Fisher's linear discriminant analysis (LDA), one of the most popular dimensionality reduction algorithms for classification, has three particular problems: it fails to find the nonlinear structure hidden in the high dimensional data; it assumes all samples contribute equivalently to reduce dimension for classification; and it suffers from the matrix singularity problem. In this paper, we propose a new algorithm, termed Discriminative Locality Alignment (DLA), to deal with these problems. The algorithm operates in the following three stages: first, in part optimization, discriminative information is imposed over patches, each of which is associated with one sample and its neighbors; then, in sample weighting, each part optimization is weighted by the margin degree, a measure of the importance of a given sample; and finally, in whole alignment, the alignment trick is used to align all weighted part optimizations to the whole optimization. Furthermore, DLA is extended to the semi-supervised case, i.e., semi-supervised DLA (SDLA), which utilizes unlabeled samples to improve the classification performance. Thorough empirical studies on the face recognition demonstrate the effectiveness of both DLA and SDLA. © 2008 Springer Berlin Heidelberg.
CITATION STYLE
Zhang, T., Tao, D., & Yang, J. (2008). Discriminative locality alignment. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5302 LNCS, pp. 725–738). Springer Verlag. https://doi.org/10.1007/978-3-540-88682-2_55
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