Support/document Confidence Interval Ellipse

[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()

[dangotbanned]

@z4668640 could you please summarize - ideally in a few lines - what the feature request is here?

[z4668640]

@z4668640 could you please summarize - ideally in a few lines - what the feature request is here?

What I mean is that I want to use Altair to get a confidence interval similar to the one in the first PCA scatter plot above.
The rest is that I tried to solve the matter myself, but failed.

[dangotbanned]

@z4668640 could you please summarize - ideally in a few lines - what the feature request is here?

What I mean is that I want to use Altair to get a confidence interval similar to the one in the first PCA scatter plot above. The rest is that I tried to solve the matter myself, but failed.

Thanks @z4668640 that is helpful

Could you add a code block between this text and the ggplot2 output (in #3715 (comment)), so we can see what API(s) were used to get that result please?

The following is a PCA scatter plot drawn in R language ggplot2.

Using R is fine, but if you wanted to go the extra mile - maybe try rewriting it using https://github.com/has2k1/plotnine

[dangotbanned]

I believe plotnine.stat_ellipse would be an example of implementing this with numpy, scipy
Source code

I also found an old closed PR (#514 by @essicolo) that would have added an example for this.
The blocker at the time is no longer an issue as (#3202 by @joelostblom) added scipy as a docs dependency.

I'm working on cleaning up that example right now.
Is something like this what you'd be hoping to see @z4668640?

[z4668640]

This looks like what I want. Thank you very much for your help. These diagrams look beautiful and I would appreciate a tutorial on how to use them. @dangotbanned

[z4668640]

cloud you let me know when this tutorial is ready? I would appreciate it.

[dangotbanned]

cloud you let me know when this tutorial is ready? I would appreciate it.

Will do @z4668640

[dangotbanned]

cloud you let me know when this tutorial is ready? I would appreciate it.

@z4668640 Thank you for raising this issue, we'll have this example in the docs in the next minor release (5.6.0) of altair.

If you are feeling eager, the example code has been merged and can be found at deviation_ellipses.py.

Note

The code may change before release, but there are currently no plans to do so

[z4668640]

@dangotbanned Thank you very much for your help. I can't wait to try this. Hats off to you.