A kernel estimate method for characteristic function-based uncertainty importance measure

Xu, Xingwang; Lü, Zhenzhou; Luo, Xiaopeng

doi:10.1016/j.apm.2016.09.028

Cited by 14 publications

(8 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To overcome the inability of most MNRS models to analyze infinite sets, the Lebesgue measure [34] is introduced into the MNRS model for infinite sets in multilabel neighborhood decision systems. For any R M that denotes M -dimensional Euclidean space, suppose that E is a point set of R M , for an open interval I i of each column that is covered by E, namely, ∞ i=1 I i ⊃ E, it follows that the sum of all the volumes is µ = ∞ i=1 |I i | and all constitute a number set that is bounded from below.…”

Section: B Lebesgue Measure-based Mnrsmentioning

confidence: 99%

Hybrid Multilabel Feature Selection Using BPSO and Neighborhood Rough Sets for Multilabel Neighborhood Decision Systems

et al. 2019

View full text Add to dashboard Cite

Recently, feature selection for multilabel classification has attracted substantial attention in many fields; however, some of the available methods ignore the correlations among labels and yield low classification performance. In addition, most feature selection algorithms that are based on multilabel neighborhood rough sets (MNRS) can only deal with finite sets for multilabel data. To address the issues, this paper presents a novel hybrid filter-wrapper multilabel feature selection method that is based on binary particle swarm optimization (BPSO) and MNRS with the Lebesgue measure for multilabel neighborhood decision systems. First, to overcome the problem that the traditional correlation-based feature selection (CFS) algorithm ignores the dependencies among labels, two types of average correlation between single labels and label sets and among labels are presented. Via combination with information-entropy-based uncertainty measures, a new average correlation among labels is studied. A novel comprehensive evaluation function of CFS (NCFS) is constructed. Then, NCFS is introduced as a fitness function into the original BPSO and improved BPSO algorithms to optimize multilabel classification in the early and later stages, respectively, and the optimization process is terminated when the maximum number of iterations is reached. Next, the Lebesgue measure of the neighborhood class is developed for investigating the neighborhood approximation accuracy and the dependency degree based on MNRS. Various properties are deduced, and the relationships among these measures are used to evaluate the uncertainty and correlations among labels of multilabel data. Finally, a hybrid filter-wrapper feature selection algorithm using NCFS-BPSO is designed for preliminarily eliminating redundant features to decrease the complexity, and a heuristic forward multilabel feature selection algorithm is proposed for improving the performance of multilabel classification. Experimental results on fifteen multilabel datasets demonstrate that our proposed algorithms are effective in selecting significant features and realizing great classification performance in multilabel neighborhood decision systems.

show abstract

Section: B Lebesgue Measure-based Mnrsmentioning

confidence: 99%

Hybrid Multilabel Feature Selection Using BPSO and Neighborhood Rough Sets for Multilabel Neighborhood Decision Systems

et al. 2019

View full text Add to dashboard Cite

show abstract

“…. , 7) are estimated by the proposed method with 4072 samples and the MCS method with 4 3 10 6 samples. Inputs (unit) q…”

Section: Example 3: the Speed Reducer Problemmentioning

confidence: 99%

“…Several kinds of GSA techniques also known as importance measures have been proposed by researchers for different purposes. [2][3][4][5][6][7][8][9][10] The momentindependent importance measure, also called the moment-independent GSA, suggested by Borgonovo 6 is one of the popular GSAs.…”

Section: Introductionmentioning

confidence: 99%

A vine copula–based method for analyzing the moment-independent importance measure of the multivariate output

Zhou

Yan

Cheng

2018

Proceedings of the Institution of Mechanical Engineers, Part O:

Self Cite

View full text Add to dashboard Cite

The moment-independent importance measure technique for exploring how uncertainty allocates from output to inputs has been widely used to help engineers estimate the degree of confidence of decision results and assess risks. Solving the Borgonovo moment-independent importance measure in the presence of the multivariate output is still a challenging problem due to “curse of dimensionality,” and it is investigated in this contribution. For easily estimating the moment-independent importance measure, a novel method based on the vine copula is proposed. In the proposed method for estimating moment-independent importance measure, three steps are included. First, the moment-independent importance measure is expressed as a product of bivariate copula density functions through the vine copula trees. Second, the marginal probability density functions are obtained by the maximum entropy under the constraint of the fractional moments. Finally, the post-processed is executed to directly estimate the moment-independent importance measure by estimated copula density functions. The proposed method can handle multivariate output easily. The results of several examples indicate the validity and benefits of the proposed method.

show abstract

“…Song and Li [ 26 ] stated Lebesgue theorem in non-additive measure theory. Xu et al [ 27 ] introduced Lebesgue integral over infinite interval and presented a computation method based on kernel function for uncertainty measures. Halcinová et al [ 28 ] investigated the weighted Lebesgue integral by Lebesgue differentiation theorem, and used Lebesgue measure to develop the standard weighted L p -based sizes.…”

Section: Introductionmentioning

confidence: 99%

A Neighborhood Rough Sets-Based Attribute Reduction Method Using Lebesgue and Entropy Measures

Sun

Wang

et al. 2019

Entropy

View full text Add to dashboard Cite

For continuous numerical data sets, neighborhood rough sets-based attribute reduction is an important step for improving classification performance. However, most of the traditional reduction algorithms can only handle finite sets, and yield low accuracy and high cardinality. In this paper, a novel attribute reduction method using Lebesgue and entropy measures in neighborhood rough sets is proposed, which has the ability of dealing with continuous numerical data whilst maintaining the original classification information. First, Fisher score method is employed to eliminate irrelevant attributes to significantly reduce computation complexity for high-dimensional data sets. Then, Lebesgue measure is introduced into neighborhood rough sets to investigate uncertainty measure. In order to analyze the uncertainty and noisy of neighborhood decision systems well, based on Lebesgue and entropy measures, some neighborhood entropy-based uncertainty measures are presented, and by combining algebra view with information view in neighborhood rough sets, a neighborhood roughness joint entropy is developed in neighborhood decision systems. Moreover, some of their properties are derived and the relationships are established, which help to understand the essence of knowledge and the uncertainty of neighborhood decision systems. Finally, a heuristic attribute reduction algorithm is designed to improve the classification performance of large-scale complex data. The experimental results under an instance and several public data sets show that the proposed method is very effective for selecting the most relevant attributes with high classification accuracy.

show abstract

A kernel estimate method for characteristic function-based uncertainty importance measure

Cited by 14 publications

References 27 publications

Hybrid Multilabel Feature Selection Using BPSO and Neighborhood Rough Sets for Multilabel Neighborhood Decision Systems

Hybrid Multilabel Feature Selection Using BPSO and Neighborhood Rough Sets for Multilabel Neighborhood Decision Systems

A vine copula–based method for analyzing the moment-independent importance measure of the multivariate output

A Neighborhood Rough Sets-Based Attribute Reduction Method Using Lebesgue and Entropy Measures

Contact Info

Product

Resources

About