关键词: 谱方法, 流形学习, 锚点, 邻接矩阵

Abstract: Learning algorithm of spectral manifold aims at discovering a low-dimensional representation in the high-dimensional vector space, which has been widely used recently. Although it has achieved many proud achievements, there is a very big bottleneck that computational complexity is very high, which limits its application in practice. This paper proposes a novel approach, called fast learning algorithm of spectral manifold (FSM). FSM includes two technologies to reduce high computational complexity: (1) FSM selects p anchor points from n data points through random selection or k-means selection and represents the data points as the linear combinations of these anchor points. Thus this paper designs a new form of adjacency matrix, which reduces the computational complexity of adjacency graph. (2) Linear manifold learning can be used for computing the low-dimensional parameterization of high-dimensional data effectively, which reduces the computational complexity of the optimal eigenvalue. The experimental results on face databases (Yale, ORL and extended Yale B) show the effectiveness of the proposed FSM method.

Key words: spectral method, manifold learning, anchor points, adjacency matrix