Related papers: A Tensor SVD-based Classification Algorithm Applie…
Trajectory data, including time series and longitudinal measurements, are increasingly common in health-related domains such as biomedical research and epidemiology. Real-world trajectory data frequently exhibit heterogeneity across…
This paper focus on recovering multi-dimensional data called tensor from randomly corrupted incomplete observation. Inspired by reweighted $l_1$ norm minimization for sparsity enhancement, this paper proposes a reweighted singular value…
A novel method for common and individual feature analysis from exceedingly large-scale data is proposed, in order to ensure the tractability of both the computation and storage and thus mitigate the curse of dimensionality, a major…
Accurate and early diagnosis of pneumonia through X-ray imaging is essential for effective treatment and improved patient outcomes. Recent advancements in machine learning have enabled automated diagnostic tools that assist radiologists in…
Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on…
Tensor data with rich structural information becomes increasingly important in process modeling, monitoring, and diagnosis. Here structural information is referred to structural properties such as sparsity, smoothness, low-rank, and…
Recently, tensor singular value decomposition (t-SVD) has emerged as a promising tool for hyperspectral image (HSI) processing. In the t-SVD, there are two key building blocks: (i) the low-rank enhanced transform and (ii) the accompanying…
Coupled decompositions are a widely used tool for data fusion. As the volume of data increases, so does the dimensionality of matrices and tensors, highlighting the need for more efficient coupled decomposition algorithms. This paper…
The Randomized Singular Value Decomposition (RSVD) is a widely used algorithm for efficiently computing low-rank approximations of large matrices, without the need to construct a full-blown SVD. Of interest, of course, is the approximation…
In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…
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,…
The randomized singular value decomposition (SVD) is a popular and effective algorithm for computing a near-best rank $k$ approximation of a matrix $A$ using matrix-vector products with standard Gaussian vectors. Here, we generalize the…
The Singular Value Decomposition (SVD) is one of the most important matrix factorizations, enjoying a wide variety of applications across numerous application domains. In statistics and data analysis, the common applications of SVD such as…
We present TensoRF, a novel approach to model and reconstruct radiance fields. Unlike NeRF that purely uses MLPs, we model the radiance field of a scene as a 4D tensor, which represents a 3D voxel grid with per-voxel multi-channel features.…
This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…
The Large Margin Distribution Machine (LMDM) is a recent advancement in classifier design that optimizes not just the minimum margin (as in SVM) but the entire margin distribution, thereby improving generalization. However, existing LMDM…
Vision-Language Models (VLMs) have revolutionized multi-modal learning by jointly processing visual and textual information. Yet, they face significant challenges due to the high computational and memory demands of processing long sequences…
In this paper, we investigate tensor recovery problems within the tensor singular value decomposition (t-SVD) framework. We propose the partial sum of the tubal nuclear norm (PSTNN) of a tensor. The PSTNN is a surrogate of the tensor tubal…
While low-rank matrix prior has been exploited in dynamic MR image reconstruction and has obtained satisfying performance, tensor low-rank models have recently emerged as powerful alternative representations for three-dimensional dynamic MR…
This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries. Our study rests heavily on a recently proposed tensor algebraic…