# psm: Compute Posterior Similarity Matrix In T4cluster: Tools for Cluster Analysis

## Description

Let clustering be a label from data of N observations and suppose we are given M such labels. Posterior similarity matrix, as its name suggests, computes posterior probability for a pair of observations to belong to the same cluster, i.e.,

P_{ij} = P(\textrm{label}(X_i) = \textrm{label}(X_j))

under the scenario where multiple clusterings are samples drawn from a posterior distribution within the Bayesian framework. However, it can also be used for non-Bayesian settings as psm is a measure of uncertainty embedded in any algorithms with non-deterministic components.

## Usage

 1 psm(partitions) 

## Arguments

 partitions partitions can be provided in either (1) an (M\times N) matrix where each row is a clustering for N objects, or (2) a length-M list of length-N clustering labels.

## Value

an (N\times N) matrix, whose elements (i,j) are posterior probability for an observation i and j belong to the same cluster.

pcm
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 # ------------------------------------------------------------- # PSM with 'iris' dataset + k-means++ # ------------------------------------------------------------- ## PREPARE WITH SUBSET OF DATA data(iris) X = as.matrix(iris[,1:4]) lab = as.integer(as.factor(iris[,5])) ## EMBEDDING WITH PCA X2d = Rdimtools::do.pca(X, ndim=2)$Y ## RUN K-MEANS++ 100 TIMES partitions = list() for (i in 1:100){ partitions[[i]] = kmeanspp(X)$cluster } ## COMPUTE PSM iris.psm = psm(partitions) ## VISUALIZATION opar <- par(no.readonly=TRUE) par(mfrow=c(1,2), pty="s") plot(X2d, col=lab, pch=19, main="true label") image(iris.psm[,150:1], axes=FALSE, main="PSM") par(opar)