广义的监督局部保留投影算法

Generalized Supervised Locality Preserving Projection

针对监督的局部保留投影算法(Supervised Locality Preserving Projection,SLPP)在小样本情况下矩阵的奇异性问题,该文提出了一种广义的监督局部保留投影算法(Generalized Supervised Locality Preserving Projection,GSLPP)。GSLPP在大样本情况下等价于SLPP,在小样本情况下却可以等价转换到一个低维空间中来求解,从而有效解决了小样本问题。最后,实验结果验证了该方法的有效性。

Supervised Locality Preserving Projection （SLPP） is a generalization of Locality Preserving Projection （LPP） in the case of supervised learning. In this paper the drawback of SLPP in the high-dimensional and small sample size case is pointed out, and a new algorithm called Generalized Supervised Locality Preserving Projection （GSLPP） is proposed. The relationship between SLPP and GSLPP is theoretically analyzed. In the small sample size case GSLPP can be solved equivalently in lower-dimensionality space. Finally, the effectiveness of the proposed algorithm is verified by experimental results.