XLSTAT: Training a one-class support vector machine

 

Dataset for Example

The dataset is extracted from the data science platform, Kaggle and might be accessed at this address.

The “Banknotes” dataset is made up of a list of 200 banknotes with some information: This dataset contains 7 variables; One is qualitative and informs on the banknotes' authenticity and the others are quantitative variables and inform on banknotes' shapes.

Counterfeit: in case the banknote is genuine we put “0”, in the contrary case the banknote is counterfeit we put “1”. 100 banknotes are counterfeits when the 100 others are genuine in this dataset. Length, Left, Right, Bottom, Top, Diagonal are quantitative variables.

A second dataset of 10 banknotes is available and will be used to predict if those banknotes are genuines or counterfeits.

The data will be used to learn how to detect anomalies using a One-class SVM on the “Banknotes” dataset and evaluate how well the algorithm performs based on a 10-fold cross-validation.

 

Setting Up

• Open XLSTAT.

• Click on the Machine Learning menu and select the One-class Support Vector Machine feature.

 

• Once you have clicked on the button, the dialog box appears.

In the General tab:

• In the Quantitative field, we select all quantitative variables: “Length”, “Left”, “Right”, “Bottom”, “Top” and “Diagonal”. To select multiple columns, you may use the Ctrl key.

• To use the references we have for each banknote, check Known classes and select the binary variable “Counterfeit”.

• Enter “1” as the outlier class because it is the class of the counterfeit banknotes.

• As the name of each variable is present at the top of the table, we must check the Variable labels checkbox.

In the Options tab:

• For SMO parameters, the Nu field sets the regularization level, i.e., the allowed percentage of outliers. A value closer to 1 allows more outliers.

• Keep the tolerance at its default; it controls the precision of the optimization. Higher tolerance speeds up the process but reduces accuracy.

• Choose Standardization for preprocessing.

• Select linear kernels.

• Enable 10-fold cross-validation to assess classifier performance.

In the Prediction tab:

• Select the 6 quantitative variables to predict the 10 new observations.

• Check the Variable labels box, as each variable name appears in the first row.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The first table shows cross-validation performance, including classification error rate, f-score, and balanced accuracy (BAC) for each fold. The mean classification error rate is 29.1% with the chosen parameters.

The following table displays performance metrics on the training dataset including 10 indicators:

For One-class classification, the F-score (78%) is preferred and indicates good anomaly detection. The ROC curve shows (1 – specificity, sensitivity) across thresholds, ideally near the upper left corner, which is true here.

The first table summarizes the optimized SVM classifier. Outlier class is 1, with 200 training observations, 113 support vectors identified, and a bias close to zero.

The second table lists all 113 support vectors with their alpha values. Along with the bias, this fully describes the optimized classifier.

Finally, the predicted classes for the 10 new observations are shown: the first column gives the predicted class, and the second shows the decision function values.

As we chose « 1 » as the outlier class, then observations predicted as “1” are outliers according to the method.