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. ©Copyright 2013, Institute of Software, the Chinese Academy of Sciences.