Stable and orthogonal local discriminant embedding using trace ratio criterion for dimensionality reduction
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Stable orthogonal local discriminant embedding (SOLDE) is a recently proposed dimensionality reduction method, in which the similarity, diversity and interclass separability of the data samples are well utilized to obtain a set of orthogonal projection vectors. By combining multiple features of data, it outperforms many prevalent dimensionality reduction methods. However, the orthogonal projection vectors are obtained by a step-by-step procedure, which makes it computationally expensive. By generalizing the objective function of the SOLDE to a trace ratio problem, we propose a stable and orthogonal local discriminant embedding using trace ratio criterion (SOLDE-TR) for dimensionality reduction. An iterative procedure is provided to solve the trace ratio problem, due to which the SOLDE-TR method is always faster than the SOLDE. The projection vectors of the SOLDE-TR will always converge to a global solution, and the performances are always better than that of the SOLDE. Experimental results on two public image databases demonstrate the effectiveness and advantages of the proposed method.
KeywordsTrace ratio criterion Manifold learning Dimensionality reduction Diversity
This paper is supported by National Natural Science Foundation of China (No.61401471 and No.61501471); General Financial from the China Postdoctoral Science Foundation (No.2014M552589) and Special Financial from the China Postdoctoral Science Foundation (No.2015T81114).
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