Dimensionality reduction methods have commonly been used as principled ways to understand high-dimensional data. In this paper, a novel non-linear method named supervised data-dependent kernel sparsity preserving projection (SDKSPP) is proposed for dimensionality reduction. SDKSPP is a non-linear extension of sparsity preserving projection, it adopts a data-dependent kernel (DK) instead of standard kernels to achieve performance improvements. Different from previous dimensionality reduction methods based on DK, SDKSPP can simultaneously optimize the coefficients in DK and explore the manifold structure, i.e., the sparse reconstructive relationship of data. The manifold structure in the feature space is shared in the label space so that the information of labels can be utilized to help optimizing the coefficients in DK and improving the discriminative ability. After the optimal sparse reconstructive relationship is obtained, a transform matrix that can preserve this relationship is calculated to project the mapped data into a low-dimensional space. The effectiveness of the proposed method is tested and compared on nine popular databases.
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This work is partially supported by the National Natural Science Foundation of China (No. 61573088, No. 61573087 and No. 61433004).
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