ranksem: Compute Semblance For a Given Input Matrix or Data Frame

In Semblance: A Data-Driven Similarity Kernel on Probability Spaces

Description

Kernel methods can operate in a high-dimensional, implicit feature space with low computational cost. Here, we present a rank-based Mercer kernel to compute a pair-wise similarity metric, corresponding to informative representation of data. We tailor the development of a kernel to encode our prior knowledge about the data distribution over a probability space. The philosophical concept behind our construction is that objects whose feature values fall on the extreme of that feature<e2><80><99>s probability mass distribution are more similar to each other, than objects whose feature values lie closer to the mean. This idea represents a fundamentally novel way of assessing similarity between two observations. Our kernel (henceforth called <e2><80><99>Semblance<e2><80><99>) naturally lends itself to the construction of a distance metric that emphasizes features whose values lie far away from the mean of their probability distribution. Semblance relies on properties empirically determined from the data and does not assume an underlying distribution. The use of feature ranks on a probability space ensures that Semblance is computational efficacious, robust to outliers, and statistically stable, thus making it widely applicable algorithm for pattern analysis. This R package accompanies the research article "Semblance: A Data-driven Kernel Redefines the Notion of Similarity", to appear in Science Advances.

Usage

ranksem(X)

Arguments

X	a matrix X with n observations and m features, whose Semblance Gram Matrix is to be computed

Value

The resultant Gram Matrix after applying Semblance kernel to the input

Examples

# Simulation Example when the user inputs a matrix with single-cell gene expression data
ngenes = 10
ncells = 10
nclust = 2
mu=c(100, 0) #mean in cluster 1, cluster 2 for informative genes
sigma=c(0.01, 1) #stdev in cluster 1, cluster 2 for informative genes
size.rare.clust = 0.1
prop.info.genes = 0.2
n.info.genes=round(prop.info.genes*ngenes)
n.clust1.cells = round(ncells*size.rare.clust)
mu1=c(rep(mu[1]*sigma[2], n.info.genes), rep(0, ngenes-n.info.genes))
mu2=c(rep(mu[2]*sigma[2], n.info.genes), rep(0, ngenes-n.info.genes))
sig1=c(rep(sigma[1], n.info.genes), rep(1, ngenes-n.info.genes))
sig2=c(rep(sigma[2], n.info.genes), rep(1, ngenes-n.info.genes))
X=matrix(ncol=ngenes, nrow=ncells, data=0)
for(i in 1:n.clust1.cells){
  X[i,] = rnorm(ngenes, mean=mu1, sd=sig1)
}
for(i in (n.clust1.cells+1):ncells){
  X[i,] = rnorm(ngenes, mean=mu2, sd=sig2)
}
#Compute kernels/distances
rks=ranksem(X)

Semblance documentation built on May 2, 2019, 6:46 a.m.