A Novel Dimensionality Reduction Method Based on Tensor and Lorentzian Geometry
一种基于张量和洛仑兹几何的降维方法

Traditional vector-based dimensionality reduction algorithms consider an m×n image as a high dimensional vector in Rm×n. However, because this representation usually causes the lost of the local spatial information, it can not describe the image well. Intrinsically, an image is a 2D tensor and some feature extracted from the image (e.g. Gabor feature, LBP feature) may be a higher tensor. In this paper, we consider the nature of the image feature and propose the tensor Lorentzian discriminant projection algorithm, which can be considered as the tensor generation of the newly proposed Lorentzian discriminant projection (LDP). With regard to an image, this algorithm directly uses the hue matrix to compute, so it keeps the local spatial information well. In addition, this method can be naturally extended to the higher tensor space to deal with more complicated image features, such as Gabor feature and LBP feature. The experimental results on face and texture recognition show that our algorithm achieves better recognition accuracy while being much more efficient.