ASAP – A sub-sampling approach for preserving topological structures modeled with geodesic topographic mapping

Taghribi, Abolfazl; Canducci, Marco; Rijcke, S. De; Bunte, Kerstin; Tiňo, Peter

doi:10.1016/j.neucom.2021.05.108

Cited by 7 publications

(3 citation statements)

References 26 publications

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“…Learning on topological structures like manifolds and subspaces follows the same framework, considering attraction and repulsing more general in the respective vector spaces [ 57 , 58 ]. An interesting variant, where the prototypes are spherically adapted according to an ARS to keep them on a hypersphere, was proposed—denoted as Angle-LVQ [ 59 ].…”

Section: Vector Quantizationmentioning

confidence: 99%

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Quantum Computing Approaches for Vector Quantization—Current Perspectives and Developments

Engelsberger

Villmann

2023

Entropy

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In the field of machine learning, vector quantization is a category of low-complexity approaches that are nonetheless powerful for data representation and clustering or classification tasks. Vector quantization is based on the idea of representing a data or a class distribution using a small set of prototypes, and hence, it belongs to interpretable models in machine learning. Further, the low complexity of vector quantizers makes them interesting for the application of quantum concepts for their implementation. This is especially true for current and upcoming generations of quantum devices, which only allow the execution of simple and restricted algorithms. Motivated by different adaptation and optimization paradigms for vector quantizers, we provide an overview of respective existing quantum algorithms and routines to realize vector quantization concepts, maybe only partially, on quantum devices. Thus, the reader can infer the current state-of-the-art when considering quantum computing approaches for vector quantization.

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Section: Vector Quantizationmentioning

confidence: 99%

“…From a mathematical point of view, the qSLERP approach is similar to the update used in Angle-LVQ [ 59 ] for non-quantum systems.…”

Section: Quantum Approaches For Vector Quantizationmentioning

confidence: 99%

Quantum Computing Approaches for Vector Quantization—Current Perspectives and Developments

Engelsberger

Villmann

2023

Entropy

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“…In other words, the distribution of particles forming a given noisy manifold will be attributed a likelihood to belong to the manifold since the structure will be modelled as a mixture of Gaussian probability distributions. In this work, the manifolds are considered to be one-dimensional, however previous work demonstrated the efficiency of this modelling technique for higher dimensional manifolds with unknown topology (Canducci et al 2022b) or given spherical topology (Canducci et al 2021;Taghribi et al 2022b).…”

Section: Sgtmmentioning

confidence: 99%

Swarm Intelligence-based Extraction and Manifold Crawling Along the Large-Scale Structure

Petra¹,

Peletier²,

Canducci³

et al. 2023

Preprint

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The distribution of galaxies and clusters of galaxies on the mega-parsec scale of the Universe follows an intricate pattern now famously known as the Large-Scale Structure or the Cosmic Web. To study the environments of this network, several techniques have been developed that are able to describe its properties and the properties of groups of galaxies as a function of their environment. In this work we analyze the previously introduced framework: 1-Dimensional Recovery, Extraction, and Analysis of Manifolds (1-DREAM) on N-body cosmological simulation data of the Cosmic Web. The 1-DREAM toolbox consists of five Machine Learning methods, whose aim is the extraction and modelling of 1-dimensional structures in astronomical big data settings. We show that 1-DREAM can be used to extract structures of different density ranges within the Cosmic Web and to create probabilistic models of them. For demonstration, we construct a probabilistic model of an extracted filament and move through the structure to measure properties such as local density and velocity. We also compare our toolbox with a collection of methodologies which trace the Cosmic Web. We show that 1-DREAM is able to split the network into its various environments with results comparable to the state-of-the-art methodologies. A detailed comparison is then made with the public code DisPerSE, in which we find that 1-DREAM is robust against changes in sample size making it suitable for analyzing sparse observational data, and finding faint and diffuse manifolds in low density regions.

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Tracking the Temporal-Evolution of Supernova Bubbles in Numerical Simulations

Canducci

Taghribi

Rijcke

et al. 2021

Intelligent Data Engineering and Automated Learning – IDEAL 2021

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ASAP – A sub-sampling approach for preserving topological structures modeled with geodesic topographic mapping

Cited by 7 publications

References 26 publications

Quantum Computing Approaches for Vector Quantization—Current Perspectives and Developments

Quantum Computing Approaches for Vector Quantization—Current Perspectives and Developments

Swarm Intelligence-based Extraction and Manifold Crawling Along the Large-Scale Structure

Tracking the Temporal-Evolution of Supernova Bubbles in Numerical Simulations

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