Optimized data fusion for K-means Laplacian clustering

Motivation: We propose a novel algorithm to combine multiple kernels and Laplacians for clustering analysis. The new algorithm is formulated on a Rayleigh quotient objective function and is solved as a bi-level alternating minimization procedure. Using the proposed algorithm, the coefficients of kernels and Laplacians can be optimized automatically. Results: Three variants of the algorithm are proposed. The performance is systematically validated on two real-life data fusion applications. The proposed Optimized Kernel Laplacian Clustering (OKLC) algorithms perform significantly better than other methods. Moreover, the coefficients of kernels and Laplacians optimized by OKLC show some correlation with the rank of performance of individual data source. Though in our evaluation the K values are predefined, in practical studies, the optimal cluster number can be consistently estimated from the eigenspectrum of the combined kernel Laplacian matrix.