Dimension Reduction Algorithm Based On NSST System Transform And Two Order Tensor Principal Component Analysis

As the rapid development of science and technology, the computer technology has been widely used in various aspects. However, in computer applications, the problem of dealing with high dimensional data both for simple data and big data is a challenge that people has to face. It is known that manifold learning can extract the geometric feature structure, so it can be applied to the high dimensional data structure. Dimensionality reduction technology is one of the manifold learning methods. The original technology of dimension reduction, which includes PCA, LDA, and LPP and so on, transforms data into vector structure and reduces the dimensionality of the data. That not only increases the time, but also destroys the original structure of data. The current research can not meet the requirements of reducing dimension effect in various fields.As a concept in physics, Tensor has been applied to the mathematics and computer science in recently years. Not only the tensor is able to maintain its physical quantity, but also can reach the goal through the process of operation. Compared to the method of traditional vector dimension reducing,the tensor can get better effect when it used to dimension reducing. With the framework of manifolds learning, it has made the research about dimensionality reduction based on the nonsubsampled shearlet transform(NSST) system and tensor subspace.The main work of this paper is as follows:1. There is a series of related content about tensor space; it is point out that the image can be reduction dimension not only in the form of vector, but in tensor subspace. Compared to vector mode, tensor method is better to keep image features; the experiments have shown the different results with the two methods in decreased dimension.2. It is also proposed that the analysis of principal components in tensor subspace, on the basis of the principal component analysis(PCA) algorithm. To get more detail information of the picture, it also applies the NSST system to this algorithm. Compared to the experimental analysis, the new algorithm can get better reduced dimension effect.