Tensor-Ring Decomposition with Index-Splitting

Tensor Ring Decomposition

Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the complicated tensor networks. However, the TT decomposition highly depends on permutations of tensor dimensions, due to its strictly sequential multilinear products ...

Tensor Decomposition with Smoothness

Tensor Decomposition with Smoothness

Real data tensors are typically high dimensional; however, their intrinsic information is preserved in low-dimensional space, which motivates the use of tensor decompositions such as Tucker decomposition. Frequently, real data tensors smooth in addition to being low dimensional, which implies that adjacent elements are similar or continuously changing. These elements typically appear as spatial...

Clustering Patients with Tensor Decomposition

In this paper we present a method for the unsupervised clustering of high-dimensional binary data, with a special focus on electronic healthcare records. We present a robust and efficient heuristic to face this problem using tensor decomposition. We present the reasons why this approach is preferable for tasks such as clustering patient records, to more commonly used distance-based methods. We ...

Tensor Decomposition with Missing Indices

How can we decompose a data tensor if the indices are partially missing? Tensor decomposition is a fundamental tool to analyze the tensor data. Suppose, for example, we have a 3rd-order tensor X where each element Xijk takes 1 if user i posts word j at location k on Twitter. Standard tensor decomposition expects all the indices are observed. However, in some tweets, location k can be missing. I...