相关论文: Harmonic Retrieval with $L_1$-Tucker Tensor Decomp…

In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…

Tensors naturally model many real world processes which generate multi-aspect data. Such processes appear in many different research disciplines, e.g, chemometrics, computer vision, psychometrics and neuroimaging analysis. Tensor…

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…

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…

Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…

The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…

Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…

We study symmetric tensor decompositions, i.e. decompositions of the input symmetric tensor T of order 3 as sum of r 3rd-order tensor powers of u_i where u_i are vectors in \C^n. In order to obtain efficient decomposition algorithms, it is…

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…

This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…

Big data analysis has become a crucial part of new emerging technologies such as the internet of things, cyber-physical analysis, deep learning, anomaly detection, etc. Among many other techniques, dimensionality reduction plays a key role…

The growing prevalence of tensor data, or multiway arrays, in science and engineering applications motivates the need for tensor decompositions that are robust against outliers. In this paper, we present a robust Tucker decomposition…

This paper studies the Tensor Robust Principal Component (TRPCA) problem which extends the known Robust PCA (Candes et al. 2011) to the tensor case. Our model is based on a new tensor Singular Value Decomposition (t-SVD) (Kilmer and Martin…

Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…

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…

Let us consider a case where all of the elements in some continuous slices are missing in tensor data. In this case, the nuclear-norm and total variation regularization methods usually fail to recover the missing elements. The key problem…

In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data. We consider the problem of recovering Gaussian mixture models from datasets. We investigate symmetric…

In this paper, we take a step towards developing efficient hard thresholding methods for low-rank tensor recovery from memory-efficient linear measurements with tensorial structure. Theoretical guarantees for many standard iterative…

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…

Comparing tensors and identifying their (dis)similar structures is fundamental in understanding the underlying phenomena for complex data. Tensor decomposition methods help analysts extract tensors' essential characteristics and aid in…