Related papers: Non-Euclidean Self-Organizing Maps

We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the…

We study the statistical meaning of the minimization of distortion measure and the relation between the equilibrium points of the SOM algorithm and the minima of distortion measure. If we assume that the observations and the map lie in an…

A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of…

Nowadays, with the advance of technology, there is an increasing amount of unstructured data being generated every day. However, it is a painful job to label and organize it. Labeling is an expensive, time-consuming, and difficult task. It…

The self-organizing map (SOM) is an unsupervised artificial neural network that is widely used in, e.g., data mining and visualization. Supervised and semi-supervised learning methods have been proposed for the SOM. However, their teacher…

This work presents a mathematical treatment of the relation between Self-Organizing Maps (SOMs) and Gaussian Mixture Models (GMMs). We show that energy-based SOM models can be interpreted as performing gradient descent, minimizing an…

Some argue that biologically inspired algorithms are the future of solving difficult problems in computer science. Others strongly believe that the future lies in the exploration of mathematical foundations of problems at hand. The field of…

Leachates from garbage dumps can significantly compromise their surrounding area. Even if the distance between these and the populated areas could be considerable, the risk of affecting the aquifers for public use is imminent in most cases.…

Self-organizing map(SOM) have been widely applied in clustering, this paper focused on centroids of clusters and what they reveal. When the input vectors consists of time, latitude and longitude, the map can be strongly linked to physical…

In this paper, a new implementation of the adaptation of Kohonen self-organising maps (SOM) to dissimilarity matrices is proposed. This implementation relies on the branch and bound principle to reduce the algorithm running time. An…

In the recent years, there is a growing interest in semi-supervised learning, since, in many learning tasks, there is a plentiful supply of unlabeled data, but insufficient labeled ones. Hence, Semi-Supervised learning models can benefit…

We introduce a multidimensional, neural-network approach to reveal and measure urban segregation phenomena, based on the Self-Organizing Map algorithm (SOM). The multidimensionality of SOM allows one to apprehend a large number of variables…

This paper presents a novel time series clustering method, the self-organising eigenspace map (SOEM), based on a generalisation of the well-known self-organising feature map (SOFM). The SOEM operates on the eigenspaces of the embedded…

We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces $\ell_1$ and $\ell_{\infty}$. We first establish properties of mappings which are monotone with respect to the non-Euclidean norms…

In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with…

In numerous applicative contexts, data are too rich and too complex to be represented by numerical vectors. A general approach to extend machine learning and data mining techniques to such data is to really on a dissimilarity or on a kernel…

In the era of foundation models and Large Language Models (LLMs), Euclidean space is the de facto geometric setting of our machine learning architectures. However, recent literature has demonstrated that this choice comes with fundamental…

In this paper we address an important economic question. Is there, as mainstream economic theory asserts it, an homogeneous labor market with mechanisms which govern supply and demand for work, producing an equilibrium with its remarkable…

Websites of a particular class form increasingly complex networks, and new tools are needed to map and understand them. A way of visualizing this complex network is by mapping it. A map highlights which members of the community have similar…

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data…