A Scalable Two-Stage Approach for a Class of Dimensionality Reduction Techniques

Liang Sun, Betul Ceran, and Jieping Ye

Introduction

This software package implements an efficient two-stage approach to a class of dimensionality reduction techniques, including Canonical Correlation Analysis (CCA), Linear Discriminant Analysis (LDA), Orthonormalized Partial Least Squares (OPLS), and Hypergraph Spectral Learning. The two-stage approach solves a least squares problem in the first stage, which can be solved very efficiently using the iterative conjugate gradient algorithm, e.g., LSQR. In the second stage, the data is projected onto a low-dimensional space, and then we solve a generalized eigenvalue problem in the reduced space.

Compared with previous work, the two-stage approach does not require any assumption on the data. The two-stage approach can be further extended to the regularization setting, which improves its applicability in practice. The time complexity of the two-stage approach is linear in terms of both the sample size and the data dimensionality.

Feedback

Please report any bug to Liang Sun (sun.liang@asu.edu). 

Download

Two-Stage package is distributed for non-commercial use only.