Clustering multivariate functional data using unsupervised binary trees

Abstract

We propose a model-based clustering algorithm for a general class of functional data for which the components could be curves or images. The random functional data realizations could be measured with error at discrete, and possibly random, points in the definition domain. The idea is to build a set of binary trees by recursive splitting of the observations. The number of groups are determined in a data-driven way. The new algorithm provides easily interpretable results and fast predictions for online data sets. Results on simulated datasets reveal good performance in various complex settings. The methodology is applied to the analysis of vehicle trajectories on a German roundabout.

Block Hunter: Federated Learning for Cyber Threat Hunting in Blockchain-based IIoT Networks

“…A forest of isolation trees is the foundation of the isolation forest algorithm, where cells in the dataset are randomly selected from the data to form a forest of normal and outlier cells. These trees are binary trees that have zero or two child nodes, and an isolation forest contains isolation trees of this type [8], [29]. Consider that X is either a leaf node that does not have any children or a parent node that has two children named XL and XR.…”

FDApy: a Python package for functional data

“…The FDApy package implements fCUBT for the clustering of functional data objects defined on potentially different domains, developed by [8]. The implementation of the method is build upon the functional data classes defined in the package.…”

“…After giving a short review of the methodology in Section 7.1, we explain how to effectively use it in Section 7.2. For a detailed description, please refer to [8].…”

“…An implementation of MFPCA for data defined on different domains, as described in [10], is implemented. Moreover, the fCUBT algorithm [8], used to create partition in the data, is also available. All methods are implemented using the defined classes.…”