One-Class SVM

The algorithm maps data into a kernel feature space and constructs a maximal-margin hyperplane that separates the training data from the origin. The ν (nu) parameter controls the upper bound on the fraction of training errors and the lower bound on the fraction of support vectors, effectively tuning the model's sensitivity to outliers. Points falling on the origin side of the hyperplane are classified as anomalies.

One-Class SVM employs kernel functions to implicitly project data into high-dimensional spaces where complex, non-linear decision boundaries become linearly separable. Common kernels include:

• RBF (Radial Basis Function): Captures localized, spherical boundaries around normal clusters
• Polynomial Kernel: Models higher-order feature interactions
• Sigmoid Kernel: Approximates neural network activation behavior The choice of kernel and its hyperparameters (e.g., γ in RBF) critically determines the granularity of the learned boundary.

Only a subset of training points—the support vectors—define the decision boundary. These are the data points lying exactly on or within the margin. The model's complexity and memory footprint are proportional to the number of support vectors, not the total training set size. In open set emitter recognition, support vectors represent the most characteristic or borderline examples of a known transmitter's fingerprint, enabling efficient inference on resource-constrained edge devices.

The optimization problem is solved in its Lagrangian dual form, which expresses the decision function solely in terms of inner products between data points. This dual formulation enables the kernel trick and transforms the problem into a convex quadratic programming task with a single global minimum—guaranteeing reproducibility. The Sequential Minimal Optimization (SMO) algorithm is commonly used to efficiently solve this dual problem by decomposing it into the smallest possible sub-problems.

The learned model outputs a real-valued decision score for each test sample, not just a binary label. The sign of the decision function indicates class membership (positive for normal, negative for anomaly), while the magnitude reflects the distance from the boundary. This continuous score is invaluable for open set emitter recognition, as it allows operators to set calibrated rejection thresholds based on Extreme Value Theory (EVT) or operational risk tolerance, rather than relying on a hard binary cutoff.

Unlike binary classifiers that require both positive and negative examples, One-Class SVM is trained exclusively on normal class samples. This makes it inherently robust to severe class imbalance—a critical advantage in emitter recognition where comprehensive libraries of adversary or unknown device signatures are unavailable by definition. The model does not require assumptions about the distribution or prevalence of anomalies, making it ideal for open set recognition scenarios where the space of unknowns is unbounded.