Scatter Balance: An Angle-Based Supervised Dimensionality Reduction

Subspace selection is widely applied in data classification, clustering, and visualization. The samples projected into subspace can be processed efficiently. In this paper, we research the linear discriminant analysis (LDA) and maximum margin criterion (MMC) algorithms intensively and analyze the ef...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2015-02, Vol.26 (2), p.277-289
Main Authors: Liu, Shenglan, Feng, Lin, Qiao, Hong
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Algorithms
Balancing
Discriminant analysis
Eigenvalues and eigenfunctions
Linear discriminant
Matrix decomposition
Metal matrix composites
Neural networks
Null space
Optimized production technology
Principal component analysis
Reduction
Repositories
Scatter
scatter matrix
small sample size problem
subspace selection
Subspaces
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Summary:Subspace selection is widely applied in data classification, clustering, and visualization. The samples projected into subspace can be processed efficiently. In this paper, we research the linear discriminant analysis (LDA) and maximum margin criterion (MMC) algorithms intensively and analyze the effects of scatters to subspace selection. Meanwhile, we point out the boundaries of scatters in LDA and MMC algorithms to illustrate the differences and similarities of subspace selection in different circumstances. Besides, the effects of outlier classes on subspace selection are also analyzed. According to the above analysis, we propose a new subspace selection method called angle linear discriminant embedding (ALDE) on the basis of angle measurement. ALDE utilizes the cosine of the angle to get new within-class and between-class scatter matrices and avoids the small sample size problem simultaneously. To deal with high-dimensional data, we extend ALDE to a two-stage ALDE (TS-ALDE). The synthetic data experiments indicate that ALDE can balance the within-class and between-class scatters and be robust to outlier classes. The experimental results based on UCI machine-learning repository and image databases show that TS-ALDE has a lower time complexity than ALDE while processing high-dimensional data.
ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2014.2314698