Tensor Decomposition With Generalized Lasso Penalties

We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multiway data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner parallel to the generalized lasso for regression and smoothing problems. Our approach presents many nontrivial challenges at the intersection of modeling and computation, which are studied in detail. An efficient coordinate-wise optimization algorithm for PTD is presented, and its convergence properties are characterized. The method is applied both to simulated data and real data on flu hospitalizations in Texas and motion-capture data from video cameras. These results show that our penalized tensor decomposition can offer major improvements on existing methods for analyzing multiway data that exhibit smooth spatial or temporal features.

我们提出了一种用于惩罚张量分解（Penalized Tensor Decomposition, PTD）的方法，可对多向数据中平滑变化的隐因子进行估计。该方法推广了现有稀疏张量分解与惩罚矩阵分解的相关研究，其推广思路与求解回归及平滑问题的广义Lasso（Generalized Lasso）方法相仿。我们的方法在建模与计算的交叉领域存在诸多非平凡挑战，本文对此展开了详尽研究。文中提出了一种针对PTD的高效坐标优化算法，并对其收敛性进行了理论刻画。该方法被分别应用于模拟数据、德克萨斯州流感住院病例的真实数据以及摄像机采集的动作捕捉数据。实验结果表明，针对具备平滑空间或时间特征的多向数据，本文提出的惩罚张量分解方法相较现有分析方法可实现显著性能提升。