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Feature selection has been widely used in machine learning for a long time. In this paper, we propose a supervised local sparse discriminative feature selection method named LSDFS to obtain sparse features by imposing ℓ 2 , 0 -norm constraint on transformation matrix. Differently from traditional approaches, our method does not require approximation or relaxation schemes, such as ℓ 2 , p -norm to solve long-standing challenge. Our method is based on the trace difference form of Linear Discriminant Analysis (LDA), which can efficiently obtain discriminative information in low-dimensional space. In order to explore the local structure of data which contains more discriminative information, we adopt a sparse connections graph between anchor points and data points instead of fully-connected graph with time-consuming, and add a decay parameter to avoid trivial solutions, making the model more precisely. Extensive experiments conducted on synthetic datasets and several real-world datasets have demonstrated the advantages of our method. [ABSTRACT FROM AUTHOR]

Linear Discriminant Analysis (LDA) is one of most important methods in dimensionality reduction domain, which is limited with Gaussian assumption. Because of the complexity of real data, data often presents non-Gaussian distribution that points in same class can be divided into several sub-clusters and center point is not enough to describe the distribution of data. In order to solve non-Gaussian data, LDA-based methods consider local structure information through measuring each pairwise distance of full connection graph. However, the strategy of establishing fully-connected graph is at expense of high computational complexity and limits it practical and industrial applications. We propose a Fast Local Representation Learning (FLRL) method which leverages anchor points to establish anchor-based graph and uses similarity matrix to depict the relationships of each pairwise connections. Notably, to avoid the affect of noises and redundant features in original space, anchor points and similarity matrix are updated alternately in subspace that local structure of data will be more precise to learn. Extensive pattern classification and image retrieval experiments on several synthetic datasets, well-known datasets and deep features datasets demonstrate the advantages of our method over the state-of-the-art methods. Our source code available on : https://github.com/superzcy/FLRL. [ABSTRACT FROM AUTHOR]