A nonlinear correlation measure for multivariable data set

Wang, Qiang; Shen, Yi; Zhang, Jian Qiu

doi:10.1016/j.physd.2004.11.001

Cited by 134 publications

(71 citation statements)

References 13 publications

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“…The results show that the new entropy quantizes the correlation in [0,1] for both linear and nonlinear cases (Wang et al 2005).…”

Section: Nonlinear Correlation Information Entropymentioning

confidence: 97%

“…The authors in Wang et al (2005) proposed a new nonlinear correlation information entropy for multi-variable analysis. The results show that the new entropy quantizes the correlation in [0,1] for both linear and nonlinear cases (Wang et al 2005).…”

Section: Nonlinear Correlation Information Entropymentioning

confidence: 99%

“…We find NCIE (Wang et al 2005) to be a very robust measure for both linearly and nonlinearly correlated datasets, which has been applied to the analysis of neurophysiological signals (Pereda et al 2005), the quantification of the dependence among noisy data (Khan et al 2007), etc. Therefore, we adopt NCIE as a correlation measure in objective reduction and study its impact on online objective reduction approaches.…”

Section: Introductionmentioning

confidence: 99%

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Objective reduction based on nonlinear correlation information entropy

Wang

Yao

2015

Soft Comput

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It is hard to obtain the entire solution set of a many-objective optimization problem (MaOP) by multiobjective evolutionary algorithms (MOEAs) because of the difficulties brought by the large number of objectives. However, the redundancy of objectives exists in some problems with correlated objectives (linearly or nonlinearly). Objective reduction can be used to decrease the difficulties of some MaOPs. In this paper, we propose a novel objective reduction approach based on nonlinear correlation information entropy (NCIE). It uses the NCIE matrix to measure the linear and nonlinear correlation between objectives and a simple method to select the most conflicting objectives during the execution of MOEAs. We embed our approach into both Pareto-based and indicator-based MOEAs to analyze the impact of our reduction method on the performance of these algorithms. The results show that our approach significantly improves the performance of Pareto-based MOEAs on both reducible and irreducible MaOPs, but does not much help the performance of indicator-based MOEAs.

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“…The results show that the new entropy quantizes the correlation in [0,1] for both linear and nonlinear cases (Wang et al 2005).…”

Section: Nonlinear Correlation Information Entropymentioning

confidence: 97%

Section: Nonlinear Correlation Information Entropymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Objective reduction based on nonlinear correlation information entropy

Wang

Yao

2015

Soft Comput

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“…Correlation is another effective tool for analyzing the relationship between objectives. Different metrics have been proposed to measure the degree of correlation (both linear and non-linear), covariance, mutual information entropy [151], and non-linear correlation information entropy (NCIE) [152,153], for instance. Based on these relations, many mature data mining techniques can be employed to choose a subset of conflicting objectives to simplify the original problem, such as feature selection [146], principal component analysis (PCA) [154], and maximum variance unfolding (MVU) [155].…”

Section: Relationship Between Objectivesmentioning

confidence: 99%

A mini-review on preference modeling and articulation in multi-objective optimization: current status and challenges

Wang

Olhofer

Jin

2017

Complex Intell. Syst.

128

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Evolutionary multi-objective optimization aims to provide a representative subset of the Pareto front to decision makers. In practice, however, decision makers are usually interested in only a particular part of the Pareto front of the multi-objective optimization problem. This is particularly true when the number of objectives becomes large. Over the past decade, preference-based multi-objective optimization has attracted increasing attention from both academia and industry due to its significance in both theory and practice. Significant progress has been made in evolutionary multiobjective optimization and multi-criteria decision communities, although many open issues still remain to be addressed. This paper provides a concise review on preference-based multi-objective optimization, including various preference modeling methods and existing preference-based optimization methods, as well as a brief discussion of the main future challenges.

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“…OBJECTIVE ASSESSMENT METHOD AND ALGORITHM Objective evaluation methods [7] of image fusion can be roughly divided into two categories: independent single factor rating and a joint single factor evaluation. Factor of independent factors rating include: information entropy, average gradient and edge retention [8]- [11].The paper mainly make a study of independent factors rating.…”

mentioning

confidence: 99%

An Improved Adaptive Fusion Image Windows Based Technology

Xia¹

2013

IJIET

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In dim condition, by using a light sensor and infrared sensor can make up for human’s visual defects and make better observation of the object and background environment. If combining the image information from the two sensors at the same time and the same place, you can generate a new image with more information, precision and credibility; however traditional windows based weighted average fusion algorithm has some limitations, the paper put forward an fusion algorithm with an improved adaptive threshold based on windows in dim conditions. By contrast experiment, it proved that the value of entropy, average gradient and edge retention of the improved method have been all increased, and the effect of image fusion has also been changed better

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A nonlinear correlation measure for multivariable data set

Cited by 134 publications

References 13 publications

Objective reduction based on nonlinear correlation information entropy

Objective reduction based on nonlinear correlation information entropy

A mini-review on preference modeling and articulation in multi-objective optimization: current status and challenges

An Improved Adaptive Fusion Image Windows Based Technology

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