Factor Modelling for Biclustering Large-dimensional Matrix-valued Time Series
用于高维矩阵时间序列双聚类的因子建模AI 解读 ↓
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用于高维矩阵时间序列双聚类的因子建模
- 研究问题
- 高维矩阵时间序列同时存在全局共同变化和局部行列群组变化时，如何恢复两类因子结构，并同时识别潜在行聚类与列聚类？
- 方法与思路
- 作者建立双向潜在因子结构，先估计全局载荷空间，再向其正交补投影提取局部结构，以载荷进行 K-means 聚类并估计因子数。
- 材料陈述的贡献
- 摘要称全局载荷估计在温和条件下具有更快收敛率，并给出局部载荷、因子数和聚类成员估计的一致性与显式收敛率。
- 阅读关注点
- 核对共同与局部因子的区分条件、弱因子强度和维度增长方式，关注投影误差传播、因子数选择及聚类一致性所需条件。
- 阅读边界
- 这是预印本，同行评审及接收状态未核实。摘要未说明温和条件和具体收敛率，也未交代真实数据场景，不能据此认定普遍更优。
原文摘要
A novel unsupervised learning method is proposed in this paper for biclustering large-dimensional matrix-valued time series based on an entirely new latent two-way factor structure. Each block cluster is characterized by its own row and column cluster-specific factors in addition to some common matrix factors which impact on all the matrix time series. We first estimate the global loading spaces by projecting the observation matrices onto the row or column loading space corresponding to common factors. The loading spaces for cluster-specific factors are then further recovered by projecting the observation matrices onto the orthogonal complement space of the estimated global loading spaces. To identify the latent row/column clusters simultaneously for matrix-valued time series, we provide a $K$-means algorithm based on the estimated row/column factor loadings of the cluster-specific weak factors. Theoretically, we derive faster convergence rates for global loading matrices than those of the state-of-the-art methods available in the literature under mild conditions. We also propose an one-pass eigenvalue-ratio method to estimate the numbers of global and cluster-specific factors. The consistency with explicit convergence rates is also established for the estimators of the local loading matrices, the factor numbers and the latent cluster memberships. Numerical experiments with both simulated data as well as a real data example are also reported to illustrate the usefulness of our proposed method.