Tensor Data Processing for Pattern Recognition
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Solution Overview
Problem
Existing vector mode algorithms for processing tensor data face issues such as the curse of dimensionality, overlearning, and small sample sizes, leading to high time complexity and frequent local minimum values, which affect their efficiency and accuracy in pattern recognition.
Innovation Solution
The method introduces a within class scatter matrix into the objective function to maximize between-class distance while minimizing within-class distance, transforming N vector modes of quadratic programming subproblems into a multiple quadratic programming problem under a single tensor mode, using tensor rank one decomposition and sequential minimal optimization to obtain an optimal projection tensor for efficient pattern recognition.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If vector mode algorithm is used to process tensor data, then the processing can be performed with existing algorithms, but the spatial information and inner correlation of tensor data are destroyed and the number of parameters increases excessively
Solution Approach 1:
The patent transitions from vector mode processing to tensor mode processing, changing the dimensional representation of data. Instead of flattening tensor data into vectors (which increases parameters and destroys spatial structure), the method operates directly on tensor data in its native multi-dimensional form, preserving spatial information and reducing the number of parameters needed.
Solution Approach 2:
The patent segments the high-dimensional parameter space by utilizing the inherent multi-dimensional structure of tensor data. By processing each dimension separately through mode projections and maintaining the tensor structure, the method divides the complex high-dimensional problem into manageable lower-dimensional subproblems.
2Loss of information
If tensor mode algorithm is used to solve the objective function, then the spatial information is preserved, but the time complexity increases and local minimum values occur frequently
Solution Approach 1:
The patent applies segmentation by decomposing the tensor optimization problem into N separate mode projection subproblems. Each subproblem operates on a single mode of the tensor, transforming a complex non-convex optimization problem into multiple simpler quadratic programming problems that can be solved more efficiently and with fewer local minima.
Solution Approach 2:
The patent changes the optimization approach by moving from direct tensor space optimization to mode projection space optimization. By projecting tensor data onto lower-dimensional subspaces along each mode and solving quadratic programming problems in these projected spaces, the method reduces computational complexity while preserving essential spatial information.
3Adaptability or versatility
If feature extraction (vectorization) is performed on tensor data, then the data can be processed by existing algorithms, but the inner correlation of tensor data is destroyed
Solution Approach 1:
Instead of vectorizing tensor data (flattening it into a 1D array), the patent operates in the tensor's native multi-dimensional space. By performing mode projections along each dimension and solving optimization problems in these projected spaces, the method maintains algorithm compatibility through standardized quadratic programming while preserving the inner correlations inherent in the tensor structure.
Data Source
AI summary
A method for processing tensor data for pattern recognition and a computer device are provided. The method includes: constructing a decision function by the optimal projection tensor W which has been rank-one decomposed together with the offset scalar b, and inputting to-be-predicted tensor data which has been rank-one decomposed into the decision function for prediction.