## Abstract

Over the past few decades, much attention has been drawn to large-scale incremental data analysis, where researchers are faced with huge amounts of high-dimensional data acquired incrementally. In such a case, conventional algorithms that compute the result from scratch whenever a new sample comes are highly inefficient. To conquer this problem, we propose a new incremental algorithm incremental regularized least squares (IRLS) that incrementally computes the solution to the regularized least squares (RLS) problem with multiple columns on the right-hand side. More specifically, for an RLS problem with c (c > 1) columns on the right-hand side, we update its unique solution by solving an RLS problem with a single column on the right-hand side whenever a new sample arrives, instead of solving an RLS problem with c columns on the right-hand side from scratch. As a direct application of IRLS, we consider the supervised dimensionality reduction of large-scale data and focus on linear discriminant analysis (LDA). We first propose a new batch LDA model that is closely related to the RLS problem, and then apply IRLS to develop a new incremental LDA algorithm. Experimental results on real-world datasets demonstrate the effectiveness and efficiency of our algorithms.

Original language | English |
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Pages (from-to) | B414-B439 |

Number of pages | 26 |

Journal | SIAM Journal on Scientific Computing |

Volume | 38 |

Issue number | 3 |

DOIs | |

Publication status | Published - 25 May 2016 |

## Scopus Subject Areas

- Computational Mathematics
- Applied Mathematics

## User-Defined Keywords

- Incremental regularized least squares
- Linear discriminant analysis
- Lsqr
- Supervised dimensionality reduction