Jan Aerts

D. M. Bot, J. Peeters, J. Liesenborgs et al.

Clustering algorithms are often used to find subpopulations in exploratory data analysis workflows. Not only the clusters themselves, but also their shape can represent meaningful subpopulations. In this paper, we present FLASC, an algorithm that detects branches within clusters to identify such subpopulations. FLASC builds upon HDBSCAN*, a state-of-the-art density-based clustering algorithm, and detects branches in a post-processing step that describes within-cluster connectivity. Two variants of the algorithm are presented, which trade computational cost for noise robustness. We show that both variants scale similarly to HDBSCAN* in terms of computational cost and provide stable outputs using synthetic data sets, resulting in an efficient flare-sensitive clustering algorithm. In addition, we demonstrate the benefit of branch-detection on two real-world data sets.

Daniel M. Bot, Jan Aerts

Dimensionality reduction algorithms are often used to visualise high-dimensional data. Previously, studies have used prior information to enhance or suppress expected patterns in projections. In this paper, we adapt such techniques for domain knowledge guided interactive exploration. Inspired by Mapper and STAD, we present three types of lens functions for UMAP, a state-of-the-art dimensionality reduction algorithm. Lens functions enable analysts to adapt projections to their questions, revealing otherwise hidden patterns. They filter the modelled connectivity to explore the interaction between manually selected features and the data's structure, creating configurable perspectives each potentially revealing new insights. The effectiveness of the lens functions is demonstrated in two use cases and their computational cost is analysed in a synthetic benchmark. Our implementation is available in an open-source Python package: https://github.com/vda-lab/lensed_umap.

Daniel Alcaide, Jan Aerts

The connection of edges in a graph generates a structure that is independent of a coordinate system. This visual metaphor allows creating a more flexible representation of data than a two-dimensional scatterplot. In this work, we present STAD (Spanning Trees as Approximation of Data), a dimensionality reduction method to approximate the high-dimensional structure into a graph with or without formulating prior hypotheses. STAD generates an abstract representation of high-dimensional data by giving each data point a location in a graph which preserves the distances in the original high-dimensional space. The STAD graph is built upon the Minimum Spanning Tree (MST) to which new edges are added until the correlation between the distances from the graph and the original dataset is maximized. Additionally, STAD supports the inclusion of additional functions to focus the exploration and allow the analysis of data from new perspectives, emphasizing traits in data which otherwise would remain hidden. We demonstrate the effectiveness of our method by applying it to two real-world datasets: traffic density in Barcelona and temporal measurements of air quality in Castile and León in Spain.