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Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…

Consider a data set collected by (individuals-features) pairs in different times. It can be represented as a tensor of three dimensions (Individuals, features and times). The tensor biclustering problem computes a subset of individuals and…

A matrix always has a full rank submatrix such that the rank of this matrix is equal to the rank of that submatrix. This property is one of the corner stones of the matrix rank theory. We call this property the max-full-rank-submatrix…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

Modern sensing and metrology systems now stream terabytes of heterogeneous, high-dimensional (HD) data profiles, images, and dense point clouds, whose natural representation is multi-way tensors. Understanding such data requires regression…

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…

In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polynomials is limited to kernels as in support vector machines,…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…

Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised…

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For…

There have been many studies on analyzing self-supervised speech Transformers, in particular, with layer-wise analysis. It is, however, desirable to have an approach that can pinpoint exactly a subset of neurons that is responsible for a…

Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…

Tensor train is a hierarchical tensor network structure that helps alleviate the curse of dimensionality by parameterizing large-scale multidimensional data via a set of network of low-rank tensors. Associated with such a construction is a…

Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…

Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we…

We study low-rank parameterizations of weight matrices with embedded spectral properties in the Deep Learning context. The low-rank property leads to parameter efficiency and permits taking computational shortcuts when computing mappings.…