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)
        try:
            return clf.predict_proba(cov[np.newaxis, ...])[0, 1]
        except ValueError:
            return np.nan


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(),
]
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=0.00193
  test time    =0.00122
 k-NN:
  training time=0.00004
  test time    =0.00770
 SVC:
  training time=0.00242
  test time    =0.00108
Dataset n°2
 MDM:
  training time=0.00180
  test time    =0.00116
 k-NN:
  training time=0.00003
  test time    =0.00794
 SVC:
  training time=0.00270
  test time    =0.00112
Dataset n°3
 MDM:
  training time=0.00308
  test time    =0.00112
 k-NN:
  training time=0.00003
  test time    =0.01717
 SVC:
  training time=0.00369
  test time    =0.00115
Dataset n°4
 MDM:
  training time=0.00343
  test time    =0.00109
 k-NN:
  training time=0.00003
  test time    =0.01711
 SVC:
  training time=0.00366
  test time    =0.00118

Classifiers with Euclidean metric

plot_classifiers("euclid")

Dataset n°1
 MDM:
  training time=0.00031
  test time    =0.00093
 k-NN:
  training time=0.00004
  test time    =0.00278
 SVC:
  training time=0.00103
  test time    =0.00086
Dataset n°2
 MDM:
  training time=0.00032
  test time    =0.00092
 k-NN:
  training time=0.00003
  test time    =0.00276
 SVC:
  training time=0.00109
  test time    =0.00082
Dataset n°3
 MDM:
  training time=0.00031
  test time    =0.00085
 k-NN:
  training time=0.00003
  test time    =0.00455
 SVC:
  training time=0.00133
  test time    =0.00090
Dataset n°4
 MDM:
  training time=0.00032
  test time    =0.00091
 k-NN:
  training time=0.00003
  test time    =0.00469
 SVC:
  training time=0.00123
  test time    =0.00086

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