About the method of drawing confidence intervals

[z4668640]

What is your suggestion?

Hello author, can Altair add confidence interval ellipses for different groups of points in the plot after drawing PCA scatter plot?
The following is a PCA scatter plot drawn in R language ggplot2.

Here is the PCA scatter plot I am drawing now with altair and the implementation code.

chart = alt.Chart(data).mark_circle(size=60).encode(
    x=alt.X(pc1_column, title='Principal Component 1'),
    y=alt.Y(pc2_column, title='Principal Component 2'),
    color=alt.Color('Environment1', title='Environment'), 
#    tooltip=['Index', pc1_column, pc2_column]
)
chart.display()

Is there any solution at the moment? thx.

Have you considered any alternative solutions?

That was one of my attempt, but it obviously didn't work.
I don't have any good ideas right now.

kmeans = KMeans(n_clusters=3, random_state=0).fit(data[[pc1_column, pc2_column]])
data['Cluster'] = kmeans.labels_

chart = alt.Chart(data).mark_circle(size=60).encode(
    x=alt.X(pc1_column, title='Principal Component 1'),
    y=alt.Y(pc2_column, title='Environment'),
    color=alt.Color('Environment1', title='Environment'),
    tooltip=[pc1_column, pc2_column, 'Environment1']
)

def plot_confidence_ellipses_altair(df, chart):
    for cluster in df['Cluster'].unique():
        cluster_data = df[df['Cluster'] == cluster]
        mean_x = cluster_data[pc1_column].mean()
        mean_y = cluster_data[pc2_column].mean()
        cov_matrix = np.cov(cluster_data[pc1_column], cluster_data[pc2_column])
        eigvals, eigvecs = np.linalg.eigh(cov_matrix)
        order = eigvals.argsort()[::-1]
        eigvals, eigvecs = eigvals[order], eigvecs[:, order]
        theta = np.degrees(np.arctan2(*eigvecs[:, 0][::-1]))
        width, height = 2 * np.sqrt(chi2.ppf(0.95, 2)) * np.sqrt(eigvals)

        ellipse_df = pd.DataFrame({
            'x': mean_x + width / 2 * np.cos(np.linspace(0, 2 * np.pi, 100)) * np.cos(np.radians(theta)) -
                 height / 2 * np.sin(np.linspace(0, 2 * np.pi, 100)) * np.sin(np.radians(theta)),
            'y': mean_y + width / 2 * np.sin(np.linspace(0, 2 * np.pi, 100)) * np.cos(np.radians(theta)) +
                 height / 2 * np.cos(np.linspace(0, 2 * np.pi, 100)) * np.sin(np.radians(theta))
        })

        chart += alt.Chart(ellipse_df).mark_line(color='red', opacity=0.5, strokeWidth=2).encode(
            x=alt.X('x:Q', title='Principal Component 1'),
            y=alt.Y('y:Q', title='Environment')
        )

    return chart

chart = plot_confidence_ellipses_altair(data, chart)
chart.display()