Perron Cluster Analysis and Its Connection to Graph Partitioning for Noisy Data

The problem of clustering data can be formulated as a graph partitioning problem. Spectral methods for obtaining optimal solutions have reveceived a lot of attention recently. We describe Perron Cluster Cluster Analysis (PCCA) and, for the first time, establish a connection to spectral graph partitioning. We show that in our approach a clustering can be efficiently computed using a simple linear map of the eigenvector data. To deal with the prevalent problem of noisy and possibly overlapping data we introduce the minChi indicator which helps in selecting the number of clusters and confirming the existence of a partition of the data. This gives a non-probabilistic alternative to statistical mixture-models. We close with showing favorable results on the analysis of gene expression data for two different cancer types.