Detecting Gradual Structure Changes of Non-parametric Distributions via Kernel Complexity
So Hirai, Kenji Yamanishi · 2021 IEEE International Conference on Big Data (Big Data) · 2021
This study is concerned with an algorithm to detect structural change with KC in nonparametric distributions. We propose an index of the quantification of structural information for nonparametric distributions with the aim of detecting their changes in time series data. In a parametric model such as a Gaussian mixture model, the number of clusters can represent the structural information. However, the notion of structural information for modeling data nonparametrically does not exist. Herein we introduce the novel notion of kernel complexity (KC) as structural information in a nonparametric setting. The key idea of KC is to combine the information bias by the Gini index with the quantity of information measured by the normalized maximum likelihood (NML) code length. We empirically show the similarities between KC and the number of clusters in a parametric model under certain conditions. Using synthetic and real datasets, we empirically demonstrate that our framework enables us to detect the structural changes underlying the data. We use the synthetic datasets to demonstrate the usefulness of our method with some characteristic data distribution. We then use real datasets to evaluate the validity of the detected results both quantitatively and qualitatively.