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The Singular Value Decomposition (SVD) of matrices is a widely used tool in scientific computing. In many applications of machine learning, data analysis, signal and image processing, the large datasets are structured into tensors, for…
This paper discusses weighted tensor Golub-Kahan-type bidiagonalization processes using the t-product. This product was introduced in [M. E. Kilmer and C. D. Martin, Factorization strategies for third order tensors, Linear Algebra Appl.,…
This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tubal product (t-product). The random projection method is utilized to compute the…
To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the…
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…
Tensor decompositions are powerful tools for analyzing multi-dimensional data in their original format. Besides tensor decompositions like Tucker and CP, Tensor SVD (t-SVD) which is based on the t-product of tensors is another extension of…
This chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data. We describe SVD methods for visualization of gene expression data, representation of the data using a…
In this paper, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor…
Identity verification of authentic persons by their multiview faces is a real valued problem in machine vision. Multiview faces are having difficulties due to non-linear representation in the feature space. This paper illustrates the…
Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…
The tensor Singular Value Decomposition (t-SVD) for third order tensors that was proposed by Kilmer and Martin~\cite{2011kilmer} has been applied successfully in many fields, such as computed tomography, facial recognition, and video…
Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in…
Most recently, tensor-SVD is implemented on multi-view self-representation clustering and has achieved the promising results in many real-world applications such as face clustering, scene clustering and generic object clustering. However,…
In this paper a novel efficient method for representation of facial action units by encoding an image sequence as a fourth-order tensor is presented. The multilinear tensor-based extension of the biased discriminant analysis (BDA)…
In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently…
The big data era is swamping areas including data analysis, machine/deep learning, signal processing, statistics, scientific computing, and cloud computing. The multidimensional feature and huge volume of big data put urgent requirements to…
High-dimensional image data often require dimensionality reduction before further analysis. This paper provides a purely analytical comparison of two linear techniques-Principal Component Analysis (PCA) and Singular Value Decomposition…
In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…
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…
By representing documents as mixtures of topics, topic modeling has allowed the successful analysis of datasets across a wide spectrum of applications ranging from ecology to genetics. An important body of recent work has demonstrated the…