A Variant of the Trace Quotient Formulation for Dimensionality Reduction

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Abstract

Due to its importance to classification and clustering, dimensionality reduction or distance metric learning has been studied in depth in recent years. In this work, we demonstrate the weakness of a widely-used class separability criterion—trace quotient for dimensionality reduction—and propose new criteria for the dimensionality reduction problem. The proposed optimization problem can be efficiently solved using semidefinite programming, similar to the technique in [1]. Experiments on classification and clustering are performed to evaluate the proposed algorithm. Results show the advantage of the our proposed algorithm.