Abstract
We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals how the tensor dimensions (features) interact with each other. However, since the factors are a priori unknown, the corresponding optimization problems are inherently non-convex. The existing guaranteed algorithms which handle this non-convexity incur an irreducible error (bias), and only apply to cases where all factors have the same structure. To this end, we develop a provable algorithm for online structured tensor factorization, wherein one of the factors obeys some incoherence conditions, and the others are sparse. Specifically we show that, under some relatively mild conditions on initialization, rank, and sparsity, our algorithm recovers the factors exactly (up to scaling and permutation) at a linear rate. Complementary to our theoretical results, our synthetic and real-world data evaluations showcase superior performance compared to related techniques.
| Original language | English (US) |
|---|---|
| Journal | Advances in Neural Information Processing Systems |
| Volume | 2020-December |
| State | Published - 2020 |
| Event | 34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online Duration: Dec 6 2020 → Dec 12 2020 |
Bibliographical note
Funding Information:The authors graciously acknowledge the support from the DARPA YFA, Grant N66001-14-1-4047. The authors would also like to express their gratitude to Prof. Nikos Sidiropoulos and Di Xiao for their helpful discussions. The research work was undertaken when Sirisha Rambhatla was a doctoral student at the Department of Electrical and Computer Engineering, University of Minnesota – Twin Cities, Minneapolis, MN.
Funding Information:
The authors graciously acknowledge the support from the DARPA YFA, Grant N66001-14-1-4047. The authors would also like to express their gratitude to Prof. Nikos Sidiropoulos and Di Xiao for their helpful discussions. The research work was undertaken when Sirisha Rambhatla was a doctoral student at the Department of Electrical and Computer Engineering, University of Minnesota ? Twin Cities, Minneapolis, MN.
Publisher Copyright:
© 2020 Neural information processing systems foundation. All rights reserved.