2023/09/12 by Enrique Alvarado, Alvarado, Enrique, Robin Belton +11
Computer Science · #62H30 #62R07 #62R40 #68T09 #Advanced Clustering Algorithms Research #Algebraic Topology (math.AT) #Data Management and Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2309.06634
openalex publication_date 2023/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. However, the Mapper algorithm requires tuning several parameters in order to generate a ``nice" Mapper graph. This paper focuses on selecting the cover parameter. We present an algorithm that optimizes the cover of a Mapper graph by splitting a cover repeatedly according to a statistical test for normality. Our algorithm is based on G-means clustering which searches for the optimal number of clusters in k-means by iteratively applying the Anderson-Darling test. Our splitting procedure employs a Gaussian mixture model to carefully choose the cover according to the distribution of the given data. Experiments for synthetic and real-world datasets demonstrate that our algorithm generates covers so that the Mapper graphs retain the essence of the datasets, while also running significantly faster than a previous iterative method.