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Density peaks algorithm based on information entropy and merging strategy for power load curve clustering

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Abstract

To solve the problems of density peaks clustering (DPC) algorithm sensitive to cutoff distance and subjectivity of clustering center selection, we propose an improved density peaks algorithm based on information entropy and merging strategy (DPC-IEMS) for realizing power load curve clustering. First, a cutoff distance optimization method based on information entropy is proposed. This method uses sparrow search algorithm (SSA) to find the minimum value of information entropy about the product of local density and relative distance to calculate the optimal cutoff distance suitable for the load datasets. Then, a merging strategy is proposed to realize the adaptive selection of clustering centers. This strategy first generates a large number of initial sub-clusters by DPC, and then merges the sub-clusters using the fusion condition until the final iteration condition is satisfied. The performance of DPC-IEMS algorithm is evaluated on the U.S. load datasets and the Chinese load datasets, and the effectiveness and practicality of DPC-IEMS algorithm for power load curve clustering are fully demonstrated.

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Availability of data and materials

The U.S. load data are available to download from https://dx.doi.org/10.25984/1876417. The Chinese load data cannot be shared for privacy reasons.

Abbreviations

DPC:

Density peaks clustering algorithm

SSA:

Sparrow search algorithm

FCM:

Fuzzy C-means

KNN:

K-Nearest neighbor

SC:

Silhouette coefficient

CH:

Calinski Harabasz score

DVI:

Dunn validity Index

DBI:

Davies Bouldin score

WPD:

Wavelet packet decomposition

DWT:

Discrete wavelet transform

PCA:

Principal component analysis

DPC-IE:

DPC algorithm based on information entropy

DPC-MS:

DPC algorithm based on merging strategy

DPC-IEMS:

Density peaks algorithm based on information entropy and merging strategy

\(\rho_{i}\) :

The local density of DPC

\(\delta_{i}\) :

The relative distance of DPC

\(d_{c}\) :

The cutoff distance of DPC

\(d_{ij}\) :

The Euclidean distance between point i and point j

\(\gamma_{i}\) :

The product of local density and relative distance

\(CL^{\prime}\) :

The initial sub-clusters

\(ICl^{\prime}\) :

The initial sub-cluster center indexes

\(Cl^{\prime}_{j}\) :

The j-th initial sub-clusters

\(icl^{\prime}_{j}\) :

The j-th initial sub-cluster center index

\(d_{near}\) :

Distance between the cluster center of the initial subcluster and the cluster's nearest neighbor curve

FT:

The fusion threshold

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Funding

This work was supported by the National Natural Science Foundation of China (No.42075129) and Hebei Province Natural Science Foundation (No.E2021202179).

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  1. Yumeng Yang, Li Wang and Zizhen Cheng hava equally contributed to this work.

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  1. School of Electronic and Information Engineering, Hebei University of Technology, Tianjin, 300401, China

    Yumeng Yang, Li Wang & Zizhen Cheng

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Contributions

YY: Conceptualization, Methodology, Formal analysis, Validation, Investigation, Software, Writing- Original Draft, Resources, Visualization. LW: Conceptualization, Methodology, Formal analysis, Validation, Writing- Original Draft, Writing—Review & Editing, Funding acquisition. ZC: Data Curation, Visualization.

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Correspondence to Li Wang.

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Yang, Y., Wang, L. & Cheng, Z. Density peaks algorithm based on information entropy and merging strategy for power load curve clustering. J Supercomput 80, 8801–8832 (2024). https://doi.org/10.1007/s11227-023-05793-0

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