Related papers: Spherical Matrix Factorization
In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
Approximate matrix factorization techniques with both nonnegativity and orthogonality constraints, referred to as orthogonal nonnegative matrix factorization (ONMF), have been recently introduced and shown to work remarkably well for…
Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…
Non-negative Matrix Factorisation (NMF) has been extensively used in machine learning and data analytics applications. Most existing variations of NMF only consider how each row/column vector of factorised matrices should be shaped, and…
Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…
For most optimisation methods an essential assumption is the vector space structure of the feasible set. This condition is not fulfilled if we consider optimisation problems over the sphere. We present an algorithm for solving a special…
Matrix Factorization (MF) has found numerous applications in Machine Learning and Data Mining, including collaborative filtering recommendation systems, dimensionality reduction, data visualization, and community detection. Motivated by the…
Matrix completion is one of the key problems in signal processing and machine learning. In recent years, deep-learning-based models have achieved state-of-the-art results in matrix completion. Nevertheless, they suffer from two drawbacks:…
Laplacian-based methods are popular for the dimensionality reduction of data lying in $\mathbb{R}^N$. Several theoretical results for these algorithms depend on the fact that the Euclidean distance locally approximates the geodesic distance…
Spherical k-Means is frequently used to cluster document collections because it performs reasonably well in many settings and is computationally efficient. However, the time complexity increases linearly with the number of clusters k, which…
We propose a linear time and constant space algorithm for computing Euclidean projections onto sets on which a normalized sparseness measure attains a constant value. These non-convex target sets can be characterized as intersections of a…
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…
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…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…
Automated per-instance algorithm selection and configuration have shown promising performances for a number of classic optimization problems, including satisfiability, AI planning, and TSP. The techniques often rely on a set of features…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…