.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/miscellaneous/plot_outlier_detection_bench.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_miscellaneous_plot_outlier_detection_bench.py: ========================================== Evaluation of outlier detection estimators ========================================== This example compares two outlier detection algorithms, namely :ref:`local_outlier_factor` (LOF) and :ref:`isolation_forest` (IForest), on real-world datasets available in :class:`sklearn.datasets`. The goal is to show that different algorithms perform well on different datasets and contrast their training speed and sensitivity to hyperparameters. The algorithms are trained (without labels) on the whole dataset assumed to contain outliers. 1. The ROC curves are computed using knowledge of the ground-truth labels and displayed using :class:`~sklearn.metrics.RocCurveDisplay`. 2. The performance is assessed in terms of the ROC-AUC. .. GENERATED FROM PYTHON SOURCE LINES 20-24 .. code-block:: Python # Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause .. GENERATED FROM PYTHON SOURCE LINES 25-40 Dataset preprocessing and model training ======================================== Different outlier detection models require different preprocessing. In the presence of categorical variables, :class:`~sklearn.preprocessing.OrdinalEncoder` is often a good strategy for tree-based models such as :class:`~sklearn.ensemble.IsolationForest`, whereas neighbors-based models such as :class:`~sklearn.neighbors.LocalOutlierFactor` would be impacted by the ordering induced by ordinal encoding. To avoid inducing an ordering, on should rather use :class:`~sklearn.preprocessing.OneHotEncoder`. Neighbors-based models may also require scaling of the numerical features (see for instance :ref:`neighbors_scaling`). In the presence of outliers, a good option is to use a :class:`~sklearn.preprocessing.RobustScaler`. .. GENERATED FROM PYTHON SOURCE LINES 40-81 .. code-block:: Python from sklearn.compose import ColumnTransformer from sklearn.ensemble import IsolationForest from sklearn.neighbors import LocalOutlierFactor from sklearn.pipeline import make_pipeline from sklearn.preprocessing import ( OneHotEncoder, OrdinalEncoder, RobustScaler, ) def make_estimator(name, categorical_columns=None, iforest_kw=None, lof_kw=None): """Create an outlier detection estimator based on its name.""" if name == "LOF": outlier_detector = LocalOutlierFactor(**(lof_kw or {})) if categorical_columns is None: preprocessor = RobustScaler() else: preprocessor = ColumnTransformer( transformers=[("categorical", OneHotEncoder(), categorical_columns)], remainder=RobustScaler(), ) else: # name == "IForest" outlier_detector = IsolationForest(**(iforest_kw or {})) if categorical_columns is None: preprocessor = None else: ordinal_encoder = OrdinalEncoder( handle_unknown="use_encoded_value", unknown_value=-1 ) preprocessor = ColumnTransformer( transformers=[ ("categorical", ordinal_encoder, categorical_columns), ], remainder="passthrough", ) return make_pipeline(preprocessor, outlier_detector) .. GENERATED FROM PYTHON SOURCE LINES 82-83 The following `fit_predict` function returns the average outlier score of X. .. GENERATED FROM PYTHON SOURCE LINES 83-99 .. code-block:: Python from time import perf_counter def fit_predict(estimator, X): tic = perf_counter() if estimator[-1].__class__.__name__ == "LocalOutlierFactor": estimator.fit(X) y_pred = estimator[-1].negative_outlier_factor_ else: # "IsolationForest" y_pred = estimator.fit(X).decision_function(X) toc = perf_counter() print(f"Duration for {model_name}: {toc - tic:.2f} s") return y_pred .. GENERATED FROM PYTHON SOURCE LINES 100-119 On the rest of the example we process one dataset per section. After loading the data, the targets are modified to consist of two classes: 0 representing inliers and 1 representing outliers. Due to computational constraints of the scikit-learn documentation, the sample size of some datasets is reduced using a stratified :class:`~sklearn.model_selection.train_test_split`. Furthermore, we set `n_neighbors` to match the expected number of anomalies `expected_n_anomalies = n_samples * expected_anomaly_fraction`. This is a good heuristic as long as the proportion of outliers is not very low, the reason being that `n_neighbors` should be at least greater than the number of samples in the less populated cluster (see :ref:`sphx_glr_auto_examples_neighbors_plot_lof_outlier_detection.py`). KDDCup99 - SA dataset --------------------- The :ref:`kddcup99_dataset` was generated using a closed network and hand-injected attacks. The SA dataset is a subset of it obtained by simply selecting all the normal data and an anomaly proportion of around 3%. .. GENERATED FROM PYTHON SOURCE LINES 121-135 .. code-block:: Python import numpy as np from sklearn.datasets import fetch_kddcup99 from sklearn.model_selection import train_test_split X, y = fetch_kddcup99( subset="SA", percent10=True, random_state=42, return_X_y=True, as_frame=True ) y = (y != b"normal.").astype(np.int32) X, _, y, _ = train_test_split(X, y, train_size=0.1, stratify=y, random_state=42) n_samples, anomaly_frac = X.shape[0], y.mean() print(f"{n_samples} datapoints with {y.sum()} anomalies ({anomaly_frac:.02%})") .. rst-class:: sphx-glr-script-out .. code-block:: none 10065 datapoints with 338 anomalies (3.36%) .. GENERATED FROM PYTHON SOURCE LINES 136-138 The SA dataset contains 41 features out of which 3 are categorical: "protocol_type", "service" and "flag". .. GENERATED FROM PYTHON SOURCE LINES 140-155 .. code-block:: Python y_true = {} y_pred = {"LOF": {}, "IForest": {}} model_names = ["LOF", "IForest"] cat_columns = ["protocol_type", "service", "flag"] y_true["KDDCup99 - SA"] = y for model_name in model_names: model = make_estimator( name=model_name, categorical_columns=cat_columns, lof_kw={"n_neighbors": int(n_samples * anomaly_frac)}, iforest_kw={"random_state": 42}, ) y_pred[model_name]["KDDCup99 - SA"] = fit_predict(model, X) .. rst-class:: sphx-glr-script-out .. code-block:: none Duration for LOF: 0.91 s Duration for IForest: 0.24 s .. GENERATED FROM PYTHON SOURCE LINES 156-164 Forest covertypes dataset ------------------------- The :ref:`covtype_dataset` is a multiclass dataset where the target is the dominant species of tree in a given patch of forest. It contains 54 features, some of which ("Wilderness_Area" and "Soil_Type") are already binary encoded. Though originally meant as a classification task, one can regard inliers as samples encoded with label 2 and outliers as those with label 4. .. GENERATED FROM PYTHON SOURCE LINES 166-180 .. code-block:: Python from sklearn.datasets import fetch_covtype X, y = fetch_covtype(return_X_y=True, as_frame=True) s = (y == 2) + (y == 4) X = X.loc[s] y = y.loc[s] y = (y != 2).astype(np.int32) X, _, y, _ = train_test_split(X, y, train_size=0.05, stratify=y, random_state=42) X_forestcover = X # save X for later use n_samples, anomaly_frac = X.shape[0], y.mean() print(f"{n_samples} datapoints with {y.sum()} anomalies ({anomaly_frac:.02%})") .. rst-class:: sphx-glr-script-out .. code-block:: none 14302 datapoints with 137 anomalies (0.96%) .. GENERATED FROM PYTHON SOURCE LINES 181-190 .. code-block:: Python y_true["forestcover"] = y for model_name in model_names: model = make_estimator( name=model_name, lof_kw={"n_neighbors": int(n_samples * anomaly_frac)}, iforest_kw={"random_state": 42}, ) y_pred[model_name]["forestcover"] = fit_predict(model, X) .. rst-class:: sphx-glr-script-out .. code-block:: none Duration for LOF: 0.94 s Duration for IForest: 0.18 s .. GENERATED FROM PYTHON SOURCE LINES 191-199 Ames Housing dataset -------------------- The `Ames housing dataset `_ is originally a regression dataset where the target are sales prices of houses in Ames, Iowa. Here we convert it into an outlier detection problem by regarding houses with price over 70 USD/sqft. To make the problem easier, we drop intermediate prices between 40 and 70 USD/sqft. .. GENERATED FROM PYTHON SOURCE LINES 201-220 .. code-block:: Python import matplotlib.pyplot as plt from sklearn.datasets import fetch_openml X, y = fetch_openml(name="ames_housing", version=1, return_X_y=True, as_frame=True) y = y.div(X["Lot_Area"]) # None values in pandas 1.5.1 were mapped to np.nan in pandas 2.0.1 X["Misc_Feature"] = X["Misc_Feature"].cat.add_categories("NoInfo").fillna("NoInfo") X["Mas_Vnr_Type"] = X["Mas_Vnr_Type"].cat.add_categories("NoInfo").fillna("NoInfo") X.drop(columns="Lot_Area", inplace=True) mask = (y < 40) | (y > 70) X = X.loc[mask] y = y.loc[mask] y.hist(bins=20, edgecolor="black") plt.xlabel("House price in USD/sqft") _ = plt.title("Distribution of house prices in Ames") .. image-sg:: /auto_examples/miscellaneous/images/sphx_glr_plot_outlier_detection_bench_001.png :alt: Distribution of house prices in Ames :srcset: /auto_examples/miscellaneous/images/sphx_glr_plot_outlier_detection_bench_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 221-226 .. code-block:: Python y = (y > 70).astype(np.int32) n_samples, anomaly_frac = X.shape[0], y.mean() print(f"{n_samples} datapoints with {y.sum()} anomalies ({anomaly_frac:.02%})") .. rst-class:: sphx-glr-script-out .. code-block:: none 2714 datapoints with 30 anomalies (1.11%) .. GENERATED FROM PYTHON SOURCE LINES 227-230 The dataset contains 46 categorical features. In this case it is easier use a :class:`~sklearn.compose.make_column_selector` to find them instead of passing a list made by hand. .. GENERATED FROM PYTHON SOURCE LINES 232-247 .. code-block:: Python from sklearn.compose import make_column_selector as selector categorical_columns_selector = selector(dtype_include="category") cat_columns = categorical_columns_selector(X) y_true["ames_housing"] = y for model_name in model_names: model = make_estimator( name=model_name, categorical_columns=cat_columns, lof_kw={"n_neighbors": int(n_samples * anomaly_frac)}, iforest_kw={"random_state": 42}, ) y_pred[model_name]["ames_housing"] = fit_predict(model, X) .. rst-class:: sphx-glr-script-out .. code-block:: none Duration for LOF: 0.67 s Duration for IForest: 0.19 s .. GENERATED FROM PYTHON SOURCE LINES 248-256 Cardiotocography dataset ------------------------ The `Cardiotocography dataset `_ is a multiclass dataset of fetal cardiotocograms, the classes being the fetal heart rate (FHR) pattern encoded with labels from 1 to 10. Here we set class 3 (the minority class) to represent the outliers. It contains 30 numerical features, some of which are binary encoded and some are continuous. .. GENERATED FROM PYTHON SOURCE LINES 258-266 .. code-block:: Python X, y = fetch_openml(name="cardiotocography", version=1, return_X_y=True, as_frame=False) X_cardiotocography = X # save X for later use s = y == "3" y = s.astype(np.int32) n_samples, anomaly_frac = X.shape[0], y.mean() print(f"{n_samples} datapoints with {y.sum()} anomalies ({anomaly_frac:.02%})") .. rst-class:: sphx-glr-script-out .. code-block:: none 2126 datapoints with 53 anomalies (2.49%) .. GENERATED FROM PYTHON SOURCE LINES 267-276 .. code-block:: Python y_true["cardiotocography"] = y for model_name in model_names: model = make_estimator( name=model_name, lof_kw={"n_neighbors": int(n_samples * anomaly_frac)}, iforest_kw={"random_state": 42}, ) y_pred[model_name]["cardiotocography"] = fit_predict(model, X) .. rst-class:: sphx-glr-script-out .. code-block:: none Duration for LOF: 0.03 s Duration for IForest: 0.12 s .. GENERATED FROM PYTHON SOURCE LINES 277-285 Plot and interpret results ========================== The algorithm performance relates to how good the true positive rate (TPR) is at low value of the false positive rate (FPR). The best algorithms have the curve on the top-left of the plot and the area under curve (AUC) close to 1. The diagonal dashed line represents a random classification of outliers and inliers. .. GENERATED FROM PYTHON SOURCE LINES 287-312 .. code-block:: Python import math from sklearn.metrics import RocCurveDisplay cols = 2 pos_label = 0 # mean 0 belongs to positive class datasets_names = y_true.keys() rows = math.ceil(len(datasets_names) / cols) fig, axs = plt.subplots(nrows=rows, ncols=cols, squeeze=False, figsize=(10, rows * 4)) for ax, dataset_name in zip(axs.ravel(), datasets_names): for model_idx, model_name in enumerate(model_names): display = RocCurveDisplay.from_predictions( y_true[dataset_name], y_pred[model_name][dataset_name], pos_label=pos_label, name=model_name, ax=ax, plot_chance_level=(model_idx == len(model_names) - 1), chance_level_kw={"linestyle": ":"}, ) ax.set_title(dataset_name) _ = plt.tight_layout(pad=2.0) # spacing between subplots .. image-sg:: /auto_examples/miscellaneous/images/sphx_glr_plot_outlier_detection_bench_002.png :alt: KDDCup99 - SA, forestcover, ames_housing, cardiotocography :srcset: /auto_examples/miscellaneous/images/sphx_glr_plot_outlier_detection_bench_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 313-334 We observe that once the number of neighbors is tuned, LOF and IForest perform similarly in terms of ROC AUC for the forestcover and cardiotocography datasets. The score for IForest is slightly better for the SA dataset and LOF performs considerably better on the Ames housing dataset than IForest. Recall however that Isolation Forest tends to train much faster than LOF on datasets with a large number of samples. LOF needs to compute pairwise distances to find nearest neighbors, which has a quadratic complexity with respect to the number of observations. This can make this method prohibitive on large datasets. Ablation study ============== In this section we explore the impact of the hyperparameter `n_neighbors` and the choice of scaling the numerical variables on the LOF model. Here we use the :ref:`covtype_dataset` dataset as the binary encoded categories introduce a natural scale of euclidean distances between 0 and 1. We then want a scaling method to avoid granting a privilege to non-binary features and that is robust enough to outliers so that the task of finding them does not become too difficult. .. GENERATED FROM PYTHON SOURCE LINES 336-363 .. code-block:: Python X = X_forestcover y = y_true["forestcover"] n_samples = X.shape[0] n_neighbors_list = (n_samples * np.array([0.2, 0.02, 0.01, 0.001])).astype(np.int32) model = make_pipeline(RobustScaler(), LocalOutlierFactor()) linestyles = ["solid", "dashed", "dashdot", ":", (5, (10, 3))] fig, ax = plt.subplots() for model_idx, (linestyle, n_neighbors) in enumerate(zip(linestyles, n_neighbors_list)): model.set_params(localoutlierfactor__n_neighbors=n_neighbors) model.fit(X) y_pred = model[-1].negative_outlier_factor_ display = RocCurveDisplay.from_predictions( y, y_pred, pos_label=pos_label, name=f"n_neighbors = {n_neighbors}", ax=ax, plot_chance_level=(model_idx == len(n_neighbors_list) - 1), chance_level_kw={"linestyle": (0, (1, 10))}, linestyle=linestyle, linewidth=2, ) _ = ax.set_title("RobustScaler with varying n_neighbors\non forestcover dataset") .. image-sg:: /auto_examples/miscellaneous/images/sphx_glr_plot_outlier_detection_bench_003.png :alt: RobustScaler with varying n_neighbors on forestcover dataset :srcset: /auto_examples/miscellaneous/images/sphx_glr_plot_outlier_detection_bench_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 364-369 We observe that the number of neighbors has a big impact on the performance of the model. If one has access to (at least some) ground truth labels, it is then important to tune `n_neighbors` accordingly. A convenient way to do so is to explore values for `n_neighbors` of the order of magnitud of the expected contamination. .. GENERATED FROM PYTHON SOURCE LINES 371-403 .. code-block:: Python from sklearn.preprocessing import MinMaxScaler, SplineTransformer, StandardScaler preprocessor_list = [ None, RobustScaler(), StandardScaler(), MinMaxScaler(), SplineTransformer(), ] expected_anomaly_fraction = 0.02 lof = LocalOutlierFactor(n_neighbors=int(n_samples * expected_anomaly_fraction)) fig, ax = plt.subplots() for model_idx, (linestyle, preprocessor) in enumerate( zip(linestyles, preprocessor_list) ): model = make_pipeline(preprocessor, lof) model.fit(X) y_pred = model[-1].negative_outlier_factor_ display = RocCurveDisplay.from_predictions( y, y_pred, pos_label=pos_label, name=str(preprocessor).split("(")[0], ax=ax, plot_chance_level=(model_idx == len(preprocessor_list) - 1), chance_level_kw={"linestyle": (0, (1, 10))}, linestyle=linestyle, linewidth=2, ) _ = ax.set_title("Fixed n_neighbors with varying preprocessing\non forestcover dataset") .. image-sg:: /auto_examples/miscellaneous/images/sphx_glr_plot_outlier_detection_bench_004.png :alt: Fixed n_neighbors with varying preprocessing on forestcover dataset :srcset: /auto_examples/miscellaneous/images/sphx_glr_plot_outlier_detection_bench_004.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 404-427 On the one hand, :class:`~sklearn.preprocessing.RobustScaler` scales each feature independently by using the interquartile range (IQR) by default, which is the range between the 25th and 75th percentiles of the data. It centers the data by subtracting the median and then scale it by dividing by the IQR. The IQR is robust to outliers: the median and interquartile range are less affected by extreme values than the range, the mean and the standard deviation. Furthermore, :class:`~sklearn.preprocessing.RobustScaler` does not squash marginal outlier values, contrary to :class:`~sklearn.preprocessing.StandardScaler`. On the other hand, :class:`~sklearn.preprocessing.MinMaxScaler` scales each feature individually such that its range maps into the range between zero and one. If there are outliers in the data, they can skew it towards either the minimum or maximum values, leading to a completely different distribution of data with large marginal outliers: all non-outlier values can be collapsed almost together as a result. We also evaluated no preprocessing at all (by passing `None` to the pipeline), :class:`~sklearn.preprocessing.StandardScaler` and :class:`~sklearn.preprocessing.SplineTransformer`. Please refer to their respective documentation for more details. Note that the optimal preprocessing depends on the dataset, as shown below: .. GENERATED FROM PYTHON SOURCE LINES 429-457 .. code-block:: Python X = X_cardiotocography y = y_true["cardiotocography"] n_samples, expected_anomaly_fraction = X.shape[0], 0.025 lof = LocalOutlierFactor(n_neighbors=int(n_samples * expected_anomaly_fraction)) fig, ax = plt.subplots() for model_idx, (linestyle, preprocessor) in enumerate( zip(linestyles, preprocessor_list) ): model = make_pipeline(preprocessor, lof) model.fit(X) y_pred = model[-1].negative_outlier_factor_ display = RocCurveDisplay.from_predictions( y, y_pred, pos_label=pos_label, name=str(preprocessor).split("(")[0], ax=ax, plot_chance_level=(model_idx == len(preprocessor_list) - 1), chance_level_kw={"linestyle": (0, (1, 10))}, linestyle=linestyle, linewidth=2, ) ax.set_title( "Fixed n_neighbors with varying preprocessing\non cardiotocography dataset" ) plt.show() .. image-sg:: /auto_examples/miscellaneous/images/sphx_glr_plot_outlier_detection_bench_005.png :alt: Fixed n_neighbors with varying preprocessing on cardiotocography dataset :srcset: /auto_examples/miscellaneous/images/sphx_glr_plot_outlier_detection_bench_005.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 38.124 seconds) .. _sphx_glr_download_auto_examples_miscellaneous_plot_outlier_detection_bench.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/miscellaneous/plot_outlier_detection_bench.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_outlier_detection_bench.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_outlier_detection_bench.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_outlier_detection_bench.zip ` .. include:: plot_outlier_detection_bench.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_