Classifier comparison

A comparison of several classifiers on low-dimensional synthetic datasets, adapted to SPD matrices from [1]. The point of this example is to illustrate the nature of decision boundaries of different classifiers, used with different metrics [2]. This should be taken with a grain of salt, as the intuition conveyed by these examples does not necessarily carry over to real datasets.

The 3D plots show training matrices in solid colors and testing matrices semi-transparent. The lower right shows the classification accuracy on the test set.

# Authors: Quentin Barthélemy
#
# License: BSD (3-clause)

from functools import partial
from time import time
import warnings

import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
import numpy as np
from sklearn.model_selection import train_test_split

from pyriemann.classification import (
    MDM,
    KNearestNeighbor,
    SVC,
)
from pyriemann.datasets import make_matrices, make_gaussian_blobs

@partial(np.vectorize, excluded=["clf"])
def get_proba(cov_00, cov_01, cov_11, clf):
    cov = np.array([[cov_00, cov_01], [cov_01, cov_11]])
    with warnings.catch_warnings():
        warnings.simplefilter("ignore", category=RuntimeWarning)
        return clf.predict_proba(cov[np.newaxis, ...])[0, 1]


def plot_classifiers(metric):
    fig = plt.figure(figsize=(12, 10))
    fig.suptitle(f"Classifiers with metric='{metric}'", fontsize=16)
    i = 1

    # iterate over datasets
    for i_dataset, (X, y) in enumerate(datasets):
        print(f"Dataset n°{i_dataset+1}")

        # split dataset into training and test part
        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, 0].min(), X[:, 0, 0].max()
        y_min, y_max = X[:, 0, 1].min(), X[:, 0, 1].max()
        z_min, z_max = X[:, 1, 1].min(), X[:, 1, 1].max()

        # just plot the dataset first
        ax = plt.subplot(n_datasets, n_classifs + 1, i, projection="3d")
        if i_dataset == 0:
            ax.set_title("Input matrices")
        # plot the training matrices
        ax.scatter(
            X_train[:, 0, 0],
            X_train[:, 0, 1],
            X_train[:, 1, 1],
            c=y_train,
            cmap=cm_bright,
            edgecolors="k"
        )
        # plot the testing matrices
        ax.scatter(
            X_test[:, 0, 0],
            X_test[:, 0, 1],
            X_test[:, 1, 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_zlim(z_min, z_max)
        ax.set_xticklabels(())
        ax.set_yticklabels(())
        ax.set_zticklabels(())
        i += 1

        rx = np.arange(x_min, x_max, (x_max - x_min) / 50)
        ry = np.arange(y_min, y_max, (y_max - y_min) / 50)
        rz = np.arange(z_min, z_max, (z_max - z_min) / 50)

        # iterate over classifiers
        for name, clf in zip(names, classifs):
            clf.set_params(**{"metric": metric})

            t0 = time()
            clf.fit(X_train, y_train)
            t1 = time() - t0
            t0 = time()
            score = clf.score(X_test, y_test)
            t2 = time() - t0
            print(
                f" {name}:\n  training time={t1:.5f}\n  test time    ={t2:.5f}"
            )

            ax = plt.subplot(n_datasets, n_classifs + 1, i, projection="3d")

            # plot the decision boundaries for horizontal 2D planes going
            # through the mean value of the third coordinates
            xx, yy = np.meshgrid(rx, ry)
            zz = get_proba(xx, yy, X[:, 1, 1].mean()*np.ones_like(xx), clf=clf)
            zz = np.ma.masked_where(~np.isfinite(zz), zz)
            ax.contourf(xx, yy, zz, zdir="z", offset=z_min, cmap=cm, alpha=0.5)

            xx, zz = np.meshgrid(rx, rz)
            yy = get_proba(xx, X[:, 0, 1].mean()*np.ones_like(xx), zz, clf=clf)
            yy = np.ma.masked_where(~np.isfinite(yy), yy)
            ax.contourf(xx, yy, zz, zdir="y", offset=y_max, cmap=cm, alpha=0.5)

            yy, zz = np.meshgrid(ry, rz)
            xx = get_proba(X[:, 0, 0].mean()*np.ones_like(yy), yy, zz, clf=clf)
            xx = np.ma.masked_where(~np.isfinite(xx), xx)
            ax.contourf(xx, yy, zz, zdir="x", offset=x_min, cmap=cm, alpha=0.5)

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

            if i_dataset == 0:
                ax.set_title(name)
            ax.text(
                1.3 * x_max,
                y_min,
                z_min,
                ("%.2f" % score).lstrip("0"),
                size=15,
                horizontalalignment="right",
                verticalalignment="bottom"
            )
            ax.set_xlim(x_min, x_max)
            ax.set_ylim(y_min, y_max)
            ax.set_zlim(z_min, z_max)
            ax.set_xticks(())
            ax.set_yticks(())
            ax.set_zticks(())

            i += 1

    plt.show()

Classifiers and Datasets

names = [
    "MDM",
    "k-NN",
    "SVC",
]
classifs = [
    MDM(),
    KNearestNeighbor(n_neighbors=3),
    SVC(probability=True),
]
n_classifs = len(classifs)

rs = np.random.RandomState(2022)
n_matrices, n_channels = 50, 2
y = np.concatenate([np.zeros(n_matrices), np.ones(n_matrices)])

datasets = [
    (
        np.concatenate([
            make_matrices(
                n_matrices, n_channels, "spd", rs, evals_low=10, evals_high=14
            ),
            make_matrices(
                n_matrices, n_channels, "spd", rs, evals_low=13, evals_high=17
            )
        ]),
        y
    ),
    (
        np.concatenate([
            make_matrices(
                n_matrices, n_channels, "spd", rs, evals_low=10, evals_high=14
            ),
            make_matrices(
                n_matrices, n_channels, "spd", rs, evals_low=11, evals_high=15
            )
        ]),
        y
    ),
    make_gaussian_blobs(
        2*n_matrices, n_channels, random_state=rs, class_sep=1., class_disp=.5,
        n_jobs=4
    ),
    make_gaussian_blobs(
        2*n_matrices, n_channels, random_state=rs, class_sep=.5, class_disp=.5,
        n_jobs=4
    )
]
n_datasets = len(datasets)

cm = plt.cm.RdBu
cm_bright = ListedColormap(["#FF0000", "#0000FF"])

Classifiers with affine-invariant Riemannian metric

plot_classifiers("riemann")

Dataset n°1
 MDM:
  training time=0.00217
  test time    =0.00096
 k-NN:
  training time=0.00003
  test time    =0.00848
 SVC:
  training time=0.00260
  test time    =0.00098
Dataset n°2
 MDM:
  training time=0.00216
  test time    =0.00093
 k-NN:
  training time=0.00003
  test time    =0.00850
 SVC:
  training time=0.00252
  test time    =0.00096
Dataset n°3
 MDM:
  training time=0.00360
  test time    =0.00093
 k-NN:
  training time=0.00004
  test time    =0.01964
 SVC:
  training time=0.00429
  test time    =0.00124
Dataset n°4
 MDM:
  training time=0.00414
  test time    =0.00102
 k-NN:
  training time=0.00003
  test time    =0.01897
 SVC:
  training time=0.00420
  test time    =0.00113

Classifiers with Euclidean metric

plot_classifiers("euclid")

Dataset n°1
 MDM:
  training time=0.00038
  test time    =0.00079
 k-NN:
  training time=0.00004
  test time    =0.00306
 SVC:
  training time=0.00099
  test time    =0.00069
Dataset n°2
 MDM:
  training time=0.00037
  test time    =0.00075
 k-NN:
  training time=0.00004
  test time    =0.00297
 SVC:
  training time=0.00113
  test time    =0.00065
Dataset n°3
 MDM:
  training time=0.00042
  test time    =0.00070
 k-NN:
  training time=0.00004
  test time    =0.00496
 SVC:
  training time=0.00120
  test time    =0.00066
Dataset n°4
 MDM:
  training time=0.00037
  test time    =0.00088
 k-NN:
  training time=0.00004
  test time    =0.00518
 SVC:
  training time=0.00171
  test time    =0.00070

References

[1]

https://scikit-learn.org/stable/auto_examples/classification/plot_classifier_comparison.html # noqa

[2]

Review of Riemannian distances and divergences, applied to SSVEP-based BCI S. Chevallier, E. K. Kalunga, Q. Barthélemy, E. Monacelli. Neuroinformatics, Springer, 2021, 19 (1), pp.93-106