We introduce methodology to construct an emulator for environmental and ecological spatiotemporal processes that uses the higher-order singular value decomposition (HOSVD) as extension of (SVD) approaches emulation. Some important advantages method are it allows use a combination supervised learning methods (e.g., random forests Gaussian process regression) also prediction values at spatial loc...

Genetic pathways usually encode molecular mechanisms that can inform targeted interventions. It is often challenging for existing machine learning approaches to jointly model genetic (higher-order features) and variants (atomic features), present clinicians interpretable models. In order build more accurate better models medicine, we introduce Pathway Augmented Nonnegative Tensor factorization ...

A tensor is a multidimensional array, where the order of tensor denotes the dimension of the array. For example, a scalar is simply an order-0 tensor, a vector order-1, a matrix order-2, and any tensor with order-3 or greater is described as a higher order tensor. For this paper I will be focusing on the simplest higher-order tensor, the order-3 tensor, which can be visualized as a sort of Rubi...

Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting, gross corruptions and computational efficiency. To address these problems, we first propose a parallel trace norm regularized tensor decomposition method, and...

Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral co-clustering method that simultaneously clusters the rows, columns, and slices of a nonnegative three-mode tensor and generalizes to tensors with any number of m...

The topological structure of scalar, vector, and second-order tensor fields provides an important mathematical basis for data analysis and visualization. In this paper, we extend this framework towards higher-order tensors. First, we establish formal uniqueness properties for a geometrically constrained tensor decomposition. This allows us to define and visualize topological structures in symme...