Isometric Projection

Recently the problem of dimensionality reduction has received a lot of interests in many fields of information processing. We consider the case where data is sampled from a low dimensional manifold which is embedded in high dimensional Euclidean space. The most popular manifold learning algorithms include Locally Linear Embedding, ISOMAP, and Laplacian Eigenmap. However, these algorithms are nonlinear and only provide the embedding results of training samples. In this paper, we propose a novel linear dimensionality reduction algorithm, called Isometric Projection. Isometric Projection constructs a weighted data graph where the weights are discrete approximations of the geodesic distances on the data manifold. A linear subspace is then obtained by preserving the pairwise distances. In this way, Isometric Projection can be defined everywhere. Comparing to Principal Component Analysis (PCA) which is widely used in data processing, our algorithm is more capable of discovering the intrin...

• Type: Conference
• Year: 2007
• Where: AAAI
• Authors: Deng Cai, Xiaofei He, Jiawei Han
• Keywords: AAAI 2007, Dimensionality Reduction, Intelligent Agents, Isometric Projection, Low Dimensional Manifold