Subspace Learning Based on Tensor Analysis
Deng Cai, Xiaofei He, Jiawei Han · Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign) · 2005
Linear dimensionality reduction techniques have been widely used in pattern recognition and computer vision, such as face recognition, image retrieval, etc. The typical methods include Principal Component Analysis (PCA) which is unsupervised and Linear Discriminant Analysis (LDA) which is supervised. Both of them consider an m_1\\times m_2 image as a high dimensional vector in \\mathbb{R}^{m_1\\times m_2}. Such a vector representation fails to take into account the spatial locality of pixels in the image. An image is intrinsically a matrix. In this paper, we consider an image as the second order tensor in \\mathbb{R}^{m_1}\\otimes\\mathbb{R}^{m_2} and propose two novel tensor subspace learning algorithms called TensorPCA and TensorLDA. Our algorithms explicitly take into account the relationship between column vectors of the image matrix and the relationship between the row vectors of the image matrix. We compare our proposed approaches with PCA and LDA for face recognition on three standard face databases. Experimental results show that tensor analysis achieves better recognition accuracy, while being much more efficient.