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 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 np.testing.suppress_warnings() as sup:
        sup.filter(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=0.00117
  test time    =0.00200
 k-NN:
  training time=0.00003
  test time    =0.04354
 SVC:
  training time=0.00175
  test time    =0.00069
Dataset n°2
 MDM:
  training time=0.00115
  test time    =0.00200
 k-NN:
  training time=0.00003
  test time    =0.04344
 SVC:
  training time=0.00175
  test time    =0.00066
Dataset n°3
 MDM:
  training time=0.00187
  test time    =0.00335
 k-NN:
  training time=0.00003
  test time    =0.16819
 SVC:
  training time=0.00253
  test time    =0.00071
Dataset n°4
 MDM:
  training time=0.00206
  test time    =0.00338
 k-NN:
  training time=0.00003
  test time    =0.16794
 SVC:
  training time=0.00262
  test time    =0.00071

Classifiers with Euclidean metric

plot_classifiers("euclid")

Dataset n°1
 MDM:
  training time=0.00032
  test time    =0.00096
 k-NN:
  training time=0.00003
  test time    =0.01245
 SVC:
  training time=0.00082
  test time    =0.00052
Dataset n°2
 MDM:
  training time=0.00031
  test time    =0.00089
 k-NN:
  training time=0.00003
  test time    =0.01234
 SVC:
  training time=0.00111
  test time    =0.00055
Dataset n°3
 MDM:
  training time=0.00034
  test time    =0.00123
 k-NN:
  training time=0.00003
  test time    =0.04566
 SVC:
  training time=0.00105
  test time    =0.00055
Dataset n°4
 MDM:
  training time=0.00032
  test time    =0.00122
 k-NN:
  training time=0.00003
  test time    =0.04591
 SVC:
  training time=0.00139
  test time    =0.00052

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