相关论文: Multi-dimensional Signal Recovery using Low-rank D…

The ability of capturing fine spectral discriminative information enables hyperspectral images (HSIs) to observe, detect and identify objects with subtle spectral discrepancy. However, the captured HSIs may not represent true distribution…

With the rapid growth of web images, hashing has received increasing interests in large scale image retrieval. Research efforts have been devoted to learning compact binary codes that preserve semantic similarity based on labels. However,…

We propose a modular framework for multi-relational learning via tensor decomposition. In our learning setting, the training data contains multiple types of relationships among a set of objects, which we represent by a sparse three-mode…

Finding semantic correspondences is a challenging problem. With the breakthrough of CNNs stronger features are available for tasks like classification but not specifically for the requirements of semantic matching. In the following we…

It has been recently shown that incorporating priori knowledge significantly improves the performance of basic compressive sensing based approaches. We have managed to successfully exploit this idea for recovering a matrix as a summation of…

The decoupling of multivariate functions is a powerful modeling paradigm for learning multivariate input-output relations from data. For the single-layer case, established CPD-based methods are available, but the multi-layer case remained…

Often, large, high dimensional datasets collected across multiple modalities can be organized as a higher order tensor. Low-rank tensor decomposition then arises as a powerful and widely used tool to discover simple low dimensional…

Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time…

Convolutional neural networks have been proven effective in a variety of image restoration tasks. Most state-of-the-art solutions, however, are trained using images with a single particular degradation level, and their performance…

Intrinsic image decomposition is an important and long-standing computer vision problem. Given an input image, recovering the physical scene properties is ill-posed. Several physically motivated priors have been used to restrict the…

Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…

Recent advances in representation learning reveal that widely used objectives, such as contrastive and non-contrastive, implicitly perform spectral decomposition of a contextual kernel, induced by the relationship between inputs and their…

The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically…

Learning powerful feature representations for image retrieval has always been a challenging task in the field of remote sensing. Traditional methods focus on extracting low-level hand-crafted features which are not only time-consuming but…

Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…

We consider the problem of recovering two unknown vectors, $\boldsymbol{w}$ and $\boldsymbol{x}$, of length $L$ from their circular convolution. We make the structural assumption that the two vectors are members of known subspaces, one with…

Low-rank structures play important role in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold…

The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…

Protein function is inherently linked to its localization within the cell, and fluorescent microscopy data is an indispensable resource for learning representations of proteins. Despite major developments in molecular representation…

Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…