arXiv research

There has been growing interest in extending traditional vector-based machine learning techniques to their tensor forms. An example is the support tensor machine (STM) that utilizes a rank-one tensor to capture the data structure, thereby alleviating the overfitting and curse of dimensionality problems in the conventio…

The paper analyzes tensor recovery from symmetric rank-one measurements using information theory.

Estimates the probability of a random symmetric tensor being close to rank-one.

Extends MSC for triclustering tensors, using DBSCAN to find clusters.

A Riemannian manifold is called Osserman (conformally Osserman, respectively), if the eigenvalues of the Jacobi operator of its curvature tensor (Weyl tensor, respectively) are constant on the unit tangent sphere at every point. Osserman Conjecture asserts that every Osserman manifold is either flat or rank-one symmetr…

Study on estimating rank-one tensors in noisy data with heavy tails.

New tensor recovery method uses Riemannian optimization on Segre manifold.

Paper proposes a tensor model for clustering noisy multi-view data.

Study quantifies performance gap between tensor and matrix-based approaches in nested matrix-tensor model.

We formulate and solve a tensor model using a latent-variable approach.

Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex or a nonconvex cost function, which is a generalization of the matching pursuit…

Study on tensor signal estimation from incomplete data.

Researchers describe the metric structure of compact ECS manifolds.

Study on rank-one ECS manifolds, focusing on dilational type.

Study of asymmetric rank-one tensor models with non-Gaussian noise.

Killing tensors on complex projective space are identified and generated by Killing fields.

Geometrically, tensors of fixed rank form a minimal submanifold.

New insights into compact rank-one ECS manifolds, proving they are bundles over circles.

Efficient tensor decomposition for count data models achieves near-optimal multiway analysis.

The study examines continuous mean curvature functions on manifolds without conjugate points.

An algebraic curvature tensor is called Osserman if the eigenvalues of the associated Jacobi operator are constant on the unit sphere. A Riemannian manifold is called conformally Osserman if its Weyl conformal curvature tensor at every point is Osserman. We prove that a conformally Osserman manifold of dimension $n \ne…

We show that the spectral norm of a random $n_1\times n_2\times \cdots \times n_K$ tensor (or higher-order array) scales as $O\left(\sqrt{(\sum_{k=1}^{K}n_k)\log(K)}\right)$ under some sub-Gaussian assumption on the entries. The proof is based on a covering number argument. Since the spectral norm is dual to the tensor…

In recent years, a class of dictionaries have been proposed for multidimensional (tensor) data representation that exploit the structure of tensor data by imposing a Kronecker structure on the dictionary underlying the data. In this work, a novel algorithm called "STARK" is provided to learn Kronecker structured dictio…

We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for the algorithm to work and demonstrate on both synthetic and real world data that AROFAC2 is a potentially outperforming alternative to the go…

This paper sets fundamental limits for rank-one matrix estimation with varying noise levels.

New geometric structures derived from Hessian metrics and tensors.

The paper classifies Killing tensor fields on Riemannian symmetric spaces.

Study analyzes Hotelling-type tensor deflation for spiked tensors, providing insights into signal and noise.

Study uncovers complex critical points in tensor decomposition.

Paper optimizes tensor deflation for non-orthogonal signals.

Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This motivates us to consider the problem of low rank tensor recovery from a class of lin…

The paper studies phase transitions in random matrices and tensor unfolding for detecting signals.

New approach uses random matrix theory to understand tensor estimation performance.

We study stability and local minimizing properties of $L^p$- norms of Riemannian curvature tensor denoted by $\mathcal{R}_p$ by variational methods. We compute the Hessian of $\mathcal{R}_p$ at compact rank 1 symmetric spaces and prove that they are stable for $\mathcal{R}_p$ for certain values of p > 2. A similar resu…

Estimates rank-one spikes from heavy-tailed noise using self-avoiding walks.

Adaptive algorithm learns tensor network structures from data.

The digital revolution of the banking system with evolving European regulations have pushed the major banking actors to innovate by a newly use of their clients' digital information. Given highly sparse client activities, we propose CPOPT-Net, an algorithm that combines the CP canonical tensor decomposition, a multidim…

Study analyzes accuracy of tensor deflation in noisy conditions.

Two methods preserve tensor structure for reduced dimensionality in tensor regression.

The paper improves density estimation in high dimensions using tensor decompositions.

In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this factorization one can derive notion of tensor rank, referred to as the tensor tubal…

A low-rank tensor model simplifies multi-dimensional Markov chains.

Revisits CP tensor decomposition for noisy, non-orthogonal data.

Estimates joint probability distribution from 1-way marginals using low-rank tensors and random projections.

Stochastic trace estimation with tensor train random vectors

Study efficient power iteration for tensor models, proving convergence under specific conditions.

We study the problem of nonnegative rank-one approximation of a nonnegative tensor, and show that the globally optimal solution that minimizes the generalized Kullback-Leibler divergence can be efficiently obtained, i.e., it is not NP-hard. This result works for arbitrary nonnegative tensors with an arbitrary number of…

The new financial European regulations such as PSD2 are changing the retail banking services. Noticeably, the monitoring of the personal expenses is now opened to other institutions than retail banks. Nonetheless, the retail banks are looking to leverage the user-device authentication on the mobile banking applications…