Magnitude-Shape Plot synthetic example

Shows the use of the MS-Plot applied to a synthetic dataset.

# Author: Carlos Ramos Carreño
# License: MIT

# sphinx_gallery_thumbnail_number = 3

import matplotlib.pyplot as plt
import numpy as np

import skfda
from skfda.exploratory.visualization import MagnitudeShapePlot

First, we generate a synthetic dataset following [DaWe18]

random_state = np.random.RandomState(0)
n_samples = 200

fd = skfda.datasets.make_gaussian_process(
    n_samples=n_samples,
    n_features=100,
    cov=skfda.misc.covariances.Exponential(),
    mean=lambda t: 4 * t,
    random_state=random_state,
)

We now add the outliers

magnitude_outlier = skfda.datasets.make_gaussian_process(
    n_samples=1,
    n_features=100,
    cov=skfda.misc.covariances.Exponential(),
    mean=lambda t: 4 * t + 20,
    random_state=random_state,
)

shape_outlier_shift = skfda.datasets.make_gaussian_process(
    n_samples=1,
    n_features=100,
    cov=skfda.misc.covariances.Exponential(),
    mean=lambda t: 4 * t + 10 * (t > 0.4),
    random_state=random_state,
)

shape_outlier_peak = skfda.datasets.make_gaussian_process(
    n_samples=1,
    n_features=100,
    cov=skfda.misc.covariances.Exponential(),
    mean=lambda t: 4 * t - 10 * ((0.25 < t) & (t < 0.3)),
    random_state=random_state,
)

shape_outlier_sin = skfda.datasets.make_gaussian_process(
    n_samples=1,
    n_features=100,
    cov=skfda.misc.covariances.Exponential(),
    mean=lambda t: 4 * t + 2 * np.sin(18 * t),
    random_state=random_state,
)

shape_outlier_slope = skfda.datasets.make_gaussian_process(
    n_samples=1,
    n_features=100,
    cov=skfda.misc.covariances.Exponential(),
    mean=lambda t: 10 * t,
    random_state=random_state,
)

magnitude_shape_outlier = skfda.datasets.make_gaussian_process(
    n_samples=1,
    n_features=100,
    cov=skfda.misc.covariances.Exponential(),
    mean=lambda t: 4 * t + 2 * np.sin(18 * t) - 20,
    random_state=random_state,
)


fd = fd.concatenate(
    magnitude_outlier,
    shape_outlier_shift,
    shape_outlier_peak,
    shape_outlier_sin,
    shape_outlier_slope,
    magnitude_shape_outlier,
)

The data is plotted to show the curves we are working with.

labels = [0] * n_samples + [1] * 6

fd.plot(
    group=labels,
    group_colors=['lightgrey', 'black'],
)

<Figure size 640x480 with 1 Axes>

The MS-Plot is generated. In order to show the results, the plot() method is used.

msplot = MagnitudeShapePlot(fd)

msplot.plot()

<Figure size 640x480 with 1 Axes>

To show the utility of the plot, the curves are plotted showing each outlier in a different color

labels = [0] * n_samples + [1, 2, 3, 4, 5, 6]
colors = [
    'lightgrey',
    'orange',
    'blue',
    'black',
    'green',
    'brown',
    'lightblue',
]

fd.plot(
    group=labels,
    group_colors=colors,
)

<Figure size 640x480 with 1 Axes>

We now show the points in the MS-plot using the same colors

fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.scatter(
    msplot.points[:, 0].ravel(),
    msplot.points[:, 1].ravel(),
    c=colors[:1] * n_samples + colors[1:],
)
ax.set_title("MS-Plot")
ax.set_xlabel("magnitude outlyingness")
ax.set_ylabel("shape outlyingness")

Text(47.097222222222214, 0.5, 'shape outlyingness')

References

[DaWe18]

Dai, Wenlin, and Genton, Marc G. “Multivariate functional data visualization and outlier detection.” Journal of Computational and Graphical Statistics 27.4 (2018): 923-934.