Related papers: Non-Euclidean Self-Organizing Maps
In magnetospheric missions, burst mode data sampling should be triggered in the presence of processes of scientific or operational interest. We present an unsupervised classification method for magnetospheric regions, that could constitute…
A novel class of derivative-free optimization algorithms is developed. The main idea is to utilize certain non-commutative maps in order to approximate the gradient of the objective function. Convergence properties of the novel algorithms…
Self-Organizing Maps are models for unsupervised representation formation of cortical receptor fields by stimuli-driven self-organization in laterally coupled winner-take-all feedforward structures. This paper discusses modifications of the…
We solve the problem of describing all nonlocal Hamiltonian operators of hydrodynamic type with flat metrics. This problem is also equivalent to the description of all flat submanifolds with flat normal bundle in a pseudo-Euclidean space.…
Graph neural networks (GNNs) provide a powerful and scalable solution for modeling continuous spatial data. However, they often rely on Euclidean distances to construct the input graphs. This assumption can be improbable in many real-world…
We describe parametrised motion planning algorithms for systems controlling objects represented by points that move without collisions in an even dimensional Euclidean space and in the presence of up to three obstacles with \emph{a priori}…
In this paper we introduce a family of planar, modular and self-similar graphs which have small-world and scale-free properties. The main parameters of this family are comparable to those of networks associated to complex systems, and…
In this paper we address the problem of unsupervised localization of objects in single images. Compared to previous state-of-the-art method our method is fully unsupervised in the sense that there is no prior instance level or category…
A unicellular map is the embedding of a connected graph in a surface in such a way that the complement of the graph is a topological disk. In this paper we present a bijective link between unicellular maps on a non-orientable surface and…
Median clustering extends popular neural data analysis methods such as the self-organizing map or neural gas to general data structures given by a dissimilarity matrix only. This offers flexible and robust global data inspection methods…
Non-autonomous self-similar sets are a family of compact sets which are, in some sense, highly homogeneous in space but highly inhomogeneous in scale. The main purpose of this note is to clarify various regularity properties and separation…
Self-organization of orientation-wheels observed in the visual cortex is discussed from the view point of topology. We argue in a generalized model of Kohonen's feature mappings that the existence of the orientation-wheels is a consequence…
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…
Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
This paper considers generalised network, intended as networks where (a) the edges connecting the nodes are nonlinear, and (b) stochastic processes are continuously indexed over both vertices and edges. Such topological structures are…
A new approach to data stream clustering with the help of an ensemble of adaptive neuro-fuzzy systems is proposed. The proposed ensemble is formed with adaptive neuro-fuzzy self-organizing Kohonen maps in a parallel processing mode. A final…
In this paper, we propose a novel self-supervised representation learning method, Self-EMD, for object detection. Our method directly trained on unlabeled non-iconic image dataset like COCO, instead of commonly used iconic-object image…
We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambient space. Our framework accommodates manifolds with…
Symmetry in biological and physical systems is a product of self organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry based feature extrac-tion or representation by neural networks may unravel the…