DOC add Geometric SMOTE examples (#881)

Author: joaopfonseca

examples/over-sampling/plot_geometric_smote_generation_mechanism.py

@@ -0,0 +1,213 @@
+"""
+=========================
+Data generation mechanism
+=========================
+
+This example illustrates the Geometric SMOTE data 
+generation mechanism and the usage of its 
+hyperparameters.
+
+"""
+
+# Author: Georgios Douzas <[email protected]>
+# Licence: MIT
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+from sklearn.datasets import make_blobs
+from imblearn.over_sampling import SMOTE
+
+from gsmote import GeometricSMOTE
+
+print(__doc__)
+
+XLIM, YLIM = [-3.0, 3.0], [0.0, 4.0]
+RANDOM_STATE = 5
+
+
+def generate_imbalanced_data(
+    n_maj_samples, n_min_samples, centers, cluster_std, *min_point
+):
+    """Generate imbalanced data."""
+    X_neg, _ = make_blobs(
+        n_samples=n_maj_samples,
+        centers=centers,
+        cluster_std=cluster_std,
+        random_state=RANDOM_STATE,
+    )
+    X_pos = np.array(min_point)
+    X = np.vstack([X_neg, X_pos])
+    y_pos = np.zeros(X_neg.shape[0], dtype=np.int8)
+    y_neg = np.ones(n_min_samples, dtype=np.int8)
+    y = np.hstack([y_pos, y_neg])
+    return X, y
+
+
+def plot_scatter(X, y, title):
+    """Function to plot some data as a scatter plot."""
+    plt.figure()
+    plt.scatter(X[y == 1, 0], X[y == 1, 1], label='Positive Class')
+    plt.scatter(X[y == 0, 0], X[y == 0, 1], label='Negative Class')
+    plt.xlim(*XLIM)
+    plt.ylim(*YLIM)
+    plt.gca().set_aspect('equal', adjustable='box')
+    plt.legend()
+    plt.title(title)
+
+
+def plot_hyperparameters(oversampler, X, y, param, vals, n_subplots):
+    """Function to plot resampled data for various
+    values of a geometric hyperparameter."""
+    n_rows = n_subplots[0]
+    fig, ax_arr = plt.subplots(*n_subplots, figsize=(15, 7 if n_rows > 1 else 3.5))
+    if n_rows > 1:
+        ax_arr = [ax for axs in ax_arr for ax in axs]
+    for ax, val in zip(ax_arr, vals):
+        oversampler.set_params(**{param: val})
+        X_res, y_res = oversampler.fit_resample(X, y)
+        ax.scatter(X_res[y_res == 1, 0], X_res[y_res == 1, 1], label='Positive Class')
+        ax.scatter(X_res[y_res == 0, 0], X_res[y_res == 0, 1], label='Negative Class')
+        ax.set_title(f'{val}')
+        ax.set_xlim(*XLIM)
+        ax.set_ylim(*YLIM)
+
+
+def plot_comparison(oversamplers, X, y):
+    """Function to compare SMOTE and Geometric SMOTE
+    generation of noisy samples."""
+    fig, ax_arr = plt.subplots(1, 2, figsize=(15, 5))
+    for ax, (name, ovs) in zip(ax_arr, oversamplers):
+        X_res, y_res = ovs.fit_resample(X, y)
+        ax.scatter(X_res[y_res == 1, 0], X_res[y_res == 1, 1], label='Positive Class')
+        ax.scatter(X_res[y_res == 0, 0], X_res[y_res == 0, 1], label='Negative Class')
+        ax.set_title(name)
+        ax.set_xlim(*XLIM)
+        ax.set_ylim(*YLIM)
+
+
+###############################################################################
+# Generate imbalanced data
+###############################################################################
+
+###############################################################################
+# We are generating a highly imbalanced non Gaussian data set. Only two samples
+# from the minority (positive) class are included to illustrate the Geometric
+# SMOTE data generation mechanism.
+
+X, y = generate_imbalanced_data(
+    200, 2, [(-2.0, 2.25), (1.0, 2.0)], 0.25, [-0.7, 2.3], [-0.5, 3.1]
+)
+plot_scatter(X, y, 'Imbalanced data')
+
+###############################################################################
+# Geometric hyperparameters
+###############################################################################
+
+###############################################################################
+# Similarly to SMOTE and its variations, Geometric SMOTE uses the `k_neighbors`
+# hyperparameter to select a random neighbor among the k nearest neighbors of a
+# minority class instance. On the other hand, Geometric SMOTE expands the data
+# generation area from the line segment of the SMOTE mechanism to a hypersphere
+# that can be truncated and deformed. The characteristics of the above geometric
+# area are determined by the hyperparameters ``truncation_factor``,
+# ``deformation_factor`` and ``selection_strategy``. These are called geometric
+# hyperparameters and allow the generation of diverse synthetic data as shown
+# below.
+
+###############################################################################
+# Truncation factor
+# ..............................................................................
+#
+# The hyperparameter ``truncation_factor`` determines the degree of truncation
+# that is applied on the initial geometric area. Selecting the values of
+# geometric hyperparameters as `truncation_factor=0.0`,
+# ``deformation_factor=0.0`` and ``selection_strategy='minority'``, the data
+# generation area in 2D corresponds to a circle with center as one of the two
+# minority class samples and radius equal to the distance between them. In the
+# multi-dimensional case the corresponding area is a hypersphere. When
+# truncation factor is increased, the hypersphere is truncated and for
+# ``truncation_factor=1.0`` becomes a half-hypersphere. Negative values of
+# ``truncation_factor`` have a similar effect but on the opposite direction.
+
+gsmote = GeometricSMOTE(
+    k_neighbors=1,
+    deformation_factor=0.0,
+    selection_strategy='minority',
+    random_state=RANDOM_STATE,
+)
+truncation_factors = np.array([0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
+n_subplots = [2, 3]
+plot_hyperparameters(gsmote, X, y, 'truncation_factor', truncation_factors, n_subplots)
+plot_hyperparameters(gsmote, X, y, 'truncation_factor', -truncation_factors, n_subplots)
+
+###############################################################################
+# Deformation factor
+# ..............................................................................
+#
+# When the ``deformation_factor`` is increased, the data generation area deforms
+# to an ellipsis and for ``deformation_factor=1.0`` becomes a line segment.
+
+gsmote = GeometricSMOTE(
+    k_neighbors=1,
+    truncation_factor=0.0,
+    selection_strategy='minority',
+    random_state=RANDOM_STATE,
+)
+deformation_factors = np.array([0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
+n_subplots = [2, 3]
+plot_hyperparameters(gsmote, X, y, 'deformation_factor', truncation_factors, n_subplots)
+
+###############################################################################
+# Selection strategy
+# ..............................................................................
+#
+# The hyperparameter ``selection_strategy`` determines the selection mechanism
+# of nearest neighbors. Initially, a minority class sample is selected randomly.
+# When ``selection_strategy='minority'``, a second minority class sample is
+# selected as one of the k nearest neighbors of it. For
+# ``selection_strategy='majority'``, the second sample is its nearest majority
+# class neighbor. Finally, for ``selection_strategy='combined'`` the two
+# selection mechanisms are combined and the second sample is the nearest to the
+# first between the two samples defined above.
+
+gsmote = GeometricSMOTE(
+    k_neighbors=1,
+    truncation_factor=0.0,
+    deformation_factor=0.5,
+    random_state=RANDOM_STATE,
+)
+selection_strategies = np.array(['minority', 'majority', 'combined'])
+n_subplots = [1, 3]
+plot_hyperparameters(
+    gsmote, X, y, 'selection_strategy', selection_strategies, n_subplots
+)
+
+###############################################################################
+# Noisy samples
+###############################################################################
+
+###############################################################################
+# We are adding a third minority class sample to illustrate the difference
+# between SMOTE and Geometric SMOTE data generation mechanisms.
+
+X_new = np.vstack([X, np.array([2.0, 2.0])])
+y_new = np.hstack([y, np.ones(1, dtype=np.int8)])
+plot_scatter(X_new, y_new, 'Imbalanced data')
+
+###############################################################################
+# When the number of ``k_neighbors`` is increased, SMOTE results to the
+# generation of noisy samples. On the other hand, Geometric SMOTE avoids this
+# scenario when the ``selection_strategy`` values are either ``combined`` or
+# ``majority``.
+
+oversamplers = [
+    ('SMOTE', SMOTE(k_neighbors=2, random_state=RANDOM_STATE)),
+    (
+        'Geometric SMOTE',
+        GeometricSMOTE(
+            k_neighbors=2, selection_strategy='combined', random_state=RANDOM_STATE
+        ),
+    ),
+]
+plot_comparison(oversamplers, X_new, y_new)