Open-source agentic AI for transaction monitoring. Just ask Jooby.What's Jube? →
jube
  • Documentation
  • Analytical Methodology
  • Other Model Types
  • One-Class Support Vector Anomaly

One-Class Support Vector Anomaly Detection

A one-class support vector machine fits a boundary in a reshaped, kernel-induced space that wraps as tightly as its Nu parameter allows around the bulk of the rows, having only ever seen “normal” data — unlike a two-class SVM, it is never shown an anomalous example to separate from.

R equivalent

library(e1071)

set.seed(1)
n <- 200
amount <- rnorm(n, mean = 50, sd = 15)
velocity <- rpois(n, 2)
normal <- data.frame(amount, velocity)

model <- svm(normal, y = NULL, type = "one-classification", kernel = "radial",
             nu = 0.1, gamma = 0.5, scale = TRUE)
print(model)

new_cases <- data.frame(amount = c(48, 900), velocity = c(2, 40))
predict(model, new_cases, decision.values = TRUE)

Console output:


Call:
svm.default(x = normal, y = NULL, scale = TRUE, type = "one-classification", 
    kernel = "radial", gamma = 0.5, nu = 0.1)


Parameters:
   SVM-Type:  one-classification 
 SVM-Kernel:  radial 
      gamma:  0.5 
         nu:  0.1 

Number of Support Vectors:  30

    1     2 
FALSE FALSE 
attr(,"decision.values")
              /
1 -0.0003650763
2 -3.2553941825

Tool equivalent: Jube.Service.Repository.AnalyticsTrainingRun.AdvancedAnalyticsOneClassSupportVectorAnomalyTrainingService / tool SubmitOneClassSupportVectorAnomalyTraining — Kind = AnomalyDetector, recall class OneClassSupportVectorAnomalyRecall. Nu and Gamma are nu and gamma above (the kernel is fixed to Gaussian/radial for this family, unlike the two-class kernel SVM’s selectable Kernel enum). Labels are optional and never used to draw the boundary, exactly as y = NULL above; when given and both classes appear in the validation split they only Platt-calibrate the raw score (Calibrate) and report held-out quality, never reshape the boundary itself. Note both toy cases above returned FALSE (inside the boundary) despite the second row’s amount being wildly larger than anything trained on — a reminder that a tightly-fit one-class boundary in a high-gamma reshaped space can behave counter-intuitively on a single unscaled outlier, which is exactly the kind of evidence this family’s held-out metrics exist to surface before a model is promoted.

Code audit

Jube.Engine/AdvancedAnalytics/Anomaly/OneClassSupportVectorAnomalyTrainer.cs builds the design matrix (median imputation plus train-split z-scoring, OneClassSupportVectorAnomalyTrainer.cs:91-131) and then calls a real Accord class: Accord.MachineLearning.VectorMachines.Learning.OneclassSupportVectorLearning<IKernel<double[]>> (OneClassSupportVectorAnomalyTrainer.cs:139-146), with the kernel fixed to Gaussian.FromGamma(gamma) (line 141) — this family never exposes a kernel choice, unlike the two-class kernel SVM family.

Formulation

Accord’s BaseOneclassSupportVectorLearning<TModel, TKernel, TInput>.Learn (Accord.MachineLearning/VectorMachines/Learning/OneclassSupportVectorLearning.cs:315-447) is a direct implementation of Schölkopf’s ν-SVM one-class boundary, the same one LIBSVM ships (the class’s own doc comment cites “Chang and Lin, LIBSVM: A Library for Support Vector Machines, 2013” at lines 286-289). The initial Lagrange multipliers are built from n = (int)(nu * l) (OneclassSupportVectorLearning.cs:363): the first n rows get alpha = 1, one row gets the fractional remainder nu * l - n, and the rest start at 0 (lines 365-378); the quadratic program is then solved by a Fan-Chen-Lin sequential-minimal-optimisation-style solver under the box constraint 0 <= alpha <= 1 with the equality constraint enforced through the ones upper-bound vector (OneclassSupportVectorLearning.cs:358-397), and the bias term is set from the solver’s dual variable, Model.Threshold = -s.Rho (line 422). This is Schölkopf’s boundary formulation, not the older Tax & Duin support vector data description (SVDD): the class’s own remark that Nu is “an upper bound on the fraction of training errors and a lower bound of the fraction of support vectors” (OneclassSupportVectorLearning.cs:280-284) is Schölkopf’s own characterisation of ν, stated verbatim.

Nu, Gamma and the outlier-fraction mapping

Accord’s own class defaults nu to 0.5 internally (OneclassSupportVectorLearning.cs:162), but OneClassSupportVectorAnomalyTrainer.cs:142 always sets Nu = options.Nu explicitly, and OneClassSupportVectorAnomalyOptions.cs:21 defaults that to 0.1. There is no separate “expected outlier fraction” field on the DTO: Nu is that fraction, in the Schölkopf sense above — at the default 0.1, the fit is asymptotically guaranteed to treat at most about 10% of the training rows as margin errors and at least about 10% as support vectors. Gamma defaults to 0 on the options record (OneClassSupportVectorAnomalyOptions.cs:22), and the trainer maps that to 1 / variableCount (OneClassSupportVectorAnomalyTrainer.cs:137) — the classic “one over the number of features” rule of thumb, not a variance-based autoscale rule; a caller who wants the latter has to compute and pass it themselves.

Score sign and calibration

Accord’s raw decision value is bias + Σ alpha_i * K(x, sv_i) (OneClassSupportVectorAnomalyPipeline.cs:82-90), positive for rows the boundary treats as normal. Jube’s own pipeline negates it, Score(row) = -RawDecision(prepared) (OneClassSupportVectorAnomalyPipeline.cs:92-96), so that — consistently with the other anomaly families in this section — a higher score means more anomalous, the opposite convention to Accord’s own SupportVectorMachine.Decide. When labels are supplied and both classes appear in the validation split, that negated score is Platt-calibrated into a probability (OneClassSupportVectorAnomalyTrainer.cs:192-207); otherwise the raw negated decision value is reported as is (OneClassSupportVectorAnomalyTrainer.cs:175-183).

Other findings

  • The fitted machine’s support vectors, their weights and the kernel’s Gamma are the entire stored model (OneClassSupportVectorAnomalyTrainer.cs:261-280); there is no compact parametric form, so a warning is raised if the support vector set is dense (at least 90% of training rows, OneClassSupportVectorAnomalyTrainer.cs:236-238) or the snapshot is large (over 200,000 support vectors, lines 240-245).
  • trainX.Length <= variableCount is rejected outright (OneClassSupportVectorAnomalyTrainer.cs:83-84, 377-379) — there must be more rows than variables before training is attempted at all.