### Abstract

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 relationship. Results also demonstrate the efficiency and effectiveness of the equivalent least squares formulations on large-scale problems.

Original language | English (US) |
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Title of host publication | Proceedings of the 26th International Conference On Machine Learning, ICML 2009 |

Pages | 977-984 |

Number of pages | 8 |

State | Published - 2009 |

Event | 26th International Conference On Machine Learning, ICML 2009 - Montreal, QC, Canada Duration: Jun 14 2009 → Jun 18 2009 |

### Other

Other | 26th International Conference On Machine Learning, ICML 2009 |
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Country | Canada |

City | Montreal, QC |

Period | 6/14/09 → 6/18/09 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Networks and Communications
- Software

### Cite this

*Proceedings of the 26th International Conference On Machine Learning, ICML 2009*(pp. 977-984)

**A least squares formulation for a class of generalized eigenvalue problems in machine learning.** / Sun, Liang; Ji, Shuiwang; Ye, Jieping.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 26th International Conference On Machine Learning, ICML 2009.*pp. 977-984, 26th International Conference On Machine Learning, ICML 2009, Montreal, QC, Canada, 6/14/09.

}

TY - GEN

T1 - A least squares formulation for a class of generalized eigenvalue problems in machine learning

AU - Sun, Liang

AU - Ji, Shuiwang

AU - Ye, Jieping

PY - 2009

Y1 - 2009

N2 - 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 relationship. Results also demonstrate the efficiency and effectiveness of the equivalent least squares formulations on large-scale problems.

AB - 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 relationship. Results also demonstrate the efficiency and effectiveness of the equivalent least squares formulations on large-scale problems.

UR - http://www.scopus.com/inward/record.url?scp=71149101160&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=71149101160&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781605585161

SP - 977

EP - 984

BT - Proceedings of the 26th International Conference On Machine Learning, ICML 2009

ER -