Related papers: Concurrent Alternating Least Squares for multiple …

We derive nonlinear acceleration methods based on the limited memory BFGS (L-BFGS) update formula for accelerating iterative optimization methods of alternating least squares (ALS) type applied to canonical polyadic (CP) and Tucker tensor…

We propose a new arc consistency enforcement paradigm that transforms arc consistency enforcement into recurrent tensor operations. In each iteration of the recurrence, all involved processes can be fully parallelized with tensor…

Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…

Structural Health Monitoring (SHM) provides an economic approach which aims to enhance understanding the behavior of structures by continuously collects data through multiple networked sensors attached to the structure. This data is then…

The damped Gauss-Newton (dGN) algorithm for CANDECOMP/PARAFAC (CP) decomposition can handle the challenges of collinearity of factors and different magnitudes of factors; nevertheless, for factorization of an $N$-D tensor of size $I_1\times…

In general, algorithms for order-3 CANDECOMP/-PARAFAC (CP), also coined canonical polyadic decomposition (CPD), are easily to implement and can be extended to higher order CPD. Unfortunately, the algorithms become computationally demanding,…

Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets…

For reconstruction of low-rank matrices from undersampled measurements, we develop an iterative algorithm based on least-squares estimation. While the algorithm can be used for any low-rank matrix, it is also capable of exploiting a-priori…

A new implementation of the canonical polyadic decomposition (CPD) is presented. It features lower computational complexity and memory usage than the available state of art implementations available. The CPD of tensors is a challenging…

CANDECOMP/PARAFAC (CPD) approximates multiway data by sum of rank-1 tensors. Our recent study has presented a method to rank-1 tensor deflation, i.e. sequential extraction of the rank-1 components. In this paper, we extend the method to…

The (efficient and parsimonious) decomposition of higher-order tensors is a fundamental problem with numerous applications in a variety of fields. Several methods have been proposed in the literature to that end, with the Tucker and PARAFAC…

The Canonical Polyadic (CP) tensor decomposition is a well-known method for interpretable analysis of high-dimensional data. Recently, the Generalized CP method (GCP) was introduced by Hong and Kolda to allow for flexible choice of the loss…

Sparse tensors are prevalent in real-world applications, often characterized by their large-scale, high-order, and high-dimensional nature. Directly handling raw tensors is impractical due to the significant memory and computational…

We consider the problem of online subspace tracking of a partially observed high-dimensional data stream corrupted by noise, where we assume that the data lie in a low-dimensional linear subspace. This problem is cast as an online low-rank…

We introduce tensor Interpolative Decomposition (tensor ID) for the reduction of the separation rank of Canonical Tensor Decompositions (CTDs). Tensor ID selects, for a user-defined accuracy \epsilon, a near optimal subset of terms of a CTD…

In biomedical research and other fields, it is now common to generate high content data that are both multi-source and multi-way. Multi-source data are collected from different high-throughput technologies while multi-way data are collected…

Matrix factorization (MF) discovers latent features from observations, which has shown great promises in the fields of collaborative filtering, data compression, feature extraction, word embedding, etc. While many problem-specific…

Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We…

In numerous settings, it is increasingly common to deal with longitudinal data organized as high-dimensional multi-dimensional arrays, also known as tensors. Within this framework, the time-continuous property of longitudinal data often…

Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which…