The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Nonparametric clustering of functional time series electricity consumption data

전기 사용량 시계열 함수 데이터에 대한 비모수적 군집화

  • Kim, Jaehee (Department of Statistics, Duksung Women's University)
  • 김재희 (덕성여자대학교 정보통계학과)
  • Received : 2018.11.15
  • Accepted : 2018.12.22
  • Published : 2019.02.28
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Abstract

The electricity consumption time series data of 'A' University from July 2016 to June 2017 is analyzed via nonparametric functional data clustering since the time series data can be regarded as realization of continuous functions with dependency structure. We use a Bouveyron and Jacques (Advances in Data Analysis and Classification, 5, 4, 281-300, 2011) method based on model-based functional clustering with an FEM algorithm that assumes a Gaussian distribution on functional principal components. Clusterwise analysis is provided with cluster mean functions, densities and cluster profiles.

본 연구는 2016년 7월부터 2017년 6월까지 인천 소재 A 대학교의 15분 단위의 일일 전기 사용량 시계열 데이터에 대해 functional data analysis 기법을 적용하여 군집화하고 각 군집의 특성을 파악하고 예측에 활용하고자 한다. 하루동안의 A 대학교의 전기 사용량은 패턴은 주중과 주말 에 큰 차이를 보이며 스플라인 기저함수로 FPCA 구한 후 이들에 대한 가우시안 분포의 혼합모형 기반 군집분석으로 3개의 군집화가 적절해 보인다. 각 군집에 대해 평균 함수, 확률밀도함수, 일들의 분포 등을 정리해 각 군집에 대한 정보와 특징을 보여준다.

Keywords

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Figure 2.1. A University electricity consumption data.

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Figure 2.2. Everyday electricity consumption plot.

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Figure 4.1. Spline smoothing with 16 bases.

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Figure 4.2. Cluster plot with smooth curves (left: 365 curves, right: cluster means).

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Figure 4.3. Derivative plots in clusters.

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Figure 4.4. Density plot in each cluster.

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Figure 4.5. Smooth functions in each cluster (16 spline bases).

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Figure 4.6. Silhouette plot for cluster validity.

Table 4.1. Comparison of clusters via distribution according to weekdays

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Table 4.2. Comparison of clusters via distribution according to month

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Table 4.3. Classification according to functional linear discriminant functions obtained

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