报告题目: Incremental Linear Discriminant Analysis(LDA) for Data Dimensionality Reduction
报告人: Prof. Delin Chu (新加坡国立大学)
摘要: It has been a challenge problem to develop fast and efficient incremental linear discriminant analysis (LDA) algorithms although several incremental LDA algorithms have been proposed in the past. For this purpose, we conduct a new study on LDA in this paper and develop a new and efficient incremental LDA algorithm. We first propose a new batch LDA algorithm called LDA/QR which only depends on the data matrix and the sizes of data classes. LDA/QR is obtained by computing the economic QR factorization of the data matrix followed by solving a lower triangular linear system. Hence, LDA/QR is a simple and fast LDA algorithm. The relationship between LDA/QR and Uncorrelated LDA (ULDA) is also revealed. Based on LDA/QR, we develop a new incremental LDA algorithm called ILDA/QR which is the exact incremental version of LDA/QR. The main features of our incremental LDA algorithm ILDA/QR include: (i) it can easily handle not only the case that only one new sample is inserted but also the case that a chunk of new samples are added; (ii) it has pleasant computational complexity and space complexity; and (iii) it is very fast and always achieves comparative classification accuracy compared with ULDA algorithm and existing incremental LDA algorithms. Numerical experiments using some real world data demonstrate that our ILDA/QR is very efficient and competitive with the state-of-the-art incremental LDA algorithms in terms of classification accuracy, computational complexity and space complexity.