用泊松模型精准聚类计数数据，还能选出关键特征。
Poisson Subspace Clustering: Focusing on the Essentials in Count Data
- 基于泊松分布建模，最大化后验概率迭代求解。
- 在基因表达、文本等数据上实现高质量子空间聚类。
- 自动筛选相关列，结果更可解释，适合统计分析场景。
以非负整数矩阵形式存在的计数数据（如列联表）广泛存在于多个领域。传统聚类方法因忽略其独特的分布特性，常导致不可靠结果。我们提出3CPO算法，基于泊松与负二项分布等统计模型对计数数据进行建模。该算法不仅输出聚类标签，还识别出相关列的子集，提升结果可解释性。通过简单迭代算法最大化后验概率，寻找优质聚类解，并讨论其性质。大量实验表明，3CPO在基因表达、文本和经济学等多种数据域中均能有效定义高质量的子空间聚类。结果表明，3CPO是一种统计严谨且可解释的计数数据聚类方法。代码已开源：https://github.com/collinleiber/3CPO。
原文摘要 · Abstract (English)
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.
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