Accelerated Structured Matrix Factorization
提出一种基于贝叶斯收缩先验的高维矩阵分解方法，通过诱导稀疏模式并利用外部信息，结合类似Boosting算法的数值策略实现低秩成分的序贯估计，在足球热图数据分析中展示了实用性。
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insights, with interpretation favored by sparse structures. Sparsity, in addition, is beneficial in terms of regularization and, thus, to avoid over-fitting. By exploiting Bayesian shrinkage priors, we devise a computationally convenient approach for high-dimensional matrix factorization. The dependence between row and column entities is modeled by inducing flexible sparse patterns within factors. The availability of external information is accounted for in such a way that structures are allowed while not imposed. Inspired by boosting algorithms, we pair the proposed approach with a numerical strategy relying on a sequential inclusion and estimation of low-rank contributions, with a data-driven stopping rule. Practical advantages of the proposed approach are demonstrated by means of a simulation study and the analysis of soccer heatmaps obtained from new generation tracking data. Supplementary materials for this article are available online.