Constructing measures of sparsity

Giancarlo Pastor Figueroa; Inmaculada Mora-Jiménez; Riku Jäntti; Antonio J. Caamaño

doi:10.1109/TKDE.2020.3029851

Constructing measures of sparsity

Giancarlo Pastor Figueroa, Inmaculada Mora-Jiménez, Riku Jäntti, Antonio J. Caamaño

Universidad Rey Juan Carlos

Research output: Contribution to journal › Article › Scientific › peer-review

3 Citations (Scopus)

177 Downloads (Pure)

Abstract

This paper presents a rigorous but tractable study of sparsity. We postulate a definition of sparsity that is as broad as possible, so that it generates all the various measures that are useful in practice, but narrow enough that the fundamental properties of generalized sparsity still hold. As we work through the various ways of demonstrating the advantageous properties of sparsity, we illustrate its meaning from geometrical and operational perspectives. Thereafter, we construct specific measures of sparsity which are successfully qualified in complexity analysis and sparse optimization scenarios. Overall, our main objective is to construct measures of sparsity that will facilitate and enhance the design of the next innovative sensing technologies.

Original language	English
Pages (from-to)	3643 - 3654
Number of pages	12
Journal	IEEE Transactions on Knowledge and Data Engineering
Volume	34
Issue number	8
Early online date	2020
DOIs	https://doi.org/10.1109/TKDE.2020.3029851
Publication status	Published - 1 Aug 2022
MoE publication type	A1 Journal article-refereed

Keywords

axioms
complexity
concentration
diversity
effective
entropy
fairness
generalized convexity
inequality
information
sparsity
uncertainty

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10.1109/TKDE.2020.3029851

Pastor_Constructing_measures_of_sparsityAccepted author manuscript, 2.79 MB

DataFog: A Data-Driven Platform for Capacity and Resource Management in Vehicular Fog Computing
Xiao, Y. (Principal investigator)
01/01/2019 → 31/12/2022
Project: Academy of Finland: Other research funding

Cite this

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title = "Constructing measures of sparsity",

abstract = "This paper presents a rigorous but tractable study of sparsity. We postulate a definition of sparsity that is as broad as possible, so that it generates all the various measures that are useful in practice, but narrow enough that the fundamental properties of generalized sparsity still hold. As we work through the various ways of demonstrating the advantageous properties of sparsity, we illustrate its meaning from geometrical and operational perspectives. Thereafter, we construct specific measures of sparsity which are successfully qualified in complexity analysis and sparse optimization scenarios. Overall, our main objective is to construct measures of sparsity that will facilitate and enhance the design of the next innovative sensing technologies.",

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AU - Pastor Figueroa, Giancarlo

AU - Mora-Jiménez, Inmaculada

AU - Jäntti, Riku

AU - Caamaño, Antonio J.

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N2 - This paper presents a rigorous but tractable study of sparsity. We postulate a definition of sparsity that is as broad as possible, so that it generates all the various measures that are useful in practice, but narrow enough that the fundamental properties of generalized sparsity still hold. As we work through the various ways of demonstrating the advantageous properties of sparsity, we illustrate its meaning from geometrical and operational perspectives. Thereafter, we construct specific measures of sparsity which are successfully qualified in complexity analysis and sparse optimization scenarios. Overall, our main objective is to construct measures of sparsity that will facilitate and enhance the design of the next innovative sensing technologies.

AB - This paper presents a rigorous but tractable study of sparsity. We postulate a definition of sparsity that is as broad as possible, so that it generates all the various measures that are useful in practice, but narrow enough that the fundamental properties of generalized sparsity still hold. As we work through the various ways of demonstrating the advantageous properties of sparsity, we illustrate its meaning from geometrical and operational perspectives. Thereafter, we construct specific measures of sparsity which are successfully qualified in complexity analysis and sparse optimization scenarios. Overall, our main objective is to construct measures of sparsity that will facilitate and enhance the design of the next innovative sensing technologies.

KW - axioms

KW - complexity

KW - concentration

KW - diversity

KW - effective

KW - entropy

KW - fairness

KW - generalized convexity

KW - inequality

KW - information

KW - sparsity

KW - uncertainty

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DO - 10.1109/TKDE.2020.3029851

M3 - Article

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SP - 3643

EP - 3654

JO - IEEE Transactions on Knowledge and Data Engineering

JF - IEEE Transactions on Knowledge and Data Engineering

IS - 8

ER -

Constructing measures of sparsity

Abstract

Keywords

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DataFog: A Data-Driven Platform for Capacity and Resource Management in Vehicular Fog Computing

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