提出MMM模型，统一处理混合类型纵向数据的聚类问题。
MMM: Clustering Multivariate Longitudinal Mixed-type Data
- 将多变量纵向混合数据重构为三向结构，基于潜在连续变量建模。
- 可同时捕捉响应间关联、时间依赖与群体异质性，无需条件独立假设。
- 适合金融等复杂多类型纵向数据分析，兼具灵活性与简洁性。
多变量纵向混合类型数据在多个科学领域日益普遍，但聚类算法仍稀缺，主要因需同时建模连续与非连续变量在时间和维度上的依赖结构。本文提出混合矩阵（Mixture of Mixed-Matrices, MMM）模型：将数据重构为三向结构，假设非连续变量是潜在连续变量的观测，采用矩阵变正态混合分布，在潜在空间实现聚类。该模型可统一处理连续、有序、二元、名义和计数数据，以简约方式同时建模群体异质性、响应间相关性及时间依赖结构，且无需假设条件独立。通过MCMC-EM算法进行推断，并在模拟数据上验证了其推理能力；最后在真实金融数据上进行了应用。
原文摘要 · Abstract (English)
Multivariate longitudinal data of mixed-type are increasingly collected in many science domains. However, algorithms to cluster this kind of data remain scarce, due to the challenge to simultaneously model the within- and between-time dependence structures for multivariate data of mixed kind. We introduce the Mixture of Mixed-Matrices (MMM) model: reorganizing the data in a three-way structure and assuming that the non-continuous variables are observations of underlying latent continuous variables, the model relies on a mixture of matrix-variate normal distributions to perform clustering in the latent dimension. The MMM model is thus able to handle continuous, ordinal, binary, nominal and count data and to concurrently model the heterogeneity, the association among the responses and the temporal dependence structure in a parsimonious way and without assuming conditional independence. The inference is carried out through an MCMC-EM algorithm, which is detailed. An evaluation of the model through synthetic data shows its inference abilities. A real-world application on financial data is presented.
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