相关论文: Cartes auto-organis\'{e}es pour l'analyse explorat…
The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained…
This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important…
Spatio-temporal data is intrinsically high dimensional, so unsupervised modeling is only feasible if we can exploit structure in the process. When the dynamics are local in both space and time, this structure can be exploited by splitting…
This work describes the implementation and application of a correlation determination method based on Self Organizing Maps and Bayesian Inference (SOMBI). SOMBI aims to automatically identify relations between different observed parameters…
This article is dedicated to the memory of Vadim Kuznetsov, and begins with some of the author's recollections of him. Thereafter, a brief review of Somos sequences is provided, with particular focus being made on the integrable structure…
In this work, we consider the problem of Quality-Diversity (QD) optimization with multiple objectives. QD algorithms have been proposed to search for a large collection of both diverse and high-performing solutions instead of a single set…
A multimodal system with Poisson, Gaussian, and multinomial observations is considered. A generative graphical model that combines multiple modalities through common factor loadings is proposed. In this model, latent factors are like…
Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…
Self-organizing maps (SOM) are widely used for their topology preservation property: neighboring input vectors are quantified (or classified) either on the same location or on neighbor ones on a predefined grid. SOM are also widely used for…
We address the problem related to the extraction of the information in the simulation of complex dynamics quantum computation. Here we present an example where important information can be extracted efficiently by means of quantum…
This paper takes an information visualization perspective to visual representations in the general SOM paradigm. This involves viewing SOM-based visualizations through the eyes of Bertin's and Tufte's theories on data graphics. The regular…
The Self-Organizing Map (SOM) is a brain-inspired neural model that is very promising for unsupervised learning, especially in embedded applications. However, it is unable to learn efficient prototypes when dealing with complex datasets. We…
The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement, then by an advanced study launched by the Direction de la Recherche et des Etudes Technologiques in France in…
We examine a general framework for visualizing datasets of high (> 2) dimensionality, and demonstrate it using the morphology of galaxies at moderate redshifts. The distributions of various populations of such galaxies are examined in a…
The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…
In many research fields, the sizes of the existing datasets vary widely. Hence, there is a need for machine learning techniques which are well-suited for these different datasets. One possible technique is the self-organizing map (SOM), a…
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…
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…
The ${\mathcal D}$-pseudo-boson formalism is illustrated with two examples. The first one involves deformed complex Hermite polynomials built using finite-dimensional irreducible representations of the group ${\rm GL}(2,{\mathbb C})$ of…
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…