Linear discriminant analysis with generalized kernel constraint for robust image classification

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Linear discriminant analysis (LDA) as a classical supervised dimensionality reduction method has shown powerful capability in various image classification tasks. The purpose of LDA seeks an optimal linear transformation that maps the original data to a low-dimensional space. Inspired by the fact that the kernel trick can capture the nonlinear similarity of features, we propose a novel generalized distance constraint dubbed intra-class and inter-class kernel constraint (IIKC). The proposed IIKC explicitly models the category kernel distance and focuses on helping the original LDA capture more discriminant features in order to further improve the separability and magnitude difference between nearby data points. Our proposed method with IIKC aims to achieve maximum category separability by minimizing the intra-class kernel distances as well as maximizing the inter-class kernel distance, simultaneously. Extensive experimental results on six publicly available benchmark databases illustrate that the LDA-based methods embedded with the proposed IIKC significantly improve the discrimination ability and achieve a better classification performance than the original and state-of-the-art LDA algorithms.