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Robust face recognition using sparse representation in LDA space

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Abstract

In this article, we address the problem of face recognition under uncontrolled conditions. The proposed solution is a numerical robust algorithm dealing with face images automatically registered and projected via the linear discriminant analysis (LDA) into a holistic low-dimensional feature space. At the heart of this discriminative system, there are suitable nonconvex parametric mappings based on which a fixed-point technique finds the sparse representation of test images allowing their classification. We theoretically argue that the success achieved in sparsity promoting is due to the sequence of values imposed on a characteristic parameter of the used mapping family. Experiments carried out on several databases (ORL, YaleB, BANCA, FRGC v2.0) show the robustness and the ability of the system for classification purpose. In particular, within the area of sparsity promotion, our recognition system shows very good performance with respect to those achieved by the state-of-the-art \(\ell _1\) norm-based sparse representation classifier (SRC), the recently proposed \(\ell _2\) norm-based collaborative representation classifier (CRC), the LASSO-based sparse decomposition technique, and the weighted sparse representation method (WSRC), which integrates sparsity and data locality structure.

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Notes

  1. By construction, the method cannot work directly with \(k=1\). To this end, virtual samples should be created [34].

  2. MATLAB code of \(k\) -LiMapS_HFR and all tests done are available on the website http://dalab.di.unimi.it/klimaps.html.

  3. The standard deviation is always very low (varying between 0.013 and 0.019), indicating a good stability of the system.

  4. Given the high computational costs of this method, an exhaustive search of the optimal feature dimensionality would be very time consuming and beyond the scope of this work.

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Authors and Affiliations

  1. Department of Mathematics “Federigo Enriques”, University of Milan, Via Saldini 50, 20133, Milan, Italy

    Alessandro Adamo

  2. Department of Computer Science, University of Milan, Via Comelico 39, 20135, Milan, Italy

    Giuliano Grossi, Raffaella Lanzarotti & Jianyi Lin

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  1. Alessandro Adamo
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  2. Giuliano Grossi
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  3. Raffaella Lanzarotti
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  4. Jianyi Lin
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Correspondence to Raffaella Lanzarotti.

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Adamo, A., Grossi, G., Lanzarotti, R. et al. Robust face recognition using sparse representation in LDA space. Machine Vision and Applications 26, 837–847 (2015). https://doi.org/10.1007/s00138-015-0694-x

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