Identifying Customer Profiles in Power Load Time Series Using Spectral Clustering

Abstract

An application of multiway spectral clustering with out-of-sample extensions towards clustering time series is presented. The data correspond to power load time series acquired from substations in the Belgian grid for a period of 5 years. Spectral clustering methods are a class of unsupervised learning algorithms where the solutions can be obtained from the eigenvectors of a Laplacian matrix derived from the data. Nonlinearity can easily be added to the analysis by the use of nonlinear similarity functions that can be regarded as Mercer kernels. In this paper, a weighted kernel PCA formulation to spectral clustering is used to find interpretable customer profiles underlying the power consumption load time series. The main advantage of the interpretation as kernel PCA is the extension of the clustering model to out-of-sample points. The clustering model can be trained, validated and tested in a learning framework working directly with the data and without the use of pre-modeling steps. The experimental results with real-life data demonstrate the applicability of the multiway spectral clustering method compared to an existing method pre-modeling the data based on periodic autoregressions (PAR).