random_data.py

import os
from itertools import product
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns

# Increase seaborn font size
sns.set(font_scale=1.4)

# Set style
sns.set_style("whitegrid")

# Set seed for reproducibility.
np.random.seed(0)


num_data_list = [10, 100, 1000]
num_features_list = [10, 100, 1000]
num_repeat_list = np.arange(100).tolist()

df_results = []
for num_data, num_features, repeat_idx in product(
    num_data_list, num_features_list, num_repeat_list
):
    print(
        "num_data:", num_data, "num_features:", num_features, "repeat_idx:", repeat_idx
    )
    X = np.random.normal(size=(num_data, num_features))
    eigenvalues = np.square(np.linalg.svd(X, full_matrices=False, compute_uv=False))
    # Manually add the missing zeros:
    eigenvalues = np.concatenate(
        [eigenvalues, np.zeros(max(num_data, num_features) - eigenvalues.shape[0])]
    )
    df_results.append(
        pd.DataFrame(
            {
                "num_data": np.full_like(eigenvalues, fill_value=num_data),
                "num_features": np.full_like(eigenvalues, fill_value=num_features),
                "repeat_idx": np.full_like(eigenvalues, fill_value=repeat_idx),
                "Eigenvalue": eigenvalues,
            }
        )
    )

df = pd.concat(df_results).reset_index(drop=True)
df["num_features"] = df["num_features"].astype(int)
df["num_data"] = df["num_data"].astype(int)

results_dir = "results/random_data"
os.makedirs(results_dir, exist_ok=True)

plt.close()
g = sns.FacetGrid(
    data=df,
    col="num_data",
    row="num_features",
    sharey=False,
    sharex=False,
    margin_titles=True,
)
g.map_dataframe(
    sns.histplot,
    x="Eigenvalue",
    stat="probability",
    bins=100,
    line_kws={"linewidth": 0},
)
g.set_titles(
    col_template="Num Data: {col_name}", row_template="Num Features: {row_name}"
)
g.set(yscale="log")
# axes = g.axes
# for row_idx in range(axes.shape[0]):
#     for col_idx in range(axes.shape[1]):
#         axes[row_idx, col_idx].axvline(0, ls='--', c='k',
#                                        label='Chance')
plt.savefig(
    os.path.join(results_dir, f"random_data_eigenvalue_distribution.png"),
    bbox_inches="tight",
    dpi=300,
)
plt.show()
plt.close()