"""
==========================================
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.
"""
# Author: Pharuj Rajborirug
# Arturo Amor
# License: BSD 3 clause
# %%
# 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`.
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)
# %%
# The following `fit_predict` function returns the average outlier score of X.
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
# %%
# 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%.
# %%
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%})")
# %%
# The SA dataset contains 41 features out of which 3 are categorical:
# "protocol_type", "service" and "flag".
# %%
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)
# %%
# 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.
# %%
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%})")
# %%
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)
# %%
# 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.
# %%
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")
# %%
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%})")
# %%
# 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.
# %%
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)
# %%
# 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.
# %%
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%})")
# %%
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)
# %%
# 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.
# %%
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
# %%
# 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.
# %%
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")
# %%
# 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.
# %%
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")
# %%
# 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:
# %%
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()