相关论文: A geometrical setting for the classification of mu…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
Algebraic geometry, although little explored in signal processing, provides tools that are very convenient for investigating generic properties in a wide range of applications. Generic properties are properties that hold "almost…
Despite the prominence of neural network approaches in the field of recommender systems, simple methods such as matrix factorization with quadratic loss are still used in industry for several reasons. These models can be trained with…
We prove a generalization of Orlov's theorem for matrix factorizations with $n$ steps. Let $X$ be a regular scheme, $W\colon X\to \mathbb{A}^1$ a flat morphism and $D:=W^{-1}(0)$ its central fiber. We construct an appropriate triangulated…
Multilayer bootstrap network builds a gradually narrowed multilayer nonlinear network from bottom up for unsupervised nonlinear dimensionality reduction. Each layer of the network is a nonparametric density estimator. It consists of a group…
We consider the problem of classification of an object given multiple observations that possibly include different transformations. The possible transformations of the object generally span a low-dimensional manifold in the original signal…
We study categories of matrix factorizations. These categories are defined for any regular function on a suitable regular scheme. Our paper has two parts. In the first part we develop the foundations; for example we discuss derived direct…
We learn multiple hypotheses for related tasks under a latent hierarchical relationship between tasks. We exploit the intuition that for domain adaptation, we wish to share classifier structure, but for multitask learning, we wish to share…
We learn multiple hypotheses for related tasks under a latent hierarchical relationship between tasks. We exploit the intuition that for domain adaptation, we wish to share classifier structure, but for multitask learning, we wish to share…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA),…
In the context of applying the Lorentz group theory to polarization optics in the frames of Stokes-Mueller formalism, some properties of the Lorentz group are investigated. We start with the factorized form of arbitrary Lorentz matrix as a…
We propose a novel analytical model for anisotropic multi-layer cylindrical structures containing graphene layers. The general structure is formed by an aperiodic repetition of a three-layer sub-structure, where a graphene layer, with an…
Developing learning methods which do not discriminate subgroups in the population is a central goal of algorithmic fairness. One way to reach this goal is by modifying the data representation in order to meet certain fairness constraints.…
This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…
Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis,…
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…
Learning the similarity between images constitutes the foundation for numerous vision tasks. The common paradigm is discriminative metric learning, which seeks an embedding that separates different training classes. However, the main…
The method of factorization, based on the model of unstable particles with a smeared mass, is applied to the processes with an unstable particle in the intermediate state. It was shown, that in the framework of the method suggested, the…