Related papers: Boolean matrix factorization meets consecutive one…
Matrix factorization is a fundamental method in statistics and machine learning for inferring and summarizing structure in multivariate data. Modern data sets often come with "side information" of various forms (images, text, graphs) that…
Probabilistic approach to Boolean matrix factorization can provide solutions robustagainst noise and missing values with linear computational complexity. However,the assumption about latent factors can be problematic in real world…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
Non-negative matrix factorization (NMF) has proved effective in many clustering and classification tasks. The classic ways to measure the errors between the original and the reconstructed matrix are $l_2$ distance or Kullback-Leibler (KL)…
This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to…
Non-negative matrix factorization (NMF) is a key technique for feature extraction and widely used in source separation. However, existing algorithms may converge to poor local minima, or to one of several minima with similar objective value…
In continuation to our recent work on noncommutative polynomial factorization, we consider the factorization problem for matrices of polynomials and show the following results. (1) Given as input a full rank $d\times d$ matrix $M$ whose…
We propose a new encoding of the first-order connection method as a Boolean satisfiability problem. The encoding eschews tree-like presentations of the connection method in favour of matrices, as we show that tree-like calculi have a number…
We consider bivariate polynomials over the skew field of quaternions, where the indeterminates commute with all coefficients and with each other. We analyze existence of univariate factorizations, that is, factorizations with univariate…
Bayesian model-based clustering is a widely applied procedure for discovering groups of related observations in a dataset. These approaches use Bayesian mixture models, estimated with MCMC, which provide posterior samples of the model…
Matrix factorization (MF) is a common method for collaborative filtering. MF represents user preferences and item attributes by latent factors. Despite that MF is a powerful method, it suffers from not be able to identifying strong…
In this paper we address the rotation synchronization problem, where the objective is to recover absolute rotations starting from pairwise ones, where the unknowns and the measures are represented as nodes and edges of a graph,…
Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a symmetric matrix with a product of a nonnegative, low-rank matrix and its transpose. To design faster and more…
We describe a graph-based neural acceleration technique for nonnegative matrix factorization that builds upon a connection between matrices and bipartite graphs that is well-known in certain fields, e.g., sparse linear algebra, but has not…
Graphs are a natural abstraction for many problems where nodes represent entities and edges represent a relationship across entities. An important area of research that has emerged over the last decade is the use of graphs as a vehicle for…
Identifying recurring patterns in high-dimensional time series data is an important problem in many scientific domains. A popular model to achieve this is convolutive nonnegative matrix factorization (CNMF), which extends classic…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…
Many problems can be presented in an abstract form through a wide range of binary objects and relations which are defined over problem domain. In these problems, graphical demonstration of defined binary objects and solutions is the most…
Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be…