Decision boundaries

We can compare CalfCV with the nearest neighbor and linear SVM classifiers. The comparisons are on synthetic data sets to help gain intuition for the decision boundaries formed by CalfCV on several data challenges.

The example plot of CalfCV shows that while nearest neighbors does better than CalfCV on all three data sets, CalfCV is competitive with linear SVM on the moons and circles data sets.

import matplotlib.pyplot as plt
import numpy as np
from matplotlib.colors import ListedColormap
from sklearn.datasets import make_circles, make_classification, make_moons
from sklearn.inspection import DecisionBoundaryDisplay
from sklearn.model_selection import train_test_split
from sklearn.neighbors import KNeighborsClassifier
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler
from sklearn.svm import SVC

from calfcv import CalfCV

names = [
    "CalfCV",
    "Linear SVM",
    "Nearest Neighbors"
]

classifiers = [

    CalfCV(),
    SVC(kernel="linear", C=0.025),
    KNeighborsClassifier(3)
]

X, y = make_classification(
    n_features=2, n_redundant=0, n_informative=2, random_state=1, n_clusters_per_class=1
)

rng = np.random.RandomState(2)
X += 2 * rng.uniform(size=X.shape)
linearly_separable = (X, y)

datasets = [
    make_moons(noise=0.3, random_state=0),
    make_circles(noise=0.2, factor=0.5, random_state=1),
    linearly_separable,
]

figure = plt.figure(figsize=(10, 10))
i = 1
# iterate over datasets
for ds_cnt, ds in enumerate(datasets):
    # preprocess dataset, split into training and test part
    X, y = ds
    X_train, X_test, y_train, y_test = train_test_split(
        X, y, test_size=0.4, random_state=42
    )

    x_min, x_max = X[:, 0].min() - 0.5, X[:, 0].max() + 0.5
    y_min, y_max = X[:, 1].min() - 0.5, X[:, 1].max() + 0.5

    # just plot the dataset first
    cm = plt.cm.RdBu
    cm_bright = ListedColormap(["#FF0000", "#0000FF"])
    ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
    if ds_cnt == 0:
        ax.set_title("Input data")
    # Plot the training points
    ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright, edgecolors="k")
    # Plot the testing points
    ax.scatter(
        X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.6, edgecolors="k"
    )
    ax.set_xlim(x_min, x_max)
    ax.set_ylim(y_min, y_max)
    ax.set_xticks(())
    ax.set_yticks(())
    i += 1

    # iterate over classifiers
    for name, clf in zip(names, classifiers):
        ax = plt.subplot(len(datasets), len(classifiers) + 1, i)

        clf = make_pipeline(StandardScaler(), clf)
        clf.fit(X_train, y_train)
        score = clf.score(X_test, y_test)
        DecisionBoundaryDisplay.from_estimator(
            clf, X, cmap=cm, alpha=0.8, ax=ax, eps=0.5
        )

        # Plot the training points
        ax.scatter(
            X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright, edgecolors="k"
        )
        # Plot the testing points
        ax.scatter(
            X_test[:, 0],
            X_test[:, 1],
            c=y_test,
            cmap=cm_bright,
            edgecolors="k",
            alpha=0.6,
        )

        ax.set_xlim(x_min, x_max)
        ax.set_ylim(y_min, y_max)
        ax.set_xticks(())
        ax.set_yticks(())
        if ds_cnt == 0:
            ax.set_title(name)
        ax.text(
            x_max - 0.3,
            y_min + 0.3,
            ("%.2f" % score).lstrip("0"),
            size=15,
            horizontalalignment="right",
        )
        i += 1

plt.tight_layout()
plt.show()