Principal Component Analysis with Tensor Train Subspace
نویسندگان
چکیده
Tensor train is a hierarchical tensor network structure that helps alleviate the curse of dimensionality by parameterizing large-scale multidimensional data via a set of network of low-rank tensors. Associated with such a construction is a notion of Tensor Train subspace and in this paper we propose a TTPCA algorithm for estimating this structured subspace from the given data. By maintaining low rank tensor structure, TT-PCA is more robust to noise comparing with PCA or Tucker-PCA. This is borne out numerically by testing the proposed approach on the Extended YaleFace Dataset B.
منابع مشابه
Human Action Recognition Using Tensor Principal Component Analysis
Human action can be naturally represented as multidimensional arrays known as tensors. In this paper, a simple and efficient algorithm based on tensor subspace learning is proposed for human action recognition. An action is represented as a 3th-order tensor first, then tensor principal component analysis is used to reduce dimensionality and extract the most useful features for action recognitio...
متن کاملParallel Active Subspace Decomposition for Scalable and Efficient Tensor Robust Principal Component Analysis
Tensor robust principal component analysis (TRPCA) has received a substantial amount of attention in various fields. Most existing methods, normally relying on tensor nuclear norm minimization, need to pay an expensive computational cost due to multiple singular value decompositions (SVDs) at each iteration. To overcome the drawback, we propose a scalable and efficient method, named Parallel Ac...
متن کاملTensor Subspace Analysis
Previous work has demonstrated that the image variations of many objects (human faces in particular) under variable lighting can be effectively modeled by low dimensional linear spaces. The typical linear subspace learning algorithms include Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Locality Preserving Projection (LPP). All of these methods consider an n1 × n2 ...
متن کاملManifold Learning Based Gait Feature Reduction and Recognition
The moving objectives’ images are in tensor format in reality. That using for reference the thought of tensor space dimension reduction to gain the optimal gait characters with low dimension inaugurate a new gait recognition way. A novel gait expression and recognition algorithm based on the tensor space is introduced here. It is a tensor space learning algorithm that could investigate the inhe...
متن کاملSubspace Learning Based on Tensor Analysis
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 m1 × m2 image as a high dimensional vector in Rm1×m2 . Such a vector r...
متن کامل