MULTI SVDD Based on Pseudo-Density

In this paper, we present a multi-class Support Vector Data Description (SVDD) algorithm based on pseudo-density estimation. The implementation involves three key computational steps: First, we strategically select representative data points as support vectors through a sampling mechanism that prioritizes boundary instances. Second, we calculate pseudo-density values for each support vector using kernel density estimation techniques (e.g., Gaussian kernel functions) to capture local data distribution characteristics. Third, we construct the multi-SVDD model by optimizing hypersphere boundaries that incorporate both the support vectors and their density weights, enabling simultaneous multi-class classification and anomaly detection. This density-aware approach significantly improves model discrimination by weighting instances according to their regional density importance, resulting in enhanced accuracy and robustness compared to traditional SVDD implementations. The method is particularly effective for complex datasets where class distributions exhibit varying density patterns.