等谱流形学习算法

基于谱方法的流形学习算法的目标是发现嵌入在高维数据空间中的低维表示.近年来,该算法已得到广泛的应用.等谱流形学习是谱方法中的主要内容之一.等谱流形学习源于这样的结论:只要两个流形的谱相同,其内部结构就是相同的.而谱计算难以解决的问题是近邻参数的选择以及如何构造合理邻接权.为此,提出了等谱流形学习算法(isospectral manifold learning algorithm,简称IMLA).它通过直接修正稀疏重构权矩阵,将类内的判别监督信息和类间的判别监督信息同时融入邻接图,达到既能保持数据间稀疏重建关系,又能利用监督信息的目的,与PCA等算法相比具有明显的优势.该算法在3 个常用人脸数据集(Yale,ORL,Extended Yale B)上得到了验证,这进一步说明了IMLA 算法的有效性.

Isospectral Manifold Learning Algorithm

Manifold learning based on spectral method has been widely used recently for discovering a low-dimensional representation in the high-dimensional vector space. Isospectral manifold learning is one of the main contents of spectrum method. Isospectral manifold learning stems from the conclusions that if only the spectrums of manifold are the same, so are their internal structures. However, the difficult task about the calculation of the spectrum is how to select the optimal neighborhood size and construct reasonable neighboring weights. In this paper, a supervised technique called isospectral manifold learning algorithm (IMLA) is proposed. By modifying directly sparse reconstruction weight, IMLA takes into account the within-neighboring information and between-neighboring information. Thus, it not only preserves the sparse reconstructive relationship, but also sufficiently utilizes discriminant information. Compared with PCA and other algorithms, IMLA has obvious advantages. Experimental results on face databases (Yale, ORL and Extended Yale B) show the effectiveness of the IMLA method.