The Hubness Phenomenon in High-Dimensional Spaces

Mani, Priya; Vazquez, Marilyn; Metcalf-Burton, Jessica Ruth; Domeniconi, Carlotta; Fairbanks, Hillary R.; Bal, Gulce; Beer, Elizabeth

doi:10.1007/978-3-030-11566-1_2

Cited by 5 publications

(6 citation statements)

References 17 publications

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“…One of the typical phenomena is rich cluster structure. Multi-clustering and recently described hubness phenomena are important in high-dimensional data analysis and it is impossible to analyse the real life datasets without accounting of them [66,[87][88][89]. We used the granular distributions as models for multi-clustered data.…”

Section: Discussionmentioning

confidence: 99%

High-Dimensional Separability for One- and Few-Shot Learning

Gorban

Grechuk

Mirkes

et al. 2021

Entropy

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This work is driven by a practical question: corrections of Artificial Intelligence (AI) errors. These corrections should be quick and non-iterative. To solve this problem without modification of a legacy AI system, we propose special `external’ devices, correctors. Elementary correctors consist of two parts, a classifier that separates the situations with high risk of error from the situations in which the legacy AI system works well and a new decision that should be recommended for situations with potential errors. Input signals for the correctors can be the inputs of the legacy AI system, its internal signals, and outputs. If the intrinsic dimensionality of data is high enough then the classifiers for correction of small number of errors can be very simple. According to the blessing of dimensionality effects, even simple and robust Fisher’s discriminants can be used for one-shot learning of AI correctors. Stochastic separation theorems provide the mathematical basis for this one-short learning. However, as the number of correctors needed grows, the cluster structure of data becomes important and a new family of stochastic separation theorems is required. We refuse the classical hypothesis of the regularity of the data distribution and assume that the data can have a rich fine-grained structure with many clusters and corresponding peaks in the probability density. New stochastic separation theorems for data with fine-grained structure are formulated and proved. On the basis of these theorems, the multi-correctors for granular data are proposed. The advantages of the multi-corrector technology were demonstrated by examples of correcting errors and learning new classes of objects by a deep convolutional neural network on the CIFAR-10 dataset. The key problems of the non-classical high-dimensional data analysis are reviewed together with the basic preprocessing steps including the correlation transformation, supervised Principal Component Analysis (PCA), semi-supervised PCA, transfer component analysis, and new domain adaptation PCA.

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Section: Discussionmentioning

confidence: 99%

High-Dimensional Separability for One- and Few-Shot Learning

Gorban

Grechuk

Mirkes

et al. 2021

Entropy

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“…Tem sido demonstrado que o conceito hubness consiste em uma propriedade inerente de grande parte dos conjuntos de dados de alta dimensão, não sendo peculiar de conjuntos de dados específicos. O aspecto hubness pode indicar uma boa referência de pontos de centralidade [Mani et al 2019]. Os principais hubs podem ser usados efetivamente como representantes para guiar o processo de atribuic ¸ão de rótulos de imagens, de maneira similar a como ocorre nas técnicas que consideram outros tipos de representantes, por exemplo, centróides.…”

Section: Conceitos Fundamentaisunclassified

“…De uma maneira oposta, outras estratégias [Romaszewski et al 2018, Wu et al 2020] têm empregado de maneira eficaz um aspecto inerente aos dados de alta dimensão, denominado hubness, para o desenvolvimento de técnicas que permitem a classificac ¸ão em bancos de dados de alta dimensão. O aspecto hubness consiste na tendência de algumas instâncias de dados, chamadas hubs, ocorrerem com maior frequência nas listas dos K-vizinhos mais próximos de outras instâncias [Mani et al 2019]. Até onde é de conhecimento dos autores, apesar do potencial demonstrado para a classificac ¸ão de outros contextos, o aspecto hubness não foi explorado para a classificac ¸ão de fluxos de dados de imagens.…”

Section: Introduc ¸ãOunclassified

HubISC: um novo algoritmo baseado em hubness para a classificação de fluxo de dados de imagens

Lima

Faria

Barioni

2022

Anais Do XXXVII Simpósio Brasileiro De Banco De Dados (SBBD 2022)

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A classificação de fluxo de dados de imagens apresenta vários desafios. Um dos desafios inerente ao domínio de dados de imagens é a alta dimensionalidade dos dados, que pode ocasionar a chamada maldição da dimensionalidade. Trabalhos aplicados em outros contextos empregam de forma eficiente um aspecto, denominado hubness, inerente de dados de alta dimensão. Este artigo apresenta um novo algoritmo para a classificação de fluxo de dados de imagens, que incorpora o aspecto hubness. Os resultados dos experimentos mostram uma boa relação de custo e benefício do algoritmo em termos de eficácia e da porcentagem de instâncias rotuladas em relação aos algoritmos comumente usados para a classificação de fluxos de dados de imagens.

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“…First, a lower number of coordinates required to represent each structure reduces the computational time of any algorithm expected to process the generated structures. Second, high data dimensionality has a negative impact on the performance of clustering algorithms [40][41][42]. Third, unlike representations based on Cartesian coordinates, the USR-based representation is invariant to rigid-body motions (translation and rotation in 3D space).…”

Section: Stage I: Featurizing Generated Structuresmentioning

confidence: 99%

Reducing Ensembles of Protein Tertiary Structures Generated De Novo via Clustering

et al. 2020

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Controlling the quality of tertiary structures computed for a protein molecule remains a central challenge in de-novo protein structure prediction. The rule of thumb is to generate as many structures as can be afforded, effectively acknowledging that having more structures increases the likelihood that some will reside near the sought biologically-active structure. A major drawback with this approach is that computing a large number of structures imposes time and space costs. In this paper, we propose a novel clustering-based approach which we demonstrate to significantly reduce an ensemble of generated structures without sacrificing quality. Evaluations are related on both benchmark and CASP target proteins. Structure ensembles subjected to the proposed approach and the source code of the proposed approach are publicly-available at the links provided in Section 1.

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The Hubness Phenomenon in High-Dimensional Spaces

Cited by 5 publications

References 17 publications

High-Dimensional Separability for One- and Few-Shot Learning

High-Dimensional Separability for One- and Few-Shot Learning

HubISC: um novo algoritmo baseado em hubness para a classificação de fluxo de dados de imagens

Reducing Ensembles of Protein Tertiary Structures Generated De Novo via Clustering

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