Biplots in matrix format using pca

Question

This is a snippet of my dataframe:

    species bill_length_mm  bill_depth_mm   flipper_length_mm     body_mass_g   predicted_species
0   Adelie       18                   18         181             3750                Chinstrap
1   Adelie       17                   17         186             3800                Adelie
2   Adelie       18                   18         195             3250                Gentoo
3   Adelie       0                    0           0               0                  Adelie
4   Chinstrap    19                   19         193             3450                Chinstrap
5   Chinstrap    20                   20         190             3650                Gentoo
6   Chinstrap    17                   17         181             3625                Adelie
7   Gentoo       19                   19         195             4675                Chinstrap
8   Gentoo       18                   18         193             3475                Gentoo
9   Gentoo       20                   20         190             4250                Gentoo

I want to make a biplot for my data, which would be something like this:

But I want to make a biplot for every species vs predicted_species matrix, so 9 subplots,same as above, I am not sure how that can be achieved. One way could be to split into dataframes, and make a biplot for each, but that isn't very efficient and difficult for comparison.

Can anyone provide some suggestions on how this could be done?

As it happens, I answered pretty much the same question a few days ago: https://stackoverflow.com/questions/75979711/reduced-dimensions-visualization-for-true-vs-predicted-values/76024095#76024095 — Arne, Apr 18 '23 at 23:40
That was only for the dimensionality reduction, in this I want to plot the feature names along with the groups as well — Brie MerryWeather, Apr 19 '23 at 09:17

score 1 · Accepted Answer · answered Apr 19 '23 at 16:26

Combining the answer by Qiyun Zhu on how to plot a biplot with my answer on how to split the plot into the true vs. predicted subsets, you could do it like this:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA

# Load iris data.
iris = sns.load_dataset('iris')
X = iris.iloc[:, :4].values
y = iris.iloc[:, 4].values
features = iris.columns[:4]
targets = ['setosa', 'versicolor', 'virginica']

# Mock up some predictions.
iris['species_pred'] = (40 * ['setosa'] + 5 * ['versicolor'] + 5 * ['virginica']
                        + 40 * ['versicolor'] + 5 * ['setosa'] + 5 * ['virginica']
                        + 40 * ['virginica'] + 5 * ['versicolor'] + 5 * ['setosa'])

# Reduce features to two dimensions.
X_scaled = StandardScaler().fit_transform(X)
pca = PCA(n_components=2).fit(X_scaled)
X_reduced = pca.transform(X_scaled)
iris[['pc1', 'pc2']] = X_reduced


def biplot(x, y, data=None, **kwargs):
    # Plot data points.
    sns.scatterplot(data=data, x=x, y=y, **kwargs)
    
    # Calculate arrow parameters.
    loadings = pca.components_[:2].T
    pvars = pca.explained_variance_ratio_[:2] * 100
    arrows = loadings * np.ptp(X_reduced, axis=0)
    width = -0.0075 * np.min([np.subtract(*plt.xlim()), np.subtract(*plt.ylim())])

    # Plot arrows.
    horizontal_alignment = ['right', 'left', 'right', 'right']
    vertical_alignment = ['bottom', 'top', 'top', 'bottom']
    for (i, arrow), ha, va in zip(enumerate(arrows), 
                                  horizontal_alignment, vertical_alignment):
        plt.arrow(0, 0, *arrow, color='k', alpha=0.5, width=width, ec='none',
                  length_includes_head=True)
        plt.text(*(arrow * 1.05), features[i], ha=ha, va=va, 
                 fontsize='small', color='gray')

    
# Plot small multiples, corresponding to confusion matrix.
sns.set()
g = sns.FacetGrid(iris, row='species', col='species_pred', 
                  hue='species', margin_titles=True)
g.map(biplot, 'pc1', 'pc2')
plt.show()

Biplots in matrix format using pca

1 Answers1