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.