On Spectral Learning for Odeco Tensors: Perturbation, Initialization, and Algorithms

Tensors, as higher-order generalizations of matrices, have emerged as powerful tools for representing and analyzing multi-dimensional data. They naturally arise in diverse applications such as multi-relational networks, spatiotemporal measurements, neuroimaging, and latent variable models. Unlike matrices, which capture only pairwise relationships, tensors encode multi-way interactions, offering richer structural insights. Among the various tensor models, orthogonally decomposable (odeco) tensors play a special role. Their decomposition structure parallels the eigendecomposi-tion of matrices, but with important advantages in both statistical robustness and computational tractability. In particular, odeco tensors arise in the method of moments for latent variable models.