Related papers: Multi-Dictionary Tensor Decomposition
This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to…
In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…
The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…
Exact recovery of tensor decomposition (TD) methods is a desirable property in both unsupervised learning and scientific data analysis. The numerical defects of TD methods, however, limit their practical applications on real-world data. As…
Time series data, including univariate and multivariate ones, are characterized by unique composition and complex multi-scale temporal variations. They often require special consideration of decomposition and multi-scale modeling to…
This article provides next step towards solving speed bottleneck of any system that intensively uses convolutions operations (e.g. CNN). Method described in the article is applied on deformable part models (DPM) algorithm. Method described…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
Feature extraction for tensor data serves as an important step in many tasks such as anomaly detection, process monitoring, image classification, and quality control. Although many methods have been proposed for tensor feature extraction,…
High-dimensional token embeddings underpin Large Language Models (LLMs), as they can capture subtle semantic information and significantly enhance the modelling of complex language patterns. However, this high dimensionality also introduces…
The growing use of neuroimaging technologies generates a massive amount of biomedical data that exhibit high dimensionality. Tensor-based analysis of brain imaging data has been proved quite effective in exploiting their multiway nature.…
We study the best low-rank Tucker decomposition of symmetric tensors. The motivating application is decomposing higher-order multivariate moments. Moment tensors have special structure and are important to various data science problems. We…
Tensor train (TT) decomposition has drawn people's attention due to its powerful representation ability and performance stability in high-order tensors. In this paper, we propose a novel approach to recover the missing entries of incomplete…
Producing large complex simulation datasets can often be a time and resource consuming task. Especially when these experiments are very expensive, it is becoming more reasonable to generate synthetic data for downstream tasks. Recently,…
Tensor classification is gaining importance across fields, yet handling partially observed data remains challenging. In this paper, we introduce a novel approach to tensor classification with incomplete data, framed within high-dimensional…
Deep neural networks (DNNs) have enabled impressive breakthroughs in various artificial intelligence (AI) applications recently due to its capability of learning high-level features from big data. However, the current demand of DNNs for…
Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…
Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…
Dynamic community detection plays a crucial role in understanding the temporal evolution of community structures in complex networks. Existing methods based on nonnegative tensor RESCAL decomposition typically require the decomposition rank…
The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a…
Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomposition of large-scale tensors. GCP tensor decomposition is…