Conformal clustering for functional variables, With application to electricity consumption curves

Conformal Clustering (CC) is a clustering technique which also allows for anomaly detection. It involves finding a so-called ‘region of conformity’ in the feature space: at a pre-selected significance level ε, the data points within this region are grouped into clusters, while all data points outside it are considered anomalies.
In the existing literature on CC, data has typically been considered as finite-dimensional feature vectors. However, much existing data is found in functional form - for example time series data. In this work we generalise the CC technique to the domain of functional data. More specifically, we use CC to clean data from energy consumption curves, with the aim of subsequently disaggregating these energy curves into their components.
Our experiments play two roles. Firstly, to validate our expectation that conformal clustering is an effective technique for data cleaning. And secondly, to confirm that a functional approach to data analysis can provide new insights that are lacking in avector approach.