Sampling Based Tensor Common Component Analysis (TCCA) And Its Application Research

The rise of tensor in the field of big data processing has promoted the development of tensor-based data analysis algorithms,including high-order dimensionality reduction(DR)algorithms.A good dimensionality reduction algorithm will not only reduce the original data dimension,but also improve the accuracy of data analysis.Tensor Common Component Analysis(TCCA)is proposed as a novel high-order dimensionality reduction algorithm,which find a set of multi-directional projection matrices of the original data set by using simultaneous matrix factorizations,so that the original high-order high-dimensional tensor data is projected into a lower dimensional but the same order tensor space,these tensors represent the feature sets.The data structure of TCCA algorithm is unified and the implementation efficiency is high.However,the large amount of data also causes computing problems to the DR algorithms,in order to solve this problem,two kinds of improvement strategies are proposed to accelerate the running speed by using sampling methods to reduce the input data size.The first one based on the randomized column selection of CUR decomposition,and the second based on the cross approximation strategy.Both of them minimize the input data size,and by doing analysis on the sampled data,we can obtain the result similar to the original data set.Finally,the validity of these two sampling strategies is proved by doing classification experiment on two common multimedia datasets,and the effect of classification is further improved by adopting tensor distance metric in traditional KNN classifier.