine") {
rowlengths.full <- rowSums(data^2) # store the variances for each row (where colMeans=0)
kcenters <- centers*nrow(data)
rcenters <- as.matrix(data[sample(nrow(data),kcenters,replace = FALSE), ])
rowlengths.centers <- rowSums(rcenters^2)
dotprod.centers <- tcrossprod(data,rcenters)
# cos = <x,y> / sqrt(length(x)length(y))
Cosine <- dotprod.centers/sqrt(rowlengths.full)
Cosine.centers <- t(t(Cosine)/sqrt(rowlengths.centers))
Similarity <- tcrossprod(Cosine.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
else if (method == "dotproduct") {
kcenters <- centers*nrow(data)
rcenters <- as.matrix(data[sample(nrow(data),kcenters,replace = FALSE), ])
dotprod.centers <- tcrossprod(data,rcenters)
Similarity <- tcrossprod(dotprod.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
}
#####
#####
}
###
### sparse matrix:
###
else {
if (is.null(centers)) {
if (method == "correlation") {
# centeredcolumns <- data
#
# rowvar <- rowSums(centeredcolumns^2) # store the variances for each row (where colMeans=0)
#
# Cov.matrix <- tcrossprod(centeredcolumns) # calculate the covariance matrix (dot product all rows)
#
# # corr = cov(x,y) / sqrt(var(x)var(y)
# Corr.true <- Cov.matrix/sqrt(rowvar)
# Similarity <- t(t(Corr.true)/sqrt(rowvar))
#
# # scale the matrix to (0,1), excluding the diagonal
# diag(Similarity) <- rep(0,nrow(Similarity))
# Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
# diag(Similarity) <- rep(0, nrow(Similarity))
stop("Correlation does not work on a sparse matrix. Try using a dense matrix instead.")
}
else if (method == "corr.hack") {
# centeredcolumns <- data
# # # store the variances for each row (where colMeans=0)
# # rowvar <- rowSums(centeredcolumns^2)
# # calculate the covariance matrix (dot product all rows)
# Cov.matrix <- tcrossprod(centeredcolumns)
# # calculate the length of each row (eventually scale by row&col)
# cov.rowsums <- rowSums(Cov.matrix^2)
# Corr.hack <- Cov.matrix/sqrt(cov.rowsums)
# Similarity <- t(t(Corr.hack)/sqrt(cov.rowsums))
# # scale the matrix to (0,1), excluding the diagonal
# diag(Similarity) <- rep(0,nrow(Similarity))
# Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
# diag(Similarity) <- rep(0, nrow(Similarity))
stop("Correlation does not work on a sparse matrix. Try using a dense matrix instead.")
}
else if (method == "cosine") {
rowlength <- rowSums(data^2)
data <- data/sqrt(rowlength) # cosine normalizes each vector to unit length
Similarity <- tcrossprod(data)
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(0, nrow(Similarity))
}
else if (method == "dotproduct") {
Similarity <- tcrossprod(data)
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(0, nrow(Similarity))
}
}
#####
#####
##### Random centers similarity matrix #####
else {
if (is.numeric(seed)) { set.seed(seed) }
if (method == "correlation") {
centeredcolumns <- data-colMeans(data) # center the data by column
rowvar.full <- rowSums(centeredcolumns^2) # store the variances for each row (where colMeans=0)
# rcenters is rxN matrix, r = kcenters % of rows, sampled randomly
kcenters <- centers*nrow(data)
rcenters <- as.matrix(centeredcolumns[sample(nrow(data),kcenters,replace = FALSE), ])
rowvar.centers <- rowSums(rcenters^2)
dotprod.centers <- tcrossprod(centeredcolumns,rcenters)
# corr = cov(x,y) / sqrt(var(x)var(y)
Corr.true <- dotprod.centers/sqrt(rowvar.full)
Corr.centers <- t(t(Corr.true)/sqrt(rowvar.centers))
Similarity <- tcrossprod(Corr.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
else if (method == "corr.hack") {
centeredcolumns <- data-colMeans(data) # center the data by column
# rcenters is rxN matrix, r = kcenters % of rows, sampled randomly
kcenters <- centers*nrow(data)
rcenters <- as.matrix(centeredcolumns[sample(nrow(data),kcenters,replace = FALSE), ])
dotprod.centers <- tcrossprod(centeredcolumns,rcenters)
rowlengths <- rowSums(dotprod.centers)
collengths <- colSums(dotprod.centers)
# hack = cov(x,y) / sqrt(length(x)length(y))
Corr.hack <- dotprod.centers/sqrt(rowlengths)
Corrhack.centers <- t(t(Corr.hack)/sqrt(collengths))
Similarity <- tcrossprod(Corrhack.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
else if (method == "cosine") {
rowlengths.full <- rowSums(data^2) # store the variances for each row (where colMeans=0)
kcenters <- centers*nrow(data)
rcenters <- as.matrix(data[sample(nrow(data),kcenters,replace = FALSE), ])
rowlengths.centers <- rowSums(rcenters^2)
dotprod.centers <- tcrossprod(data,rcenters)
# cos = <x,y> / sqrt(length(x)length(y))
Cosine <- dotprod.centers/sqrt(rowlengths.full)
Cosine.centers <- t(t(Cosine)/sqrt(rowlengths.centers))
Similarity <- tcrossprod(Cosine.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
else if (method == "dotproduct") {
kcenters <- centers*nrow(data)
rcenters <- as.matrix(data[sample(nrow(data),kcenters,replace = FALSE), ])
dotprod.centers <- tcrossprod(data,rcenters)
Similarity <- tcrossprod(dotprod.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
}
#####
#####
} #
b <- Sys.time()
time.elapsed <- b - a
print(time.elapsed)
return(Similarity)
}
CAMCOS/camcos2017 documentation built on May 6, 2019, 9:23 a.m.
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Defines functions similarity
Documented in similarity
#' Calculate similarity matrices
#'
#' Note: this function sets the self-similarity diagonal = 0. For certain
#' applications, diagonal = 1 may be more appropriate.
#'
#' @param data Matrix.
#' @param method One of the following: "correlation", "cosine", "dotproduct", "Gaussian".
#' @param rowscaling One of the following: "L2", "L1".
#' @param colscaling Single option: "standardize" (center and divide by variance).
#' @param sigma Variance for Gaussian Kernel method.
#' @param centers Proportion of columns to be sampled, if desired (e.g. centers = .25).
#' @param seed For sampling reproducibility.
#' @param distance For use with Gaussian Kernel; options = "JSdivergence", "L1", "L2"
#' @param sparse Logical. Is the data sparse or not.
#'
#' @return Similarity matrix.
#' @seealso \code{\link{colweights}}, \code{\link{clustering}}
#' @import Matrix
#' @export
similarity <- function(data, method, rowscaling = NULL, colscaling = NULL,
sigma = NULL, centers = NULL, seed = NULL, distance = NULL, sparse = T) {
a <- Sys.time()
# require(Matrix)
##### Column scaling #####
if (!(is.null(colscaling))) {
if (colscaling == "standardize") {
data <- apply(data, 2, scale) }
else {stop("Pick a valid column scaling.")}
}
#####
#####
##### Row scaling #####
if (!(is.null(rowscaling))) {
if (rowscaling == "L2") {
data <- data/sqrt(rowSums(data^2)) }
else if (rowscaling == "L1") {
data <- data/rowSums(data) }
else {stop("Pick a valid row scaling.")}
}
#####
#####
##### Distance -> Gaussian similarity #####
if (method == "Gaussian") {
# Calculate a distance metric.
if (distance == "JSdivergence") {
jsdiv <- function(P){
nrows <- length(P[,1])
ncols <- length(P[1,])
D <- matrix(rep.int(0, nrows ** 2), nrow = nrows)
P[is.nan(P)] <- 0
for(i in 2:nrows){
p.row <- P[i,]
for(j in 1:i-1){
q.row <- P[j,]
m.row <- 1/2 * (p.row + q.row)
D[i,j] <- D[j,i] <- (1/2 * sum(p.row * log(p.row/m.row), na.rm =TRUE) + 1/2 * sum(q.row * log(q.row/m.row), na.rm = TRUE))
}
}
return(D)
}
dist <- jsdiv(data) }
else if (distance == "L2") {
dist <- as.matrix(dist(data)) }
else if (distance == "L1") {
dist <- as.matrix(dist(data, method = "manhattan")) }
else {stop("Pick a valid distance.")}
# Convert distance to similarity
if (is.null(sigma)) {stop("Choose a sigma value.")}
else { Similarity <- exp(-1 * dist^2 / (2*sigma)) }
}
#####
#####
##### Compute the NxN similarity matrix #####
###
### dense matrix:
###
if (sparse == F) {
if (is.null(centers)) {
if (method == "correlation") {
centeredcolumns <- t(t(data)-colMeans(data)) # center the data by column
rowvar <- rowSums(centeredcolumns^2) # store the variances for each row (where colMeans=0)
Cov.matrix <- tcrossprod(centeredcolumns) # calculate the covariance matrix (dot product all rows)
# corr = cov(x,y) / sqrt(var(x)var(y)
Corr.true <- Cov.matrix/sqrt(rowvar)
Similarity <- t(t(Corr.true)/sqrt(rowvar))
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(0, nrow(Similarity))
}
else if (method == "corr.hack") {
# center the data by column
centeredcolumns <- t(t(data)-colMeans(data))
# # store the variances for each row (where colMeans=0)
# rowvar <- rowSums(centeredcolumns^2)
# calculate the covariance matrix (dot product all rows)
Cov.matrix <- tcrossprod(centeredcolumns)
# calculate the length of each row (eventually scale by row&col)
cov.rowsums <- rowSums(Cov.matrix^2)
Corr.hack <- Cov.matrix/sqrt(cov.rowsums)
Similarity <- t(t(Corr.hack)/sqrt(cov.rowsums))
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(0, nrow(Similarity))
}
else if (method == "cosine") {
rowlength <- rowSums(data^2)
Dot.prods <- tcrossprod(data)
Cosines <- Dot.prods/sqrt(rowlength)
Similarity <- t(t(Cosines)/sqrt(rowlength))
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(0, nrow(Similarity))
}
else if (method == "dotproduct") {
Similarity <- tcrossprod(data)
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(0, nrow(Similarity))
}
}
#####
#####
##### Random centers similarity matrix #####
else {
if (is.numeric(seed)) { set.seed(seed) }
if (method == "correlation") {
centeredcolumns <- data-colMeans(data) # center the data by column
rowvar.full <- rowSums(centeredcolumns^2) # store the variances for each row (where colMeans=0)
# rcenters is rxN matrix, r = kcenters % of rows, sampled randomly
kcenters <- centers*nrow(data)
rcenters <- as.matrix(centeredcolumns[sample(nrow(data),kcenters,replace = FALSE), ])
rowvar.centers <- rowSums(rcenters^2)
dotprod.centers <- tcrossprod(centeredcolumns,rcenters)
# corr = cov(x,y) / sqrt(var(x)var(y)
Corr.true <- dotprod.centers/sqrt(rowvar.full)
Corr.centers <- t(t(Corr.true)/sqrt(rowvar.centers))
Similarity <- tcrossprod(Corr.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
else if (method == "corr.hack") {
centeredcolumns <- data-colMeans(data) # center the data by column
# rcenters is rxN matrix, r = kcenters % of rows, sampled randomly
kcenters <- centers*nrow(data)
rcenters <- as.matrix(centeredcolumns[sample(nrow(data),kcenters,replace = FALSE), ])
dotprod.centers <- tcrossprod(centeredcolumns,rcenters)
rowlengths <- rowSums(dotprod.centers)
collengths <- colSums(dotprod.centers)
# hack = cov(x,y) / sqrt(length(x)length(y))
Corr.hack <- dotprod.centers/sqrt(rowlengths)
Corrhack.centers <- t(t(Corr.hack)/sqrt(collengths))
Similarity <- tcrossprod(Corrhack.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
else if (method == "cosine") {
rowlengths.full <- rowSums(data^2) # store the variances for each row (where colMeans=0)
kcenters <- centers*nrow(data)
rcenters <- as.matrix(data[sample(nrow(data),kcenters,replace = FALSE), ])
rowlengths.centers <- rowSums(rcenters^2)
dotprod.centers <- tcrossprod(data,rcenters)
# cos = <x,y> / sqrt(length(x)length(y))
Cosine <- dotprod.centers/sqrt(rowlengths.full)
Cosine.centers <- t(t(Cosine)/sqrt(rowlengths.centers))
Similarity <- tcrossprod(Cosine.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
else if (method == "dotproduct") {
kcenters <- centers*nrow(data)
rcenters <- as.matrix(data[sample(nrow(data),kcenters,replace = FALSE), ])
dotprod.centers <- tcrossprod(data,rcenters)
Similarity <- tcrossprod(dotprod.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
}
#####
#####
}
###
### sparse matrix:
###
else {
if (is.null(centers)) {
if (method == "correlation") {
# centeredcolumns <- data
#
# rowvar <- rowSums(centeredcolumns^2) # store the variances for each row (where colMeans=0)
#
# Cov.matrix <- tcrossprod(centeredcolumns) # calculate the covariance matrix (dot product all rows)
#
# # corr = cov(x,y) / sqrt(var(x)var(y)
# Corr.true <- Cov.matrix/sqrt(rowvar)
# Similarity <- t(t(Corr.true)/sqrt(rowvar))
#
# # scale the matrix to (0,1), excluding the diagonal
# diag(Similarity) <- rep(0,nrow(Similarity))
# Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
# diag(Similarity) <- rep(0, nrow(Similarity))
stop("Correlation does not work on a sparse matrix. Try using a dense matrix instead.")
}
else if (method == "corr.hack") {
# centeredcolumns <- data
# # # store the variances for each row (where colMeans=0)
# # rowvar <- rowSums(centeredcolumns^2)
# # calculate the covariance matrix (dot product all rows)
# Cov.matrix <- tcrossprod(centeredcolumns)
# # calculate the length of each row (eventually scale by row&col)
# cov.rowsums <- rowSums(Cov.matrix^2)
# Corr.hack <- Cov.matrix/sqrt(cov.rowsums)
# Similarity <- t(t(Corr.hack)/sqrt(cov.rowsums))
# # scale the matrix to (0,1), excluding the diagonal
# diag(Similarity) <- rep(0,nrow(Similarity))
# Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
# diag(Similarity) <- rep(0, nrow(Similarity))
stop("Correlation does not work on a sparse matrix. Try using a dense matrix instead.")
}
else if (method == "cosine") {
rowlength <- rowSums(data^2)
data <- data/sqrt(rowlength) # cosine normalizes each vector to unit length
Similarity <- tcrossprod(data)
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(0, nrow(Similarity))
}
else if (method == "dotproduct") {
Similarity <- tcrossprod(data)
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(0, nrow(Similarity))
}
}
#####
#####
##### Random centers similarity matrix #####
else {
if (is.numeric(seed)) { set.seed(seed) }
if (method == "correlation") {
centeredcolumns <- data-colMeans(data) # center the data by column
rowvar.full <- rowSums(centeredcolumns^2) # store the variances for each row (where colMeans=0)
# rcenters is rxN matrix, r = kcenters % of rows, sampled randomly
kcenters <- centers*nrow(data)
rcenters <- as.matrix(centeredcolumns[sample(nrow(data),kcenters,replace = FALSE), ])
rowvar.centers <- rowSums(rcenters^2)
dotprod.centers <- tcrossprod(centeredcolumns,rcenters)
# corr = cov(x,y) / sqrt(var(x)var(y)
Corr.true <- dotprod.centers/sqrt(rowvar.full)
Corr.centers <- t(t(Corr.true)/sqrt(rowvar.centers))
Similarity <- tcrossprod(Corr.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
else if (method == "corr.hack") {
centeredcolumns <- data-colMeans(data) # center the data by column
# rcenters is rxN matrix, r = kcenters % of rows, sampled randomly
kcenters <- centers*nrow(data)
rcenters <- as.matrix(centeredcolumns[sample(nrow(data),kcenters,replace = FALSE), ])
dotprod.centers <- tcrossprod(centeredcolumns,rcenters)
rowlengths <- rowSums(dotprod.centers)
collengths <- colSums(dotprod.centers)
# hack = cov(x,y) / sqrt(length(x)length(y))
Corr.hack <- dotprod.centers/sqrt(rowlengths)
Corrhack.centers <- t(t(Corr.hack)/sqrt(collengths))
Similarity <- tcrossprod(Corrhack.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
else if (method == "cosine") {
rowlengths.full <- rowSums(data^2) # store the variances for each row (where colMeans=0)
kcenters <- centers*nrow(data)
rcenters <- as.matrix(data[sample(nrow(data),kcenters,replace = FALSE), ])
rowlengths.centers <- rowSums(rcenters^2)
dotprod.centers <- tcrossprod(data,rcenters)
# cos = <x,y> / sqrt(length(x)length(y))
Cosine <- dotprod.centers/sqrt(rowlengths.full)
Cosine.centers <- t(t(Cosine)/sqrt(rowlengths.centers))
Similarity <- tcrossprod(Cosine.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
else if (method == "dotproduct") {
kcenters <- centers*nrow(data)
rcenters <- as.matrix(data[sample(nrow(data),kcenters,replace = FALSE), ])
dotprod.centers <- tcrossprod(data,rcenters)
Similarity <- tcrossprod(dotprod.centers)
# scale the matrix to (0,1), excluding the diagonal
diag(Similarity) <- rep(0,nrow(Similarity))
Similarity <- (Similarity - min(Similarity))/(range(Similarity)[2] - range(Similarity)[1])
diag(Similarity) <- rep(1, nrow(Similarity))
}
}
#####
#####
} #
b <- Sys.time()
time.elapsed <- b - a
print(time.elapsed)
return(Similarity)
}
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