11,443 research outputs found

    A Family of Maximum Margin Criterion for Adaptive Learning

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    In recent years, pattern analysis plays an important role in data mining and recognition, and many variants have been proposed to handle complicated scenarios. In the literature, it has been quite familiar with high dimensionality of data samples, but either such characteristics or large data have become usual sense in real-world applications. In this work, an improved maximum margin criterion (MMC) method is introduced firstly. With the new definition of MMC, several variants of MMC, including random MMC, layered MMC, 2D^2 MMC, are designed to make adaptive learning applicable. Particularly, the MMC network is developed to learn deep features of images in light of simple deep networks. Experimental results on a diversity of data sets demonstrate the discriminant ability of proposed MMC methods are compenent to be adopted in complicated application scenarios.Comment: 14 page

    Adaptive Graph via Multiple Kernel Learning for Nonnegative Matrix Factorization

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    Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define parts-based, and linear representation of nonnegative data. Recently, Graph regularized NMF (GrNMF) is proposed to find a compact representation,which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In GNMF, an affinity graph is constructed from the original data space to encode the geometrical information. In this paper, we propose a novel idea which engages a Multiple Kernel Learning approach into refining the graph structure that reflects the factorization of the matrix and the new data space. The GrNMF is improved by utilizing the graph refined by the kernel learning, and then a novel kernel learning method is introduced under the GrNMF framework. Our approach shows encouraging results of the proposed algorithm in comparison to the state-of-the-art clustering algorithms like NMF, GrNMF, SVD etc.Comment: This paper has been withdrawn by the author due to the terrible writin

    Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

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    Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose closed-form solutions for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio
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