Big Data ‘Fork’: Tensor Product for DCT-II/DST-II/ DFT/HWT

The tensor product, denoted by ⊗ (Kronecker Product), may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras etc. The element (block)-wise inverse Jacket (BIJM) is simply calculated for big data which we called big data ‘Fork’ matrix. We use matrix decomposition method to compress or minimize the big matrix to smaller matrix. In this paper, based on the BIJM, a unified fast hybrid diagonal block-wise transform (FHDBT) algorithm is proposed. A new fast diagonal block matrix decomposition is made by the matrix product of successively lower order diagonal Jacket matrix and Hadamard matrix. The FHDBT, which is able to convert a newly developed discrete cosine transform (DCT)-II, discrete sine transform (DST)-II, discrete Fourier transform (DFT), and Haar-based wavelet transform (HWT). Comparing with pre-existing DCT-II, DST-II, DFT, and HWT, it is shown that the proposed FHDBT exhibits less the complexity as its matrix size gets larger. From the numerical experiments, it is shown that a better performance can be achieved by the use of DCT/DST-II compression scheme compared with the DCT-II only compression method.