arXiv research

Paper characterizes optimization landscape of Tucker decomposition.

FunBaT extends Tucker decomposition to handle continuous-indexed tensor data.

The emerging edge computing has promoted immense interests in compacting a neural network without sacrificing much accuracy. In this regard, low-rank tensor decomposition constitutes a powerful tool to compress convolutional neural networks (CNNs) by decomposing the 4-way kernel tensor into multi-stage smaller ones. Bu…

NA$_0$CT$^2$ improves tensor regression predictions with $\ell_0$ regularization.

A new probabilistic BTD method for tensor data.

Adaptive tensor modeling preserves continuity in multidimensional data.

Sparse Tucker decomposition with graph regularization improves time series forecasting accuracy.

Paper proposes BTuD for unsupervised feature selection.

Unified model for tensor completion using low-rank and sparse Tucker decomposition.

This work improves tensor decomposition methods, especially for large datasets.

A new kernel improves tensor classification accuracy and reduces computation time.

Paper studies nonnegative Tucker decomposition identifiability with sparsity conditions.

Knowledge graphs are structured representations of real world facts. However, they typically contain only a small subset of all possible facts. Link prediction is a task of inferring missing facts based on existing ones. We propose TuckER, a relatively straightforward but powerful linear model based on Tucker decomposi…

AL$\ell_0$CORE tensor decomposition reduces computational cost for sparse count data.

Paper compresses RNNs using HT decomposition for better performance.

A new method for traffic data imputation considering spatiotemporal correlations.

In this paper, we study the nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD). We discuss some properties of ONTD and develop a convex relaxation algorithm of the augmented Lagrangian function to solve the optimization problem. The convergence of the algorithm is given. We employ…

Optimizes neural network training by dynamically updating Tucker decomposition ranks.

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

A new diffusion model generates structured tensors for high-dimensional data.

We analyze large, multi-dimensional, sparse counting data sets, finding unsupervised groups to provide unique insights into genetic data. We create gene and biological pathway groups based on patients' variants to find common risk factors for four common types of cancer (breast, lung, prostate, and colorectal) and auti…

Infinite Tucker Decomposition (InfTucker) and random function prior models, as nonparametric Bayesian models on infinite exchangeable arrays, are more powerful models than widely-used multilinear factorization methods including Tucker and PARAFAC decomposition, (partly) due to their capability of modeling nonlinear rel…

Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a generative model that can capture specific syntactic relations between words. Under our …

Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of data. However, as the data tensor often has multiple modes and is large-scale, exist…

We introduce Bayesian Poisson Tucker decomposition (BPTD) for modeling country--country interaction event data. These data consist of interaction events of the form "country $i$ took action $a$ toward country $j$ at time $t$." BPTD discovers overlapping country--community memberships, including the number of latent com…

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

Paper introduces a new histogram estimator for nonparametric density estimation that improves performance.

Proposes a low-rank bilinear pooling model for link prediction in knowledge graphs.

Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging problem is related to determination of model complexity (i.e., multilinear rank), e…

Paper learns meaningful state and action representations from MDP trajectories.

New tensor model reduces GLM estimation error and sample complexity.

Overcomplete latent representations have been very popular for unsupervised feature learning in recent years. In this paper, we specify which overcomplete models can be identified given observable moments of a certain order. We consider probabilistic admixture or topic models in the overcomplete regime, where the numbe…

New model for network analysis using functional data.

Portfolio allocation and risk management make use of correlation matrices and heavily rely on the choice of a proper correlation matrix to be used. In this regard, one important question is related to the choice of the proper sample period to be used to estimate a stable correlation matrix. This paper addresses this qu…

Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (Smo…

Unified algorithm for tensor decomposition supports multiple loss functions and models.

This work is devoted to elaboration on the idea to use block term decomposition for group data analysis and to raise the possibility of modelling group activity with (Lr, 1) and Tucker blocks. A new generalization of block tensor decomposition was considered in application to group data analysis. Suggested approach was…

Paper introduces TSSDMN for modeling dynamic multilayer networks.

Extends RRR to capture nonlinear interactions in multi-response regression.

This work proposes a novel approach for multiple time series forecasting. At first, multi-way delay embedding transform (MDT) is employed to represent time series as low-rank block Hankel tensors (BHT). Then, the higher-order tensors are projected to compressed core tensors by applying Tucker decomposition. At the same…

Proposes a method for tensor completion with sparse factors and missing data.

We propose the Relational Tucker3 (RT) decomposition for multi-relational link prediction in knowledge graphs. We show that many existing knowledge graph embedding models are special cases of the RT decomposition with certain predefined sparsity patterns in its components. In contrast to these prior models, RT decouple…

Optimizes tensor rank selection for neural network compression.

Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to repres…

Motivation: How do we integratively analyze large-scale multi-platform genomic data that are high dimensional and sparse? Furthermore, how can we incorporate prior knowledge, such as the association between genes, in the analysis systematically? Method: To solve this problem, we propose a Scalable Network Constrained T…

Autoregressive networks can achieve promising performance in many sequence modeling tasks with short-range dependence. However, when handling high-dimensional inputs and outputs, the huge amount of parameters in the network lead to expensive computational cost and low learning efficiency. The problem can be alleviated …

New method accelerates CNNs for mobile devices by approximating tensors and quantizing weights.

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