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A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although they are not presented this way, can be viewed as spectral methods on matrices built from simple tensor networks. In this work we leverage the full power of this abstraction to design new algorithms for certain continuous tensor decomposition problems. An important and challenging family of tensor problems comes from orbit recovery, a class of inference problems involving group actions (inspired by applications such as cryo-electron microscopy). Orbit recovery problems over finite groups can often be solved via standard tensor methods. However, for infinite groups, no general algorithms are known. We give a new spectral algorithm based on tensor networks for one such problem: continuous multi-reference alignment over the infinite group SO(2). Our algorithm extends to the more general heterogeneous case.
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Regularized and smooth double core tensor factorization for heterogeneous data
We introduce a general tensor model suitable for data analytic tasks for heterogeneous datasets, wherein there are joint low-rank structures within groups of observations, but also discriminative structures across different groups. To capture such complex structures, a double core tensor (DCOT) factorization model is introduced together with a family of smoothing loss functions. By leveraging the proposed smoothing function, the model accurately estimates the model factors, even in the presence of missing entries. A linearized ADMM method is employed to solve regularized versions of DCOT factorizations, that avoid large tensor operations and large memory storage requirements. Further, we establish theoretically its global convergence, together with consistency of the estimates of the model parameters. The effectiveness of the DCOT model is illustrated on several realworld examples including image completion, recommender systems, subspace clustering, and detecting modules in heterogeneous Omics multi-modal data, since it provides more insightful decompositions than conventional tensor methods.
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- Award ID(s):
- 1838179
- PAR ID:
- 10397166
- Date Published:
- Journal Name:
- Journal of machine learning research
- ISSN:
- 1532-4435
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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