Related papers: GOCPT: Generalized Online Canonical Polyadic Tenso…

In autoregressive modeling for tensor-valued time series, Tucker decomposition, when applied to the coefficient tensor, provides a clear interpretation of supervised factor modeling but loses its efficiency rapidly with increasing tensor…

Real-world spatio-temporal data is often incomplete or inaccurate due to various data loading delays. For example, a location-disease-time tensor of case counts can have multiple delayed updates of recent temporal slices for some locations…

The fully-connected tensor network (FCTN) decomposition has recently exhibited strong modeling capabilities by connecting every pair of tensor factors, thereby capturing rich cross-mode correlations. However, this advantage comes with an…

We propose a novel algorithm for the computation of canonical polyadic decomposition (CPD) of large-scale tensors. The proposed algorithm generalizes the random projection (RAP) technique, which is often used to compute large-scale…

In this paper, a numerical method is proposed for canonical polyadic (CP) decomposition of small size tensors. The focus is primarily on decomposition of tensors that correspond to small matrix multiplications. Here, rank of the tensors is…

Recommendation systems, social network analysis, medical imaging, and data mining often involve processing sparse high-dimensional data. Such high-dimensional data are naturally represented as tensors, and they cannot be efficiently…

In this paper, the generalized eigenvalue complementarity problem for tensors (GEiCP-T) is addressed, which arises from the stability analysis of finite dimensional mechanical systems and find applications in differential dynamical systems.…

Coupled tensor decomposition (CTD) can extract joint features from multimodal data in various applications. It can be employed for federated learning networks with data confidentiality. Federated CTD achieves data privacy protection by…

It has been recently shown that sparse, nonnegative tensor factorization of multi-modal electronic health record data is a promising approach to high-throughput computational phenotyping. However, such approaches typically do not leverage…

Functional tensor decomposition can analyze multi-dimensional data with real-valued indices, paving the path for applications in machine learning and signal processing. A limitation of existing approaches is the assumption that the tensor…

Achieving chemical accuracy for strongly correlated molecules is a defining milestone for first-generation, fault-tolerant quantum computers, yet the factorial growth of three, four, and six-index tensor contractions in coupled-cluster…

Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…

Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on…

Motivated by a flurry of recent work on efficient tensor decomposition algorithms, we show that the celebrated moment matrix extension algorithm of Brachat, Comon, Mourrain, and Tsigaridas for symmetric tensor canonical polyadic (CP)…

Practical tensor data is often along with time information. Most existing temporal decomposition approaches estimate a set of fixed factors for the objects in each tensor mode, and hence cannot capture the temporal evolution of the objects'…

Coupled tensor decompositions (CTDs) perform data fusion by linking factors from different datasets. Although many CTDs have been already proposed, current works do not address important challenges of data fusion, where: 1) the datasets are…

Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…

We present a novel procedure for optimization based on the combination of efficient quantized tensor train representation and a generalized maximum matrix volume principle. We demonstrate the applicability of the new Tensor Train Optimizer…

We investigate the efficient combination of the canonical polyadic decomposition (CPD) and tensor hyper-contraction (THC) approaches. We first present a novel low-cost CPD solver which leverages a precomputed THC factorization of an…

CP decomposition is a powerful tool for data science, especially gene analysis, deep learning, and quantum computation. However, the application of tensor decomposition is largely hindered by the exponential increment of the computational…