Eigenvalue-Based Block Diagonal Representation and Application to p-Nearest Neighbor Graphs

Abstract

Block diagonal structure of the affinity matrix is advantageous, e.g. in graph-based cluster analysis, where each block corresponds to a cluster. However, constructing block diagonal affinity matrices may be challenging and computationally demanding. We propose a new eigenvalue-based block diagonal representation (EBDR) method. The idea is to estimate a block diagonal affinity matrix by finding an approximation to a vector of target eigenvalues. The target eigenvalues, which follow the ideal block-diagonal model, are efficiently determined based on a vector derived from the graph Laplacian that represents the blocks as a piece-wise linear function. The proposed EBDR shows promising performance compared to four optimally tuned state-of-the-art methods in terms of clustering accuracy and computation time using real-data examples.