Related papers: Dictionary-based Low-Rank Approximations and the M…
Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements.…
In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue…
In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the…
In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…
Sparse matrix factorization is the problem of approximating a matrix $\mathbf{Z}$ by a product of $J$ sparse factors $\mathbf{X}^{(J)} \mathbf{X}^{(J-1)} \ldots \mathbf{X}^{(1)}$. This paper focuses on identifiability issues that appear in…
It is well known that in a supervised classification setting when the number of features is smaller than the number of observations, Fisher's linear discriminant rule is asymptotically Bayes. However, there are numerous modern applications…
We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…
In this paper, we present an efficient algorithm to sample random sparse matrices to be used as check matrices for quantum Low-Density Parity-Check (LDPC) codes. To ease the treatment, we mainly describe our algorithm as a technique to…
Low-Rank Adaptation (LoRA) has emerged as one of the most effective, computationally tractable fine-tuning approaches for training Vision-Language Models (VLMs) and Large Language Models (LLMs). LoRA accomplishes this by freezing the…
For subspace recovery, most existing low-rank representation (LRR) models performs in the original space in single-layer mode. As such, the deep hierarchical information cannot be learned, which may result in inaccurate recoveries for…
We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the…
In this paper we consider the problem of clustering collections of very short texts using subspace clustering. This problem arises in many applications such as product categorisation, fraud detection, and sentiment analysis. The main…
Nonnegative Matrix Factorization (NMF) with Kullback-Leibler Divergence (NMF-KL) is one of the most significant NMF problems and equivalent to Probabilistic Latent Semantic Indexing (PLSI), which has been successfully applied in many…
It is common in modern prediction problems for many predictor variables to be counts of rarely occurring events. This leads to design matrices in which many columns are highly sparse. The challenge posed by such "rare features" has received…
The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning. Deep learning, however, with its carefully designed hierarchical structure,…
Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…
We present a probabilistic modeling and inference framework for discriminative analysis dictionary learning under a weak supervision setting. Dictionary learning approaches have been widely used for tasks such as low-level signal denoising…
We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class…
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…