IncTSVD: Incremental Tensor Singular Value Decomposition of Multidimensional Streaming Data.

Area of Science:

• Numerical Analysis
• Data Science
• Tensor Computations

Background:

• Tensor Singular Value Decomposition (TSVD) is crucial for analyzing multi-dimensional data.
• Existing TSVD methods often require large batch computations, limiting their use with streaming data or limited memory.
• Incremental Singular Value Decomposition (SVD) for matrices offers a precedent for updating decompositions.

Purpose of the Study:

• To develop an online algorithm for incrementally computing TSVD on sequences of third-order tensors.
• To address the limitations of batch-based TSVD methods for streaming tensor data and memory constraints.
• To extend the concept of incremental matrix SVD to the domain of tensor analysis.

Main Methods:

• The IncTSVD algorithm incrementally computes TSVD using a tensor-tensor concept.
• It maintains basis tensors from previous data and updates the TSVD approximation with incoming tensor data.
• Theoretical analysis and extensive numerical experiments on synthetic and real-world datasets were performed.

Main Results:

• IncTSVD demonstrated superior computational and storage efficiency compared to existing t-product based tensor decompositions.
• The method achieved accuracy comparable to standard TSVD.
• Numerical experiments validated the theoretical analysis of computational cost and approximation error.

Conclusions:

• IncTSVD is an effective method for online, incremental computation of TSVD for streaming tensor data.
• The algorithm offers significant advantages in computational and storage costs, making it suitable for memory-limited environments.
• IncTSVD provides a viable alternative to batch tensor decomposition techniques for dynamic data streams.