Coordinate Descent Optimized Trace Difference Model for Joint Clustering and Feature Extraction

Abstract

Joint clustering and dimensionality reduction methods are a promising solution to clustering due to its scalability to high-dimensional data. Some methods leverage trace ratio criterion and attain clusters by borrowing the K-means algorithm. However, trace ratio criterion has no close-formed solution for the discriminative projection matrix and the K-means algorithm has a limited capacity to handle the many-cluster problem. In this paper, Coordinate Descent Optimized Trace Difference model (CDOTD) is proposed for joint clustering and feature extraction. Formulating the objective function as a direct trace difference criterion containing a balance parameter, CDOTD harmonizes between-cluster scatter maximization and within-cluster scatter minimization by the balance parameter. Using the direct trace difference criterion, CDOTD can straightforward solve for the discriminative projection matrix and avoid obtaining a poor discriminative projection matrix in the iterative manner when a bad cluster start is given. CDOTD uses the coordinate descent method for clustering optimization, improving the ability to address the many-cluster problem. Extensive experiments show that CDOTD has achieved significant performance improvements compared to previous trace ratio criterion related joint clustering and feature extraction methods, and also outperformed other clustering methods in most cases.