相关论文: Independent component analysis for tensor-valued d…

In this article, nonstationary mixing and source models are combined for developing new fast and accurate algorithms for Independent Component or Vector Extraction (ICE/IVE), one of which stands for a new extension of the well-known…

Tucker tensor decomposition offers a more effective representation for multiway data compared to the widely used PARAFAC model. However, its flexibility brings the challenge of selecting the appropriate latent multi-rank. To overcome the…

Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates…

Low-rank tensor completion has been widely used in computer vision and machine learning. This paper develops a novel multi-modal core tensor factorization (MCTF) method combined with a tensor low-rankness measure and a better nonconvex…

Bayesian optimization (BO) has been widely used to optimize expensive and black-box functions across various domains. However, existing BO methods have not addressed tensor-output functions. To fill this gap, we propose a novel…

Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral…

A new submodule clustering method via sparse and low-rank representation for multi-way data is proposed in this paper. Instead of reshaping multi-way data into vectors, this method maintains their natural orders to preserve data intrinsic…

The time-frequency map (TFM) is frequently used in condition monitoring, necessitating further processing to select an informative frequency band (IFB) or directly detect damage. However, selecting an IFB is challenging due to the…

We introduce tensor generalized bilateral inverses (TGBIs) under the Einstein tensor product as an extension of generalized bilateral inverses (GBIs) in the matrix environment. Moreover, the TBGI class includes so far considered composite…

Computational homogenization is the gold standard for concurrent multi-scale simulations (e.g., FE2) in scale-bridging applications. Experimental and synthetic material microstructures are often represented by 3D image data. The…

In this paper, we consider inference and uncertainty quantification for low Tucker rank tensors with additive noise in the high-dimensional regime. Focusing on the output of the higher-order orthogonal iteration (HOOI) algorithm, a commonly…

In this work, we study the problem of common and unique feature extraction from noisy data. When we have N observation matrices from N different and associated sources corrupted by sparse and potentially gross noise, can we recover the…

Independent component analysis (ICA) is a cornerstone of modern data analysis. Its goal is to recover a latent random vector S with independent components from samples of X=AS where A is an unknown mixing matrix. Critically, all existing…

The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this…

Many fMRI analyses examine functional connectivity, or statistical dependencies among remote brain regions. Yet popular methods for studying whole-brain functional connectivity often yield results that are difficult to interpret. Factor…

For statistical analysis of functional Magnetic Resonance Imaging (fMRI) data sets, we propose a data-driven approach based on Independent Component Analysis (ICA) implemented in a new version of the AnalyzeFMRI R package. For fMRI data…

We propose personalized Tucker decomposition (perTucker) to address the limitations of traditional tensor decomposition methods in capturing heterogeneity across different datasets. perTucker decomposes tensor data into shared global…

Cluster analysis is a fundamental tool for pattern discovery of complex heterogeneous data. Prevalent clustering methods mainly focus on vector or matrix-variate data and are not applicable to general-order tensors, which arise frequently…

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…

Tensor decomposition plays a key role in identifying common features across a collection of matrices in many areas of science. A fundamental need in big data research is to process data tabulated as large-scale matrices using eigenvectors.…