Rank, decomposition, and uniqueness for 3-way and n-way arrays
Multiway data analysis
A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
Rank-One Approximation to High Order Tensors
SIAM Journal on Matrix Analysis and Applications
Fast Multilinear Singular Value Decomposition for Structured Tensors
SIAM Journal on Matrix Analysis and Applications
Tensor Decompositions and Applications
SIAM Review
Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
SIAM Journal on Scientific Computing
Application of reductive decomposition method for multilinear arrays (RDMMA) to animations
MMACTEE'09 Proceedings of the 11th WSEAS international conference on Mathematical methods and computational techniques in electrical engineering
Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
SIAM Journal on Matrix Analysis and Applications
Weighted singular value decomposition for folded matrices
AICT'11 Proceedings of the 2nd international conference on Applied informatics and computing theory
| Hi-index | 0.00 |
Identification of relationships between multiple factors in multidimensional data sets is of crucial importance in many areas of science. This is especially true in fields where multiple parameters interact with each other and create complex structures and dynamics. In this paper, we present a method based on Taylor series expansion for flattening of high dimensional arrays. The method uses the unit, shift, forward and backward difference operators in order to produce an array whose elements are approximately in constant form. Furthermore, the method inserts a perturbation proportionality variable t for each instance of the forward and backward difference operators. Array flattening takes place asymptotically and some of the first elements produced by the Maclaurin expansion are discarded through an appropriate affine transformation. Subsequently, t is set to be equal to 1 which results in an approximately constant array. Once such constancy is achieved, a specific type of high dimensional model representation, namely HDMR can be used in order to approximate the flattened array by truncating higher order components of HDMR. Finally, the flattened array can be multiplied by the Taylor polynomial previously used in the flattening procedure to get a good approximation of the original array.