Plot a 95% confidence ellipse for a scatter plot in Plotly

plotly_scatter_confidence_ellipse.py

import numpy as np


def confidence_ellipse(x, y, n_std=1.96, size=100):
    """
    Get the covariance confidence ellipse of *x* and *y*.

    Parameters
    ----------
    x, y : array-like, shape (n, )
        Input data.

    n_std : float
        The number of standard deviations to determine the ellipse's radiuses.

    size : int
        Number of points defining the ellipse

    Returns
    -------
    String containing an SVG path for the ellipse
    
    References (H/T)
    ----------------
    https://matplotlib.org/3.1.1/gallery/statistics/confidence_ellipse.html
    https://community.plotly.com/t/arc-shape-with-path/7205/5
    """
    if x.size != y.size:
        raise ValueError("x and y must be the same size")

    cov = np.cov(x, y)
    pearson = cov[0, 1]/np.sqrt(cov[0, 0] * cov[1, 1])
    # Using a special case to obtain the eigenvalues of this
    # two-dimensionl dataset.
    ell_radius_x = np.sqrt(1 + pearson)
    ell_radius_y = np.sqrt(1 - pearson)
    theta = np.linspace(0, 2 * np.pi, size)
    ellipse_coords = np.column_stack([ell_radius_x * np.cos(theta), ell_radius_y * np.sin(theta)])
    
    # Calculating the stdandard deviation of x from
    # the squareroot of the variance and multiplying
    # with the given number of standard deviations.
    x_scale = np.sqrt(cov[0, 0]) * n_std
    x_mean = np.mean(x)

    # calculating the stdandard deviation of y ...
    y_scale = np.sqrt(cov[1, 1]) * n_std
    y_mean = np.mean(y)
  
    translation_matrix = np.tile([x_mean, y_mean], (ellipse_coords.shape[0], 1))
    rotation_matrix = np.array([[np.cos(np.pi / 4), np.sin(np.pi / 4)],
                                [-np.sin(np.pi / 4), np.cos(np.pi / 4)]])
    scale_matrix = np.array([[x_scale, 0],
                            [0, y_scale]])
    ellipse_coords = ellipse_coords.dot(rotation_matrix).dot(scale_matrix) + translation_matrix
        
    path = f'M {ellipse_coords[0, 0]}, {ellipse_coords[0, 1]}'
    for k in range(1, len(ellipse_coords)):
        path += f'L{ellipse_coords[k, 0]}, {ellipse_coords[k, 1]}'
    path += ' Z'
    return path

""" EXAMPLE """
from plotly import graph_objects as go
from plotly.colors import DEFAULT_PLOTLY_COLORS
from sklearn.datasets import load_iris
from sklearn.decomposition import PCA

iris = load_iris()

pca = PCA(n_components=2)
scores = pca.fit_transform(iris.data)

fig = go.Figure()

for target_value, target_name in enumerate(iris.target_names):
    color = DEFAULT_PLOTLY_COLORS[target_value]
    fig.add_trace(
        go.Scatter(
            x=scores[iris.target==target_value, 0],
            y=scores[iris.target==target_value, 1],
            name=target_name,
            mode='markers',
            marker={'color': color}
        )
    )
    
    fig.add_shape(type='path',
                  path=confidence_ellipse(scores[iris.target==target_value, 0], scores[iris.target==target_value, 1]),
                  line={'dash': 'dot'},
                  line_color=color)
        
fig.show()