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SRDA: An Efficient Algorithm for Large-Scale Discriminant Analysis
January 2008 (vol. 20 no. 1)
pp. 1-12
Linear Discriminant Analysis (LDA) has been a popular method for extracting features which preserve class separability. It has been widely used in many fields of information processing. However, the computation of LDA involves dense matrices eigen-decomposition which can be computationally expensive both in 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 {\em Spectral Regression Discriminant Analysis} (SRDA). By using spectral graph analysis, SRDA casts discriminant analysis into a regression framework which 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 $O(ms)$ time and $O(ms)$ memory, where $s (\leq n)$ is the average number of non-zero features in each sample. Extensive experimental results on four real world data sets demonstrate the effectiveness and efficiency of our algorithm.

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Index Terms:
Data mining, Feature evaluation and selection
Citation:
Deng Cai, Xiaofei He, Jiawei Han, "SRDA: An Efficient Algorithm for Large-Scale Discriminant Analysis," IEEE Transactions on Knowledge and Data Engineering, vol. 20, no. 1, pp. 1-12, Jan. 2008, doi:10.1109/TKDE.2007.190669
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