"""
==========================================
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.
The algorithms are trained in an outlier detection context:
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.
#
# 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()