A Multi-Class Multi-Manifold Learning Algorithm Based on ISOMAP

The classical algorithm ISOMAP can find the intrinsic low-dimensional structures hidden in high-dimensional data uniformly distributed on or around a single manifold, but if the data are sampled from multi-class, each of which corresponds to an independent manifold, and clusters formed by data points belonging to each class are separated away, several disconnected neighborhood graphs will form, which leads to the failure of ISOMAP algorithm. In this paper, an improved version of ISOMAP, namely multi-class multi-manifold ISOMAP (MCMM-ISOMAP), is proposed. MCMM-ISOMAP constructs a single neighborhood graph not by increasing the value of neighborhood parameter, but by the following steps that first choose appropriate value with which short-circuit edges can not be introduced, second find such pairwise data each of which are two endpoints of the shortest Euclidean distance between classes, and finally make them neighborhood points each other. Thereby a single neighborhood graph will form, and then ISOMAP algorithm is applied to find the intrinsic low-dimensional embedding structure. Experimental results on synthetic and real data reveal effectiveness of the proposed method.