相关论文: Tensor Completion via Convolutional Sparse Coding …

We present sparse topical coding (STC), a non-probabilistic formulation of topic models for discovering latent representations of large collections of data. Unlike probabilistic topic models, STC relaxes the normalization constraint of…

Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor…

Convolutional neural networks (CNN) have led to many state-of-the-art results spanning through various fields. However, a clear and profound theoretical understanding of the forward pass, the core algorithm of CNN, is still lacking. In…

In this paper, we propose a novel model to recover a low-rank tensor by simultaneously performing double nuclear norm regularized low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An block successive…

This paper addresses the color image completion problem in accordance with low-rank quatenrion matrix optimization that is characterized by sparse regularization in a transformed domain. This research was inspired by an appreciation of the…

Tensor completion is the problem of estimating the missing values of high-order data from partially observed entries. Data corruption due to prevailing outliers poses major challenges to traditional tensor completion algorithms, which…

We present the multi-layer extension of the Sparse Ternary Codes (STC) for fast similarity search where we focus on the reconstruction of the database vectors from the ternary codes. To consider the trade-offs between the compactness of the…

Low-Rank Tensor Completion, a method which exploits the inherent structure of tensors, has been studied extensively as an effective approach to tensor completion. Whilst such methods attained great success, none have systematically…

We present a novel feature selection technique, Sparse Linear Centroid-Encoder (SLCE). The algorithm uses a linear transformation to reconstruct a point as its class centroid and, at the same time, uses the $\ell_1$-norm penalty to filter…

We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix…

In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…

This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model…

Tensor completion is crucial in many scientific domains with missing data problems. Traditional low-rank tensor models, including CP, Tucker, and Tensor-Train, exploit low-dimensional structures to recover missing data. However, these…

In representation learning, Convolutional Sparse Coding (CSC) enables unsupervised learning of features by jointly optimising both an \(\ell_2\)-norm fidelity term and a sparsity enforcing penalty. This work investigates using a…

Low rank tensor ring model is powerful for image completion which recovers missing entries in data acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization…

Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either…

Dimension reduction techniques are often used when the high-dimensional tensor has relatively low intrinsic rank compared to the ambient dimension of the tensor. The CANDECOMP/PARAFAC (CP) tensor completion is a widely used approach to find…

Recently the sparse representation based classification (SRC) has been proposed for robust face recognition (FR). In SRC, the testing image is coded as a sparse linear combination of the training samples, and the representation fidelity is…

Convolutional neural network (CNN) and its variants have led to many state-of-art results in various fields. However, a clear theoretical understanding about them is still lacking. Recently, multi-layer convolutional sparse coding (ML-CSC)…

The tensor data recovery task has thus attracted much research attention in recent years. Solving such an ill-posed problem generally requires to explore intrinsic prior structures underlying tensor data, and formulate them as certain forms…