Dimension-Wise Embedding for Linear Classifier Training
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Solution Overview
Problem
Current classifier training methods face high computational costs when using nonlinear classifiers, especially with large datasets, which limits their accuracy compared to linear classifiers.
Innovation Solution
The method involves embedding training samples from a first multi-dimension space into a second space of the same or higher dimensionality, allowing for the training of a linear classifier that approximates nonlinear classifiers, thereby reducing computational costs while maintaining accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If nonlinear classifiers are used to improve classification accuracy, then accuracy is improved, but computational cost increases significantly
Solution Approach 1:
The patent transforms the classification problem from the original D-dimensional feature space to a new D×E dimensional space through embedding functions. This dimensionality change allows linear classifiers in the embedded space to approximate nonlinear decision boundaries in the original space, achieving high accuracy with lower computational cost.
Solution Approach 2:
The patent introduces embedding functions as intermediary transformations that map original feature vectors to embedded vectors in a higher-dimensional space. These embedding functions serve as mediators that enable linear classifiers to achieve nonlinear classification performance by operating in the transformed space.
2Productivity
If linear classifiers are used to reduce computational cost, then computational efficiency is improved, but classification accuracy deteriorates
Solution Approach 1:
By embedding training samples and test vectors into a D×E dimensional space, the patent enables linear classifiers to achieve accuracy comparable to nonlinear classifiers. The dimensionality change creates a space where linear separation is possible while maintaining computational efficiency.
Solution Approach 2:
The patent transforms the classification problem by changing the parameters (features) through embedding functions. This parameter transformation allows linear classifiers to effectively capture nonlinear relationships by operating on transformed features in the embedded space.
3Measurement precision
If embedding functions are applied to transform training data into higher dimensional space, then classification accuracy is improved, but data processing complexity increases
Solution Approach 1:
The patent divides the embedding process into dimension-wise independent operations. Each of the D dimensions is embedded separately using its own embedding function, and the results are concatenated to form the final D×E dimensional embedded vector. This segmentation simplifies the overall processing complexity.
Solution Approach 2:
The patent applies parameter changes through embedding functions that transform each dimension independently. This approach maintains relative simplicity by operating on individual dimensions separately rather than requiring complex joint transformations of the entire feature vector.
Data Source
AI summary
A classifier training method and apparatus for training, a linear classifier trained by the method, and its use, are disclosed. In training the linear classifier, signatures for a set of training samples, such as images, in the form of multi-dimension vectors in a first multi-dimensional space, are converted to a second multi-dimension space, of the same or higher dimensionality than the first multi-dimension space, by applying a set of embedding functions, one for each dimension of the vector space. A linear classifier is trained in the second multi-dimension space. The linear classifier can approximate the accuracy of a non-linear classifier in the original space when predicting labels for new samples, but with lower computation cost in the learning phase.