Kernel Parameter Selection in Support Vector Data Description
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Solution Overview
Problem
Current support vector data description (SVDD) methods for outlier detection face challenges in accurately defining flexible boundaries around data, leading to increased false positives and inefficient outlier identification due to the reliance on circular hypersphere models, which do not effectively capture the shape of complex datasets.
Innovation Solution
The implementation of a non-transitory computer-readable medium with instructions that compute optimal support vector sets using a Gaussian kernel function, allowing for the selection of a kernel parameter value where the second derivative of the objective function exceeds zero, thereby defining a flexible boundary that closely follows the dataset's shape.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If a circular hypersphere model is used for SVDD, then the model is simple and easy to compute, but the boundary does not effectively capture the shape of complex datasets leading to increased false positives
Solution Approach 1:
The patent changes the parameter of the kernel function from a fixed circular hypersphere to a Gaussian kernel with variable bandwidth parameter. By optimizing this parameter through derivative analysis, the model adapts its shape to capture complex data distributions while maintaining computational efficiency. This resolves the contradiction by allowing the boundary to flex and conform to data shapes without increasing model complexity.
Solution Approach 2:
The patent introduces dynamic adaptability to the SVDD model through the Gaussian kernel's bandwidth parameter, which can be optimized based on the data. The boundary dynamically adjusts its flexibility to match the underlying data distribution, transitioning from a rigid circular hypersphere to an adaptive shape that captures complex structures while remaining computationally tractable.
2Productivity
If the kernel parameter is not optimized, then the computation is faster, but the boundary flexibility and outlier detection accuracy are reduced
Solution Approach 1:
The patent performs preliminary optimization of the kernel parameter by analyzing the first and second derivatives of the objective function before actual outlier detection. This preliminary action identifies the optimal bandwidth parameter that balances boundary flexibility with computational efficiency, ensuring high detection accuracy without requiring excessive computation during the main detection process.
Solution Approach 2:
The patent uses feedback from the objective function's derivatives to guide parameter selection. By computing the first derivative to find critical points and the second derivative to confirm minima, the system feedback-adjusts the kernel parameter to achieve optimal performance. This feedback mechanism ensures that the selected parameter provides the best balance between computational speed and detection reliability.
Data Source
AI summary
A computer-readable medium is configured to determine a support vector data description (SVDD). For each of a plurality of values for a kernel parameter, an optimal value of an objective function defined for an SVDD model using a kernel function, a read plurality of data points, and a respective value for the kernel parameter is computed to define a plurality of sets of support vectors. A plurality of first derivative values are computed for the objective function as a difference between the computed optimal values associated with successive values for the kernel parameter. A plurality of second derivative values are computed for the objective function as a difference between the computed plurality of first derivative values associated with successive values for the kernel parameter. A kernel parameter value is selected where the computed plurality of second derivative values first exceeds zero.