Related papers: Matrix Factorisation with Linear Filters

Matrix factorization (MF) is a versatile learning method that has found wide applications in various data-driven disciplines. Still, many MF algorithms do not adequately scale with the size of available datasets and/or lack…

Deep matrix factorizations (deep MFs) are recent unsupervised data mining techniques inspired by constrained low-rank approximations. They aim to extract complex hierarchies of features within high-dimensional datasets. Most of the loss…

Regularization is a popular technique to solve the overfitting problem of machine learning algorithms. Most regularization technique relies on parameter selection of the regularization coefficient. Plug-in method and cross-validation…

We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…

In this paper, we introduce and provide a short overview of nonnegative matrix factorization (NMF). Several aspects of NMF are discussed, namely, the application in hyperspectral imaging, geometry and uniqueness of NMF solutions,…

The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…

Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…

Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and…

The aim of this paper is twofold. First, we introduce a new class of linearizations, based on the generalization of a construction used in polynomial algebra to find the zeros of a system of (scalar) polynomial equations. We show that one…

Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…

We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…

Identifying informative components in binary data is an essential task in many research areas, including life sciences, social sciences, and recommendation systems. Boolean matrix factorization (BMF) is a family of methods that performs…

Various Non-negative Matrix factorization (NMF) based methods add new terms to the cost function to adapt the model to specific tasks, such as clustering, or to preserve some structural properties in the reduced space (e.g., local…

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…

Reinforcement learning has gained wide popularity as a technique for simulation-driven approximate dynamic programming. A less known aspect is that the very reasons that make it effective in dynamic programming can also be leveraged for…

Back-propagation with gradient method is the most popular learning algorithm for feed-forward neural networks. However, it is critical to determine a proper fixed learning rate for the algorithm. In this paper, an optimized recursive…

Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…

In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike…