Comparison of time series clustering methods and application to power consumption pattern clustering

Abstract

The development of smart grids has enabled the easy collection of a large amount of power data. There are some common patterns that make it useful to cluster power consumption patterns when analyzing s power big data. In this paper, clustering analysis is based on distance functions for time series and clustering algorithms to discover patterns for power consumption data. In clustering, we use 10 distance measures to find the clusters that consider the characteristics of time series data. A simulation study is done to compare the distance measures for clustering. Cluster validity measures are also calculated and compared such as error rate, similarity index, Dunn index and silhouette values. Real power consumption data are used for clustering, with five distance measures whose performances are better than others in the simulation.

The trilemma among CO2 emissions, energy use, and economic growth in Russia

“…Finally, as the last clustering approach, we consider the Correlation distance. We can follow Golay et al 151 , Montero and Vilar 142 , Kim and Kim 152 , and Drago and Scozzari 153 . The Pearson’s correlation distance between two time-series can be written as: where COR is the Pearson’s correlation between the two considered time-series X T and Y T .…”

“…The Pearson’s correlation distance between two time-series can be written as: where COR is the Pearson’s correlation between the two considered time-series X T and Y T . The interpretation of the Correlation distance between time-series is essential: when there is a higher correlation between two time-series, their distance becomes closer (Kim and Kim 152 ). The Correlation distance is advantageous for capturing and describing a linear pattern between different series.…”

Aplikasi Pendekatan Agglomerative Hierarchical Time Series Clustering untuk Peramalan Data Harga Minyak Goreng di Indonesia

“…Fungsi autokorelasi digunakan sebagai salah satu ukuran ketidakmiripan dan beberapa penulis telah mempelajari ini seperti Galeano, P. dan Pena, D. ( 2000) telah mengkaji ini. Misalkan, 𝑝̂𝑥 = (𝑝̂1 𝑥 , 𝑝̂2 𝑥 , … , 𝑝̂𝐿 𝑥 ) 𝑡 dan 𝑝̂𝑦 = (𝑝̂1 𝑦 , 𝑝̂2 𝑦 , … , 𝑝̂𝐿 𝑦 ) 𝑡 merupakan vektor-vektor autokorelasi hasil pendugaan dari deret waktu X dan Y untuk beberapa L seperti 𝑝̂𝑖 𝑥 ≈ 0 dan 𝑝̂𝑖 𝑦 ≈ 0 untuk i > L. Jarak ACF dari dua runtun waktu dapat di formulasikan sebagai berikut: dengan Ω adalah matriks pembobot (Kim & Kim, 2020).…”

“…Struktur seperti pohon menunjukkan urutan objek yang bergabung, sehingga sejumlah cluster tidak dapat didefinisikan langsung. Jumlah cluster dapat disesuaikan pada tingkat yang sesuai untuk membagi seluruh data menjadi beberapa cluster (Kim & Kim, 2020). Menurut Azzahra & Wijayanto (2022)…”

“…Nilai silhouette berada pada rentang [-1,1] bergantung pada seberapa kuat Pengelompokkan dari kelompok tersebut. Koefisien semakin mendekati 1 maka hasil kelompok juga semakin baik (Kim & Kim, 2020).…”