Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of node features and interactions thereof, together with the tensor data. Such data problems are common in neuroimaging, network analysis, and spatial-temporal modeling. Identifying the relationship between a high-dimensional tensor and side information is important yet challenging. Here, we develop a tensor decomposition method that incorporates multiple feature matrices as side information. Unlike unsupervised tensor decomposition, our supervised decomposition captures the effective dimension reduction of the data tensor confined to feature space of interest. An efficient alternating optimization algorithm with provable spectral initialization is further developed. Our proposal handles a broad range of data types, including continuous, count, and binary observations. We apply the method to diffusion tensor imaging data from human connectome project and multi-relational political network data. We identify the key global connectivity pattern and pinpoint the local regions that are associated with available features. Our simulation code, R-package tensorregress, and datasets used in the paper are available at https://CRAN.R-project.org/package=tensorregress.
翻译:虽然大多数高压分解方法是为单一粒子观测开发的,但科学研究往往以节点特征及其相互作用的形式收集侧面信息,并收集高压数据。这些数据问题在神经成像、网络分析和空间时空建模中很常见。确定高维抗拉和侧面信息之间的关系很重要,但挑战性仍然很大。在这里,我们开发了一种将多个特征矩阵作为侧信息纳入多个特征矩阵的反向分解方法。不同于未受监督的高压分解,我们监管的分解方法则捕捉了限制在感兴趣空间的数据分解的有效维度的减少。进一步开发了高效交替优化算法,同时可调频谱初始化。我们的提案涉及广泛的数据类型,包括连续、计数和双元观测。我们采用了从人类连接项目和多关系政治网络数据中传播高压成像数据的方法。我们确定了关键的全球连通模式,并确定了与现有特征相关的本地区域。我们的模拟代码、R-gragregregregress、MAPRresmressups。