Support Vector Machine Construction Using Angle Space Mapping
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Solution Overview
Problem
Existing support vector machine (SVM) training algorithms face computational complexity issues, especially in high-dimensional spaces and dynamic training sets, making them inefficient for real-time applications like video analysis.
Innovation Solution
The method involves mapping an angle space to fixed angle vectors, finding candidate hyperplanes based on radial distance, and selecting optimal pairs to determine a classification hyperplane with linear computational complexity, allowing for dynamic adaptation and efficient classification in high-dimensional spaces.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If quadratic programming techniques are used to construct support vector machines, then classification accuracy is improved, but computational complexity increases significantly
Solution Approach 1:
The patent segments the complex quadratic programming problem into simpler sub-problems by using iterative algorithms that break down the training process into manageable steps, reducing overall computational complexity while maintaining classification accuracy
Solution Approach 2:
The patent changes the parameters of the optimization problem by transforming the quadratic programming formulation into alternative mathematical representations that are computationally more efficient, particularly for high-dimensional spaces and large datasets
2Measurement precision
If indirect quadratic programming is used to build support vector machines, then a suitable classification hyperplane can be identified, but the process becomes complex and difficult to adapt to changes in training samples
Solution Approach 1:
The patent introduces dynamic elements into the SVM construction process by creating algorithms that can efficiently retrain and adapt when training samples change, making the system flexible and responsive to new data without requiring complete reconstruction
Solution Approach 2:
The patent performs preliminary actions by pre-processing training samples and pre-computing certain parameters before the actual classification task, enabling faster adaptation when training sets change and reducing the computational burden during retraining
3Measurement precision
If traditional SVM training algorithms are used, then classification performance is maintained, but computational efficiency decreases in high-dimensional spaces and large datasets
Solution Approach 1:
The patent addresses high-dimensional space challenges by transforming the problem into different dimensional representations or using dimensionality reduction techniques that maintain classification performance while reducing computational complexity in the original high-dimensional space
Data Source
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AI summary
Methods and systems are described for building and using a support vector machine for classifying a new sample. Training samples of one class or another class are used to build the machine by mapping the angle space to a set of angle vectors and, for each angle vector, finding candidate hyperplanes that are orthogonal to a vector at the angle vector and radiating from an origin point to the hyperplane. An optimal pair of candidate hyperplanes at one of the angle vectors is selected on the basis of the distance between the pair and the number of samples between them. The selection may be based on hard margin or soft margin approaches. A matrix-based implementation is presented. New training samples may be added, removed, or reclassified without requiring recalculation of the entire support vector machine.