Fast and incremental algorithms for exponential semi-supervised discriminant embedding

Highlights：

• Second, to the best of our knowledge, there are no incremental algorithms for matrix exponential discriminant methods till now. To fill in this gap, the second contribution of this paper is to propose incremental ESDE algorithms for incremental learning problems.

• Third, the proposed fast implementation strategy and the incremental techniques also apply to other exponential discriminant analysis methods.

摘要

•First, we propose a fast implementation on the ESDE method. The key is to equivalently transform the large matrix problem of size d into a much smaller one of size n, where d is the data dimension and n is the number of training samples, with d ≫ n in practice. Numerical results demonstrate that the proposed algorithms are at least two orders of magnitude faster than their original counterparts, with no recognition accuracy lost.•Second, to the best of our knowledge, there are no incremental algorithms for matrix exponential discriminant methods till now. To fill in this gap, the second contribution of this paper is to propose incremental ESDE algorithms for incremental learning problems.•Third, the proposed fast implementation strategy and the incremental techniques also apply to other exponential discriminant analysis methods.

论文关键词：Semi-supervised discriminant embedding (SDE),Local discriminant embedding (LDE),Exponential semi-supervised discriminant embedding (ESDE),Small-sample-size problem (SSS),Incremental algorithm,Dimensionality reduction