关键词: 判别邻域嵌入（DNE）, 张量子空间分析（TSA）, 维数约简, 判别分析, 张量学习

Abstract: Most of traditional machine learning algorithms process vectorized data, while in real world a lot of data exist in the form of tensor, such as images and video. If these tensor data are forced to be vectorized, the so called “curse of dimensionality” and “small sample size problem” will be encountered as well as the intrinsic structure will be destroyed. Thus, the good lower dimensional representation of the original data can not be captured. Discriminant neighborhood embedding (DNE) is a popular discriminant analysis method but based on vectorized data. To address this issue, this paper proposes a novel neighborhood-embedded tensor learning (NTL) which inherits the power of DNE. In addition, NTL overcomes another limitation of DNE that it neglects the role of the points out of the neighborhood of a data point. By designing an objective function elaborately (three graphs are encoded in the   object function: intraclass graph, interclass graph and other points association graph), NTL maps the data into a low dimension subspace where the data in the same class will be more compact and the data in the different class will be more separable. The experimental results on three public data bases (ORL, PIE and COIL20) demonstrate that NTL achieves better recognition rate, while being much more efficient.

Key words: discriminant neighborhood embedding (DNE), tensor subspace analysis (TSA), dimensionality reduction, discriminant analysis, tensor learning