Tensor Decomposition for Multidimensional Data Processing
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Solution Overview
Problem
Conventional methods for processing multidimensional data using high-rank tensors exceed the processing capabilities of current computing resources, leading to inefficiencies in time and resource utilization.
Innovation Solution
The method involves decomposing a reference tensor into multiple low-rank tensors, allowing for the determination of a target tensor that represents multidimensional data at a specific moment, thereby reducing computational overhead and processing time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If high-rank tensors are used to represent multidimensional data, then data completeness and dimensionality are preserved, but processing time and computational resource overhead increase significantly
Solution Approach 1:
The patent segments the high-rank tensor into multiple low-rank tensors through tensor decomposition. Instead of processing one large high-rank tensor, the system breaks it down into several smaller low-rank tensors that can be processed more efficiently while preserving the essential multidimensional information through the decomposition structure.
2Measurement precision
If high-rank tensors are used to represent multidimensional data, then comprehensive data representation is achieved, but computational resource overhead becomes unmanageable
Solution Approach 1:
The high-rank tensor is segmented into multiple low-rank tensors, reducing the computational complexity of each individual tensor while maintaining the overall data representation capability through the collective structure of the decomposed tensors.
Solution Approach 2:
The patent changes the rank parameter of the tensor from high to low through decomposition. By transforming the tensor rank parameter, the system reduces computational resource requirements while preserving the essential information through the decomposition methodology.
3Adaptability or versatility
If conventional tensor methods are used for multidimensional data processing, then all dimensions are considered simultaneously, but the processing capability requirements exceed available resources
Solution Approach 1:
The patent segments the multidimensional processing task into multiple lower-dimensional sub-tasks through tensor decomposition. Each low-rank tensor handles a portion of the multidimensional data, allowing parallel or sequential processing that improves overall productivity while maintaining adaptability to process all dimensions.
Data Source
AI summary
Embodiments of the present disclosure relate to a method, an electronic device, and a computer program product for processing data. The method includes determining a reference tensor based on a tensor representing multidimensional data, where the reference tensor is associated with a target tensor. The method further includes decomposing the reference tensor to obtain multiple low-rank tensors, where a rank of each of the low-rank tensors is lower than that of the reference tensor. The method further includes determining the target tensor based on the multiple low-rank tensors so as to determine multidimensional data at a specific moment. By means of embodiments of the present disclosure, the overhead of computing resources may be reduced, and the time for processing data may be reduced.