SRDA: An Efficient Algorithm for Large-Scale Discriminant Analysis

• Published in: IEEE transactions on knowledge and data engineering Vol. 20; no. 1; pp. 1 - 12
• Main Authors: Cai, Deng, He, Xiaofei, Han, Jiawei
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2008; IEEE Computer Society; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Applied sciences; Artificial intelligence; Computation; Computational efficiency; Computer science; control theory; systems; Data mining; Data processing. List processing. Character string processing; Discriminant analysis; Exact sciences and technology; Feature evaluation and selection; Feature extraction; Information processing; Information retrieval; Information systems. Data bases; Large-scale systems; Linear discriminant analysis; Machine learning; Mathematical analysis; Memory organisation. Data processing; Pattern recognition; Regression; Regression analysis; Software; Spectra; Spectral analysis; Studies; Data mining; Feature evaluation and selection; Separability; Discriminant analysis; Data analysis; spectral regression; Information retrieval; Information extraction; Regression analysis; Pattern recognition; Spectral analysis; Dimension reduction; dimensionality reduction; Covariance; Least squares method; Information processing; Linear Discriminant Analysis; Time complexity; Artificial intelligence; Algorithm analysis
• ISSN: 1041-4347; 1558-2191
• DOI: 10.1109/TKDE.2007.190669

Linear Discriminant Analysis (LDA) has been a popular method for extracting features that preserves class separability. The projection functions of LDA are commonly obtained by maximizing the between-class covariance and simultaneously minimizing the within-class covariance. It has been widely used in many fields of information processing, such as machine learning, data mining, information retrieval, and pattern recognition. However, the computation of LDA involves dense matrices eigendecomposition, which can be computationally expensive in both time and memory. Specifically, LDA has O(mnt + t 3 ) time complexity and requires O(mn + mt + nt) memory, where m is the number of samples, n is the number of features, and t = min(m,n). When both m and n are large, it is infeasible to apply LDA. In this paper, we propose a novel algorithm for discriminant analysis, called Spectral Regression Discriminant Analysis (SRDA). By using spectral graph analysis, SRDA casts discriminant analysis into a regression framework that facilitates both efficient computation and the use of regularization techniques. Specifically, SRDA only needs to solve a set of regularized least squares problems, and there is no eigenvector computation involved, which is a huge save of both time and memory. Our theoretical analysis shows that SRDA can be computed with O(mn) time and O(ms) memory, where .s(les n) is the average number of nonzero features in each sample. Extensive experimental results on four real-world data sets demonstrate the effectiveness and efficiency of our algorithm.