Tensor Robust PCA Based on Transformed Tensor Singular Value Decomposition for Cancer Genomic Data

The mining and analysis of genomics data provides a new idea for exploring the pathogenesis of human disease. Since these data often have the features of small samples, high-dimensional, and high redundancy, the traditional matrix decomposition method cannot fully mine the spatial structure and multiple perspective information of cancer genomics data. Inspired by the recently proposed robust tensor completion method, a tensor robust PCA method (TTTD) was proposed based on U-product and transformed tensor singular value decomposition (t-SVD) to explore the integrated cancer genomics data in this paper. Specifically, the unitary transform matrix is employed to replace the discrete Fourier transform matrix in t-SVD, which contributes to recover a lower tubal rank tensor to a certain extent. Meanwhile, the $\mathrm{L}_{2,1}-$norm is employed to learn the sparse term, and the row sparse constraint generated by it can better detect the abnormal value of the real tensor. In addition, the alternating direction method of the multiplier algorithm is used to optimize the TTTD method. Experimental results on the three integrated cancer multi-omics datasets show that the TTTD method achieves the better performance.