Streaming Generalized Canonical Polyadic Tensor Decompositions
This work addresses the need for scalable and interpretable tensor decomposition methods in streaming applications, particularly for non-Gaussian data, but it is incremental as it extends existing GCP formalism to streaming contexts.
The authors tackled the problem of computing Generalized Canonical Polyadic (GCP) tensor decompositions for streaming data, developing OnlineGCP to incrementally update factorizations with limited access to prior data, and demonstrated its utility and performance on synthetic and real datasets.
In this paper, we develop a method which we call OnlineGCP for computing the Generalized Canonical Polyadic (GCP) tensor decomposition of streaming data. GCP differs from traditional canonical polyadic (CP) tensor decompositions as it allows for arbitrary objective functions which the CP model attempts to minimize. This approach can provide better fits and more interpretable models when the observed tensor data is strongly non-Gaussian. In the streaming case, tensor data is gradually observed over time and the algorithm must incrementally update a GCP factorization with limited access to prior data. In this work, we extend the GCP formalism to the streaming context by deriving a GCP optimization problem to be solved as new tensor data is observed, formulate a tunable history term to balance reconstruction of recently observed data with data observed in the past, develop a scalable solution strategy based on segregated solves using stochastic gradient descent methods, describe a software implementation that provides performance and portability to contemporary CPU and GPU architectures and integrates with Matlab for enhanced useability, and demonstrate the utility and performance of the approach and software on several synthetic and real tensor data sets.