Related papers: Non-Euclidean Self-Organizing Maps
In some applications and in order to address real world situations better, data may be more complex than simple vectors. In some examples, they can be known through their pairwise dissimilarities only. Several variants of the Self…
Various topological techniques and tools have been applied to neural networks in terms of network complexity, explainability, and performance. One fundamental assumption of this line of research is the existence of a global (Euclidean)…
Different classes of communication network topologies and their representation in the form of adjacency matrix and its eigenvalues are presented. A self-organizing feature map neural network is used to map different classes of communication…
Numerous variants of Self-Organizing Maps (SOMs) have been proposed in the literature, including those which also possess an underlying structure, and in some cases, this structure itself can be defined by the user Although the concepts of…
Current deep learning architectures show remarkable performance when trained in large-scale, controlled datasets. However, the predictive ability of these architectures significantly decreases when learning new classes incrementally. This…
We propose a variation of the self organizing map algorithm by considering the random placement of neurons on a two-dimensional manifold, following a blue noise distribution from which various topologies can be derived. These topologies…
Recent progress on the question of the size of the class of connected and hyperconnected geometric morphisms from a given topos has led to the definition of {\em local state classifier}. We discuss a historical precedent which leads to the…
A special generic map is a smooth map regarded as a natural generalization of Morse functions with just 2 singular points on homotopy spheres. Canonical projections of unit spheres are simplest examples of such maps and manifolds admitting…
Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately current approaches fall short when the underlying space has a non trivial topology, and are only…
Self Organizing Map is trained using unsupervised learning to produce a two-dimensional discretized representation of input space of the training cases. Growing Hierarchical SOM is an architecture which grows both in a hierarchical way…
By means of hypercyclic operator theory, we complement our previous results on hypercyclic holomorphic maps between complex Euclidean spaces having slow growth rates,by showing {\it abstract abundance} rather than {\it explicit existence}.…
Attention is drawn to the possibility that self-organizing biological neural networks could spontaneously acquire the capability to carry out sophisticated computations. In particular it is shown that the effective action governing the…
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…
Chan, Har-Peled, and Jones [SICOMP 2020] developed locality-sensitive orderings (LSO) for Euclidean space. A $(\tau,\rho)$-LSO is a collection $\Sigma$ of orderings such that for every $x,y\in\mathbb{R}^d$ there is an ordering…
This paper proposes schemes for automated and weighted Self-Organizing Time Maps (SOTMs). The SOTM provides means for a visual approach to evolutionary clustering, which aims at producing a sequence of clustering solutions. This task we…
The configuration space of a non-linear sigma model is the space of maps from one manifold to another. This paper reviews the authors' work on non-linear sigma models with target a homogeneous space. It begins with a description of the…
The interpretation of ligand-target interactions at atomistic resolution is central to most efforts in computational drug discovery and optimization. However, the highly dynamic nature of protein targets, as well as possible induced fit…
The lack of generalization in learning-based autonomous driving applications is shown by the narrow range of road scenarios that vehicles can currently cover. A generalizable approach should capture many distinct road structures and…
We outline a possible theoretical framework for the quantitative modeling of networked embodied cognitive systems. We notice that: 1) information self structuring through sensory-motor coordination does not deterministically occur in Rn…
In order to perform complex actions in human environments, an autonomous robot needs the ability to understand the environment, that is, to gather and maintain spatial knowledge. Topological map is commonly used for representing large…