Tensor Decomposition Compression for Multi-Dimensional Data Integrity
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Solution Overview
Problem
Current data compression methods fail to effectively preserve the dimensional integrity of multi-dimensional data, leading to suboptimal storage reduction and computation efficiency, especially when compared to matrix-based representations.
Innovation Solution
A computer-implemented tensor decomposition method using truncated tensor-tensor decompositions that honor the dimensional integrity of data, providing a provably superior compression mechanism with efficient computation and storage reduction, suitable for parallel and distributed processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of substance
If traditional matrix-based compression methods are used, then storage reduction is achieved, but the dimensional integrity of multi-dimensional data is lost
Solution Approach 1:
The patent transitions from matrix-based (2D) compression to tensor-based (3D or higher) compression by representing multi-dimensional data in its native tensor format. This allows the compression method to operate across multiple dimensions simultaneously, preserving the inherent multi-way relationships in the data while achieving storage reduction through tensor decomposition techniques.
2Loss of substance
If data is reshaped to reveal Kronecker product structure, then storage cost is reduced, but computational complexity increases
Solution Approach 1:
The patent performs preliminary reshaping and decomposition operations during the compression phase to reveal the Kronecker product structure. By pre-processing the data into a format that exposes its underlying structure, the method enables more efficient storage while the computational complexity is managed through systematic decomposition algorithms that break down the complex reshaping task into manageable steps.
3Measurement precision
If tensor decompositions are applied to capture structural redundancies, then compression fidelity is improved, but computational efficiency deteriorates
Solution Approach 1:
The patent segments the tensor decomposition process into multiple manageable stages, including orthogonal decomposition, singular value decomposition, and iterative refinement steps. This segmentation allows the complex decomposition task to be broken down into smaller, more efficient computational units that can be processed systematically, improving both fidelity and efficiency by avoiding monolithic computation.
Solution Approach 2:
The patent implements truncated tensor decompositions that capture the most significant structural redundancies while discarding less important components. By performing partial decomposition that focuses on the dominant patterns in the data, the method achieves high compression fidelity with reduced computational effort compared to complete decomposition.
Data Source
AI summary
A tensor decomposition method, system, and computer program product include compressing multi-dimensional data by truncated tensor-tensor decompositions.