Poisson Subspace Clustering: Focusing on the Essentials in Count Data
2026-08-24 • Machine Learning
Machine Learning
AI summaryⓘ
The authors introduce 3CPO, a new method to group (cluster) data that counts things, like numbers in tables where the values can't be negative. They use special math models (Poisson and negative binomial) made for this kind of data to get better results than usual methods. Their algorithm not only finds groups but also points out which features (columns) are important, making it easier to understand why the groups formed. They tested 3CPO on different kinds of data, like gene activity and economic data, and found it works well and reliably.
count dataclusteringPoisson distributionnegative binomial distributionposterior probabilitysubspace clusteringinterpretabilitycontingency tablesiterative algorithmgene expression
Authors
Collin Leiber, Kai Puolamäki, Heikki Mannila
Abstract
Count data represented as a matrix of non-negative integer values, such as contingency tables, are prevalent across diverse domains. When clustering such data sets, specific methods are required, as generic algorithms often fail to consider their unique distributional properties, leading to unreliable outputs. An effective strategy is to use well-established statistical models such as the Poisson and negative binomial distributions. We present 3CPO, a clustering algorithm based on statistically solid modeling of count data. In addition to the cluster labels, it identifies a subset of relevant columns, enhancing the interpretability of the results. We propose a simple iterative algorithm that maximizes the posterior probability to find good clustering solutions and discuss its properties. Extensive experiments demonstrate its ability to define high-quality clusters within associated subspaces for various data domains, ranging from gene expressions and texts to economics. Our findings suggest that 3CPO is a robust solution for clustering count data in a statistically sound and interpretable manner. Our code is available at https://github.com/collinleiber/3CPO.