Path Algorithms for One-Class SVM

The One-Class Support Vector Machine (OC-SVM) is all unsupervised learning algorithm, identifying unusual or outlying points (outliers) from a given dataset. In OC-SVM, it is required to set the regularization hyperparameter and kernel hyperparameter in order to obtain a good estimate. Generally, cross-validation is often used which requires multiple runs with different hyperparameters, making it very slow. Recently, the solution path algorithm becomes popular. It can obtain every solution for all hyperparameters in a single run rather than re-solve the optimization problem multiple times. Generalizing from previous algorithms for solution path in SVMs, this paper proposes a complete set of solution path algorithms for OC-SVM, including a v-path algorithm and a kernel-path algorithm. In the kernel-path algorithm, a new method is proposed to avoid the failure of algorithm due to indefinite matrix. Using those algorithms, we call obtain the optimum hyperparameters by computing all entire path solution with the computational cost O(n(2) + cnm(3)) on v-path algorithm or O(cn(3) + cnm(3)) on kernel-path algorithm or (c: constant, n: the number of sample, m: the number of sample which on the margin).