A Tensor Based Stacked Fuzzy Networks for Efficient Data Regression

Abstract

Random vector functional link and extreme learning machine have been extended by the type-2 fuzzy sets with vector stacked methods, this extension leads to a new way to use tensor to construct learning structure for the type-2 fuzzy sets-based learning framework. In this paper, type-2 fuzzy sets-based random vector functional link, type-2 fuzzy sets-based extreme learning machine and Tikhonov-regularized extreme learning machine are fused into one network, a tensor way of stacking data is used to incorporate the nonlinear mappings when using type-2 fuzzy sets. In this way, the network could learning the sub-structure by three sub-structures' algorithms, which are merged into one tensor structure via the type-2 fuzzy mapping results. To the stacked single fuzzy neural network, the consequent part parameters learning are implemented by unfolding tensor-based matrix regression. The newly proposed stacked single fuzzy neural network shows a new way to design the hybrid fuzzy neural network with the higher order fuzzy sets and higher order data structure. The effective of the proposed stacked single fuzzy neural network are verified by the classical testing benchmarks and several statistical testing methods.

Tensor networks for quantum machine learning

“…As discussed in §4, MPS suit one-dimensional data like time series and logarithmic TTNs or two-dimensional TNs like MERA or PEPS are better suited for images depending on the amount of local correlation. For text, the information scales even steeper [110], which requires three-dimensional PEPS or high dimensional MERA variants which have not been implemented on a quantum computer yet. Exploiting symmetries reduces the need for complexity within the structure, e.g.…”