相关论文: Matrix tri-factorization over the tropical semirin…

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:…

Dimensionality reduction is considered as an important step for ensuring competitive performance in unsupervised learning such as anomaly detection. Non-negative matrix factorization (NMF) is a popular and widely used method to accomplish…

Much work on social media opinion polarization focuses on a flat categorization of stances (or orthogonal beliefs) of different communities from media traces. We extend in this work in two important respects. First, we detect not only…

Since many real-world data can be described from multiple views, multi-view learning has attracted considerable attention. Various methods have been proposed and successfully applied to multi-view learning, typically based on matrix…

We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise…

Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative…

Non-negative matrix factorization (NMF) is a common method for generating topic models from text data. NMF is widely accepted for producing good results despite its relative simplicity of implementation and ease of computation. One…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

We introduce a new method based on nonnegative matrix factorization, Neural NMF, for detecting latent hierarchical structure in data. Datasets with hierarchical structure arise in a wide variety of fields, such as document classification,…

The backpropagation algorithm for calculating gradients has been widely used in computation of weights for deep neural networks (DNNs). This method requires derivatives of objective functions and has some difficulties finding appropriate…

Clustering on the data with multiple aspects, such as multi-view or multi-type relational data, has become popular in recent years due to their wide applicability. The approach using manifold learning with the Non-negative Matrix…

Semiring algebras have been shown to provide a suitable language to formalize many noteworthy combinatorial problems. For instance, the Shortest-Path problem can be seen as a special case of the Algebraic-Path problem when applied to the…

Matrix multiplication optimization remains a fundamental challenge in computational mathematics. This work introduces a novel approach that discovers matrix multiplication schemes whose coefficients are restricted to the set $\{-1, 0, 1\}$…

This paper investigates the hybrid precoding design for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems with finite-alphabet inputs. The precoding problem is a joint optimization of analog and digital precoders, and…

Although many techniques have been applied to matrix factorization (MF), they may not fully exploit the feature structure. In this paper, we incorporate the grouping effect into MF and propose a novel method called Robust Matrix…

We consider optimization problems that are formulated and solved in the framework of tropical mathematics. The problems consist in minimizing or maximizing functionals defined on vectors of finite-dimensional semimodules over idempotent…

Dynamic graph clustering aims to detect and track time-varying clusters in dynamic graphs, revealing the evolutionary mechanisms of complex real-world dynamic systems. Matrix factorization-based methods are promising approaches for this…

Many networks including social networks, computer networks, and biological networks are found to divide naturally into communities of densely connected individuals. Finding community structure is one of fundamental problems in network…

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…

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…