提出新方法解决分类矩阵补全问题，用于病毒准种分析
Latent Structural Categorical Matrix Completion with Application to Quasispecies Analysis
- 用二值张量表示分类数据，保留离散特性
- 双循环优化框架，自适应估计隐含维度
- 适用于病毒准种重建，精度效率均更优
矩阵补全广泛应用于实值数据，但现有方法难以处理分类变量。本文提出LCMC，一种基于隐因子分解的双循环优化框架，通过三阶张量的独热编码表示分类条目，保持其离散非序数特性。外层循环通过内层反馈自适应调整隐含维度，内层循环则通过张量分解重构分类矩阵，并附有理论分析。为提升可扩展性与鲁棒性，引入分治-合并-精化策略及自适应数据缩减技术。在合成数据与真实病毒准种重建数据集上的实验表明，LCMC相比现有方法在准确率和效率上均有显著提升。
原文摘要 · Abstract (English)
Matrix completion has been extensively studied for real-valued data, but existing methods are often limited in handling categorical variables. We propose LCMC, a double-loop optimization framework for categorical matrix completion via latent factorization based on a binary tensor representation. In this setting, each categorical entry is encoded as a one-hot vector along a third tensor mode, thereby preserving its discrete, non-ordinal nature. The outer loop adaptively estimates the latent dimension by iteratively updating it with feedback from the inner loop, while the inner loop reconstructs the categorical matrix through tensor factorization, supported by a corresponding theoretical analysis. To further improve scalability and robustness, we introduce enhancements including a split-merge-refine strategy and an adaptive data reduction technique. Experiments on synthetic and real-world datasets in viral quasispecies reconstruction, demonstrate that LCMC achieves superior accuracy and efficiency compared to existing methods.
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