One class SVM toy example not understood

Question

I've been playing around with one class SVM. I think I understand the theory behind it (that it attempts to separate the data from the origin). I attempted to run a toy example which the algorithm should fit perfectly; however it seems like I'm missing something since the algorithm doesn't classify all the training examples as non anomalies. Code:

import numpy as np
from sklearn import svm
import matplotlib.pyplot as plt
import matplotlib.font_manager

xx, yy = np.meshgrid(np.linspace(-5, 5, 500), np.linspace(-5, 5, 500))

x = np.array([1, 3, 1, 3, 2])
y = np.array([1, 1, 3, 3, 2])
feature = np.vstack((x, y)).T
clf = svm.OneClassSVM(nu=0.1, kernel="rbf", gamma=0.1)
clf.fit(feature)
y_pred_train = clf.predict(feature)
Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()]) 
Z = Z.reshape(xx.shape)
print(y_pred_train)
print(feature)
plt.title("Novelty Detection")
plt.contourf(xx, yy, Z, levels=np.linspace(Z.min(), 0, 7), cmap=plt.cm.PuBu)
a = plt.contour(xx, yy, Z, levels=[0], linewidths=2, colors='darkred')
plt.contourf(xx, yy, Z, levels=[0, Z.max()], colors='palevioletred')

b1 = plt.scatter(feature[:, 0], feature[:, 1], c='white', s=40, 
edgecolors='k')

plt.show()

the prediction on the training set is [ 1 -1 1 1 1], which does not make sense.

Please advise.

Answer 1

One Class SVM is taking at least one outlier (anomaly) among your dataset. This is why you see one "wrong" label in the predicted labels.