Keywords: Multidimensional data, Spatial correlation, Tensor decomposition, Dimension reduction, Image processing
In this talk, we propose a new method to analyze spatial-correlated imaging data. In contrast to the conventional multivariate analysis where the variables are treated as vectors and correlation is represented as a matrix form, we formulate spatial correlation based on the tensor decomposition to preserve the spatial information of imaging data. Specifically, we propose an innovative algorithm to decompose the spatial correlation into a sum of rank-1 tensor such that the structure of the spatial information can be captured more fully compared to traditional approaches. Our method is effective in reducing the dimension of spatial correlated data, which is advantage in computation. In addition, we show that the proposed method can test against the null hypothesis of independent structure, and identifies the block patterns of spatial correlations of imaging data effectively and efficiently. We compare the proposed method with other competing methods through simulations and optical image data to detect early-stage breast cancer.