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ICML
2009
IEEE

A least squares formulation for a class of generalized eigenvalue problems in machine learning

9 years 6 months ago
A least squares formulation for a class of generalized eigenvalue problems in machine learning
Many machine learning algorithms can be formulated as a generalized eigenvalue problem. One major limitation of such formulation is that the generalized eigenvalue problem is computationally expensive to solve especially for large-scale problems. In this paper, we show that under a mild condition, a class of generalized eigenvalue problems in machine learning can be formulated as a least squares problem. This class of problems include classical techniques such as Canonical Correlation Analysis (CCA), Partial Least Squares (PLS), and Linear Discriminant Analysis (LDA), as well as Hypergraph Spectral Learning (HSL). As a result, various regularization techniques can be readily incorporated into the formulation to improve model sparsity and generalization ability. In addition, the least squares formulation leads to efficient and scalable implementations based on the iterative conjugate gradient type algorithms. We report experimental results that confirm the established equivalence relat...
Liang Sun, Shuiwang Ji, Jieping Ye
Added 17 Nov 2009
Updated 17 Nov 2009
Type Conference
Year 2009
Where ICML
Authors Liang Sun, Shuiwang Ji, Jieping Ye
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