Remove Outliers from dataset

Question

Once I've identified outliers in my dataset using either One-class SVM or Elliptic Envelope, how can I use these models to remove the outliers from the dataset?

Here is the example I'm looking at.

Answer 1

This example is slightly less opaque as it doesn't loop through unnamed models. I have to agree with you that the predict methods are often glossed over in the SKL manual as people focus on training methods.

But... the predict method will return a vector of 1's or -1's corresponding to non-outliers and outliers.

Here is the original example code I referenced above:

print(__doc__)

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.font_manager
from scipy import stats

from sklearn import svm
from sklearn.covariance import EllipticEnvelope

# Example settings
n_samples = 200
outliers_fraction = 0.25
clusters_separation = [0, 1, 2]

# define two outlier detection tools to be compared
classifiers = {
    "One-Class SVM": svm.OneClassSVM(nu=0.95 * outliers_fraction + 0.05,
                                     kernel="rbf", gamma=0.1),
    "robust covariance estimator": EllipticEnvelope(contamination=.1)}

# Compare given classifiers under given settings
xx, yy = np.meshgrid(np.linspace(-7, 7, 500), np.linspace(-7, 7, 500))
n_inliers = int((1. - outliers_fraction) * n_samples)
n_outliers = int(outliers_fraction * n_samples)
ground_truth = np.ones(n_samples, dtype=int)
ground_truth[-n_outliers:] = 0

# Fit the problem with varying cluster separation
for i, offset in enumerate(clusters_separation):
    np.random.seed(42)
    # Data generation
    X1 = 0.3 * np.random.randn(0.5 * n_inliers, 2) - offset
    X2 = 0.3 * np.random.randn(0.5 * n_inliers, 2) + offset
    X = np.r_[X1, X2]
    # Add outliers
    X = np.r_[X, np.random.uniform(low=-6, high=6, size=(n_outliers, 2))]

    # Fit the model with the One-Class SVM
    plt.figure(figsize=(10, 5))
    for i, (clf_name, clf) in enumerate(classifiers.items()):
        # fit the data and tag outliers
        clf.fit(X)
        y_pred = clf.decision_function(X).ravel()
        threshold = stats.scoreatpercentile(y_pred,
                                            100 * outliers_fraction)
        y_pred = y_pred > threshold
        n_errors = (y_pred != ground_truth).sum()
        # plot the levels lines and the points
        Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
        Z = Z.reshape(xx.shape)
        subplot = plt.subplot(1, 2, i + 1)
        subplot.set_title("Outlier detection")
        subplot.contourf(xx, yy, Z, levels=np.linspace(Z.min(), threshold, 7),
                         cmap=plt.cm.Blues_r)
        a = subplot.contour(xx, yy, Z, levels=[threshold],
                            linewidths=2, colors='red')
        subplot.contourf(xx, yy, Z, levels=[threshold, Z.max()],
                         colors='orange')
        b = subplot.scatter(X[:-n_outliers, 0], X[:-n_outliers, 1], c='white')
        c = subplot.scatter(X[-n_outliers:, 0], X[-n_outliers:, 1], c='black')
        subplot.axis('tight')
        subplot.legend(
            [a.collections[0], b, c],
            ['learned decision function', 'true inliers', 'true outliers'],
            prop=matplotlib.font_manager.FontProperties(size=11))
        subplot.set_xlabel("%d. %s (errors: %d)" % (i + 1, clf_name,n_errors))
        subplot.set_xlim((-7, 7))
        subplot.set_ylim((-7, 7))
    plt.subplots_adjust(0.04, 0.1, 0.96, 0.94, 0.1, 0.26)

plt.show()

And this command will return the vector of 1's and -1's:

In [7]: clf.predict(X)

Out[7]:
array([ 1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
    1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
    1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
    1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
    1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
    1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
    1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
    1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
    1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1, -1,
    1, -1,  1,  1, -1,  1, -1,  1, -1, -1,  1,  1,  1,  1,  1,  1, -1,
    1,  1, -1, -1, -1, -1, -1, -1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
   -1,  1, -1, -1, -1, -1, -1,  1, -1,  1,  1,  1,  1])

Then you can select on just the nonoutliers:

In [14]: X[clf.predict(X)==1]

Out[14]: array([[-1.85098575, -2.04147929],
   [-1.80569344, -1.54309104],
   [-2.07024601, -2.07024109],
   [-1.52623616, -1.76976958],
   [-2.14084232, -1.83723199],
   [-2.13902531, -2.13971893],
   [-1.92741132, -2.57398407],
   [-2.51747535, -2.16868626],
   [-2.30384934, -1.9057258 ],

And assign the cleaned data to a new value:

X_no_outliers=X[clf.predict(X)==1]

Hope this helps!