Efficient and interpretable spatial analysis is crucial in many fields such
as geology, sports, and climate science. Tensor latent factor models can
describe higher-order correlations for spatial data. However, they are
computationally expensive to train and are sensitive to initialization, leading
to spatially incoherent, uninterpretable results. We develop a novel
Multiresolution Tensor Learning (MRTL) algorithm for efficiently learning
interpretable spatial patterns. MRTL initializes the latent factors from an
approximate full-rank tensor model for improved interpretability and
progressively learns from a coarse resolution to the fine resolution to reduce
computation. We also prove the theoretical convergence and computational
complexity of MRTL. When applied to two real-world datasets, MRTL demonstrates
4~5x speedup compared to a fixed resolution approach while yielding accurate
and interpretable latent factors.

本文提出了一种新颖的多分辨率张量学习算法，用于在提高解释性的同时提高计算效率，该算法从粗糙的分辨率到细粒度逐步学习，证明了其理论收敛和计算复杂性，并在实际数据集中展现了 4~5 倍的性能提升。