SVDD Kernel Parameter Optimization via Incremental Sampling
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Solution Overview
Problem
The high computational time required to solve quadratic programming problems in support vector data description (SVDD) for large training datasets hinders efficient outlier identification, especially when using kernel functions like the Gaussian kernel.
Innovation Solution
The method involves incrementally computing kernel parameter values by iteratively solving objective functions for progressively larger sample sizes until convergence, using a penalized B-spline curve fit to optimize the kernel parameter, thereby reducing computational complexity and improving efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the entire training dataset is used to solve the quadratic programming problem in SVDD, then the accuracy of outlier identification is improved, but the computational time becomes very high for large datasets
Solution Approach 1:
The patent divides the training dataset into multiple smaller random samples. Instead of using the entire dataset to solve the quadratic programming problem, the method selects multiple random samples (e.g., 10 samples of size 100) and computes SVDD for each sample separately. This segmentation reduces the computational complexity from O(N) to O(k * m) where N is the total dataset size, k is the number of samples, and m is the sample size, significantly reducing computational time while maintaining acceptable accuracy.
Solution Approach 2:
The patent uses partial action by computing SVDD on only a subset of the training data rather than the complete dataset. By selecting random samples that represent the data distribution, the method achieves sufficient accuracy without the computational burden of processing all data points, effectively applying partial action to resolve the time-accuracy tradeoff.
2Manufacturing precision
If kernel function parameters are optimized using exhaustive search over all possible values, then the data boundary description is improved, but the computational complexity increases significantly
Solution Approach 1:
The patent segments the kernel parameter optimization process by evaluating parameters at discrete, predefined values rather than exhaustively searching the entire parameter space. The method computes SVDD for multiple random samples using a fixed set of kernel parameters (e.g., gamma values from 0.01 to 10 in logarithmic scale) and selects the parameter that minimizes the average SVDD cost, reducing complexity from continuous optimization to discrete evaluation.
Solution Approach 2:
The patent applies preliminary action by pre-defining a set of candidate kernel parameter values before computing SVDD for the random samples. Instead of optimizing parameters during the SVDD computation, the method prepares a discrete parameter grid in advance and evaluates only these predetermined values, significantly reducing computational complexity while maintaining adequate parameter optimization.
Data Source
AI summary
A computing device determines a kernel parameter value for a support vector data description for outlier identification. A first candidate optimal kernel parameter value is computed by computing a first optimal value of a first objective function that includes a kernel function for each of a plurality of kernel parameter values from a starting kernel parameter value to an ending kernel parameter value using an incremental kernel parameter value. The first objective function is defined for a SVDD model using observation vectors to define support vectors. A number of the observation vectors is a predefined sample size. The predefined sample size is incremented by adding a sample size increment. A next candidate optimal kernel parameter value is computed with an incremented number of vectors until a computed difference value is less than or equal to a predefined convergence value.