发表机构
University of British Columbia（不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对矩阵正态混合模型的元素级与结构性缺失，提出高效部分EM算法，可减少计算时间并实现高光谱图像的同步插补与聚类。
AI 中文摘要
存在缺失元素的矩阵型数据在观测值自然组织为二维数组的应用中频繁出现。尽管矩阵正态分布通过其克罗内克协方差结构提供了简约模型，但标准EM估计的计算开销可能很高，因为任意缺失模式通常会破坏E步中的这种可分性。本文针对存在缺失元素的矩阵型正态数据，提出一种高效的部分EM算法。该方法通过逐坐标近似更新缺失分量的条件均值与协方差，避免重复求逆特定模式的协方差矩阵，也避免构建完整的向量化协方差矩阵。我们进一步为子矩阵缺失开发了专用更新方式，其中缺失块精度保留克罗内克积结构，且协方差更新可在行与列方向独立进行。模拟研究表明，在一系列维度和缺失比例下，所提方法与精确EM相比大幅减少了计算时间，同时保留了几乎相同的观测数据似然。将其应用于高光谱图像块的真实数据显示，所提插补策略可嵌入矩阵型混合模型中，实现插补与聚类同步进行。
英文摘要
Matrix-variate data with missing entries arise frequently in applications where observations are naturally organized as two-dimensional arrays. Although the matrix normal distribution provides a parsimonious model through its Kronecker covariance structure, standard EM estimation can be computationally expensive because arbitrary missingness patterns typically destroy this separability in the E-step. In this paper, we propose an efficient partial EM algorithm for matrix-variate normal data with missing entries. The proposed method updates the conditional mean and covariance of the missing component through coordinate-wise approximations, avoiding repeated inversion of pattern-specific covariance matrices and avoiding construction of the full vectorized covariance matrix. We further develop a specialized update for submatrix missingness, where the missing-block precision retains a Kronecker product structure, and the covariance update can be carried out independently in the row and column directions. Simulation studies show that the proposed methods substantially reduce computation time compared with exact EM while preserving nearly identical observed-data likelihood across a range of dimensions and missing proportions. A real-data application to hyperspectral image patches demonstrates that the proposed imputation strategy can be embedded within a matrix-variate mixture model for simultaneous imputation and clustering.
