子空间半监督Fisher判别分析

Fisher判别分析寻找一个使样本数据类间散度与样本数据类内散度比值最大的子空间, 是一种很流行的监督式特征降维方法. 标注样本数据所属的类别通常需要大量的人工, 消耗大量的时间, 付出昂贵的成本. 为了解决同时利用有类别信息的样本数据和没有类别信息的样本数据用于寻找降维子空间的问题, 我们提出了一种子空间半监督Fisher判别分析方法. 子空间半监督Fisher判别分析寻找这样一个子空间, 这个子空间即保留了从有类别信息的样本数据中学习的类别判别结构, 也保留了从有类别信息的样本数据和没有类别信息的样本数据中学习的样本结构信息. 我们还推导了基于核的子空间半监督Fisher判别分析方法. 通过人脸识别实验验证了本文算法的有效性.

Subspace Semi-supervised Fisher Discriminant Analysis

Fisher discriminant analysis (FDA) is a popular method for supervised dimensionality reduction. FDA seeks for an embedding transformation such that the ratio of the between-class scatter to the within-class scatter is maximized. Labeled data, however, often consume much time and are expensive to obtain, as they require the efforts of human annotators. In order to cope with the problem of effectively combining unlabeled data with labeled data to find the embedding transformation, we propose a novel method, called subspace semi-supervised Fisher discriminant analysis (SSFDA), for semi-supervised dimensionality reduction. SSFDA aims to find an embedding transformation that respects the discriminant structure inferred from the labeled data and the intrinsic geometrical structure inferred from both the labeled and unlabeled data. We also show that SSFDA can be extended to nonlinear dimensionality reduction scenarios by applying the kernel trick. The experimental results on face recognition demonstrate the effectiveness of our proposed algorithm.