Related papers: Self Organizing Map algorithm and distortion measu…

This paper introduces the concept of a bi-scale metric for use in the cooperative phase of the self-organizing map (SOM) algorithm. Use of a bi-scale metric allows segmentation of the map into a number of regions, corresponding to…

This paper shows how to use the Kohonen algorithm to represent multidimensional data, by exploiting the self-organizing property. It is possible to get such maps as well for quantitative variables as for qualitative ones, or for a mixing of…

We establish quantitative stability results for classical distortion minimization problems in the theory of quasiconformal mappings. We consider the mean distortion functional and prove sharp stability estimates for the minimization…

Optimal transport maps and plans between two absolutely continuous measures $\mu$ and $\nu$ can be approximated by solving semi-discrete or fully-discrete optimal transport problems. These two problems ensue from approximating $\mu$ or both…

Self-Organizing Maps (SOM) are a classical method for unsupervised learning, vector quantization, and topographic mapping of high-dimensional data. However, existing SOM formulations often involve a trade-off between computational…

In this paper we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance…

Self-Organizing Maps (SOMs) provide topology-preserving projections of high-dimensional data, yet their use as generative models remains largely unexplored. We show that the activation pattern of a SOM -- the squared distances to its…

We propose to use Self-Organizing Maps (SOM) to map the impact of physical models onto observables. Using this approach, we are be able to determine how theories relate to each other given their signatures. In cosmology this will be…

In this work, we present the development of a neuro-inspired approach for characterizing sensorimotor relations in robotic systems. The proposed method has self-organizing and associative properties that enable it to autonomously obtain…

This article is concerned with the numerical solution of subspace optimization problems, consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed rank. Such problems are encountered in particular in…

A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…

A behavior of one class of mappings with finite distortion at a neighborhood of the origin is investigated. There is proved a lower estimate of distortion of a distance under mappings mentioned above.

Based on a quantitative version of the inverse function theorem and an appropriate saddle-point formulation we derive a quasi-optimal error estimate for the finite element approximation of harmonic maps into spheres with a nodal…

Kohonen's Adaptive Subspace Self-Organizing Map (ASSOM) learns several subspaces of the data where each subspace represents some invariant characteristics of the data. To deal with the imbalance classification problem, earlier we have…

Suppose that we have $n$ agents and $n$ items which lie in a shared metric space. We would like to match the agents to items such that the total distance from agents to their matched items is as small as possible. However, instead of having…

In this paper, we explore the two-point zeroth-order gradient estimator and identify the distribution of random perturbations that minimizes the estimator's asymptotic variance as the perturbation stepsize tends to zero. We formulate it as…

There has been an increasing interest in semi-supervised learning in the recent years because of the great number of datasets with a large number of unlabeled data but only a few labeled samples. Semi-supervised learning algorithms can work…

This paper addresses the case where data come as point sets, or more generally as discrete measures. Our motivation is twofold: first we intend to approximate with a compactly supported measure the mean of the measure generating process,…

We propose a Parton Distribution Function (PDF) fitting technique which is based on an interactive neural network algorithm using Self-Organizing Maps (SOMs). SOMs are visualization algorithms based on competitive learning among…

Finding an approximate second-order stationary point (SOSP) is a well-studied and fundamental problem in stochastic nonconvex optimization with many applications in machine learning. However, this problem is poorly understood in the…