Hyperoctant Search Clustering: A Method for Clustering Data in High-Dimensional Hyperspheres

Clustering of high-dimensional data sets is a growing need in artificial intelligence, machine learning and pattern recognition. In this paper, we propose a new clustering method based on a combinatorial-topological approach applied to regions of space defined by signs of coordinates (hyperoctants). In high-dimensional spaces, this approach often reduces the size of the dataset while preserving sufficient topological features. According to a density criterion, the method builds clusters of data points based on the partitioning of a graph, whose vertices represent hyperoctants, and whose edges connect neighboring hyperoctants under the Levenshtein distance. We call this method HyperOctant Search Clustering. We prove some mathematical properties of the method. In order to as assess its performance, we choose the application of topic detection, which is an important task in text mining. Our results suggest that our method is more stable under variations of the main hyperparameter, and remarkably, it is not only a clustering method, but also a tool to explore the dataset from a topological perspective, as it directly provides information about the number of hyperoctants where there are data points. We also discuss the possible connections between our clustering method and other research fields.