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Principal Component Analysis with Weighted Sparsity Constraint |
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PP: 79-91 |
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Author(s) |
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Thanh D. X. Duong,
Vu N. Duong,
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Abstract |
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| Given a covariance matrix, principal component analysis (PCA) with sparsity constraint
considers the problem of maximizing the variance explained by a particular linear combination
of the input variables while constraining the number of nonzero coefficients in
this combination. However, when loading an input variable is associated with an individual
cost, we need to incorporate weights, which represent the loading cost of input
variables, into sparsity constraint. And in this paper, we present a version of PCA with
weighted sparsity constraint. This problem is reduced to solving some semidefinite
programming ones via convex relaxation technique. Two applications of the PCA with
weighted sparsity constraint to refine the sparsity constraint of sparse PCA illustrate its
efficiency and reliability in practice. |
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