Plotting 2D Kernel Density Estimation with Python

Plotting 2D Kernel Density Estimation with Python

Kernel Density Estimation (KDE) is a non-parametric way to estimate the probability density function of a continuous random variable. In Python, you can use the seaborn library or the scikit-learn library to create 2D kernel density plots. Here's how to do it using both libraries:

Using Seaborn:

import seaborn as sns import numpy as np import matplotlib.pyplot as plt # Create synthetic data np.random.seed(0) x = np.random.randn(1000) y = np.random.randn(1000) # Create a 2D KDE plot using seaborn sns.kdeplot(x, y, cmap="Blues", shade=True, cbar=True) plt.xlabel("X") plt.ylabel("Y") plt.title("2D Kernel Density Estimation") plt.show()

In this example, x and y are the data arrays for the two dimensions. The sns.kdeplot() function from Seaborn creates a 2D KDE plot with the specified color map (cmap), shading, and color bar.

Using Scikit-Learn:

import numpy as np import matplotlib.pyplot as plt from sklearn.datasets import make_blobs from sklearn.neighbors import KernelDensity # Create synthetic data np.random.seed(0) n_samples = 1000 x, y = make_blobs(n_samples=n_samples, centers=1, random_state=0, cluster_std=0.6) # Create a 2D KDE plot using scikit-learn kde = KernelDensity(bandwidth=0.5, metric='euclidean', kernel='gaussian') kde.fit(np.vstack([x, y]).T) x_grid, y_grid = np.meshgrid(np.linspace(x.min(), x.max(), 100), np.linspace(y.min(), y.max(), 100)) z = np.exp(kde.score_samples(np.vstack([x_grid.ravel(), y_grid.ravel()]).T)) z = z.reshape(x_grid.shape) plt.imshow(z, origin='lower', aspect='auto', extent=[x.min(), x.max(), y.min(), y.max()], cmap='Blues') plt.colorbar(label='Density') plt.scatter(x, y, marker='o', s=5, color='red') plt.xlabel("X") plt.ylabel("Y") plt.title("2D Kernel Density Estimation") plt.show()

In this example, synthetic data is created using make_blobs() from scikit-learn. The KernelDensity class is used to estimate the KDE. The estimated density values are plotted as an image using imshow().

Choose the library and approach that best fits your needs. Seaborn provides a high-level interface for creating visualizations, while scikit-learn allows for more customization in the KDE estimation process.

Examples

  1. "Python seaborn kdeplot example"

    • Description: This query likely seeks examples or tutorials on using Seaborn's kdeplot function for plotting kernel density estimates (KDE) in Python.
    • Code Implementation:
      import seaborn as sns import matplotlib.pyplot as plt import numpy as np # Generate sample data data = np.random.multivariate_normal([0, 0], [[1, 0.5], [0.5, 1]], size=1000) # Plot KDE using seaborn sns.kdeplot(data=data) plt.title('2D Kernel Density Estimation') plt.show()

  2. "Python 2D KDE plot matplotlib"

    • Description: This query focuses on generating 2D kernel density plots using Matplotlib, a popular plotting library in Python.
    • Code Implementation:
      import matplotlib.pyplot as plt import numpy as np # Generate sample data x = np.random.normal(size=1000) y = np.random.normal(size=1000) # Create 2D KDE plot using Matplotlib plt.hist2d(x, y, bins=(30, 30), cmap='viridis') plt.colorbar() plt.title('2D Kernel Density Estimation with Matplotlib') plt.show()

  3. "Python density plot with seaborn"

    • Description: This query indicates an interest in creating density plots using Seaborn, possibly including kernel density estimates.
    • Code Implementation:
      import seaborn as sns import matplotlib.pyplot as plt import numpy as np # Generate sample data data = np.random.normal(size=1000) # Create density plot with Seaborn sns.histplot(data, kde=True) plt.title('Density Plot with Seaborn') plt.show()

  4. "2D KDE plot Python pandas"

    • Description: This query suggests an interest in creating 2D kernel density plots using Pandas, a data manipulation library often used in conjunction with Matplotlib and Seaborn.
    • Code Implementation:
      import pandas as pd import matplotlib.pyplot as plt # Generate sample DataFrame df = pd.DataFrame({ 'X': np.random.normal(size=1000), 'Y': np.random.normal(size=1000) }) # Create 2D KDE plot using Pandas df.plot.kde(cmap='viridis') plt.title('2D KDE Plot with Pandas') plt.show()

  5. "Kernel density estimation Python plotly"

    • Description: This query indicates an interest in using Plotly, a visualization library known for its interactive plots, to create kernel density estimation plots in Python.
    • Code Implementation:
      import plotly.express as px import numpy as np # Generate sample data x = np.random.normal(size=1000) y = np.random.normal(size=1000) # Create 2D KDE plot using Plotly fig = px.density_heatmap(x=x, y=y, title='2D KDE Plot with Plotly') fig.show()

  6. "Python seaborn kdeplot bandwidth"

    • Description: This query suggests an interest in adjusting the bandwidth parameter in Seaborn's kdeplot function for more control over the kernel density estimation.
    • Code Implementation:
      import seaborn as sns import matplotlib.pyplot as plt import numpy as np # Generate sample data data = np.random.normal(size=1000) # Plot KDE with bandwidth adjustment using seaborn sns.kdeplot(data=data, bw_adjust=0.5) plt.title('2D KDE Plot with Bandwidth Adjustment') plt.show()

  7. "Python 2D KDE plot jointplot"

    • Description: This query indicates an interest in using Seaborn's jointplot function to create 2D kernel density plots along with marginal histograms or density plots.
    • Code Implementation:
      import seaborn as sns import numpy as np # Generate sample data x = np.random.normal(size=1000) y = np.random.normal(size=1000) # Create 2D KDE plot with jointplot sns.jointplot(x=x, y=y, kind='kde') plt.title('2D KDE Plot with Jointplot') plt.show()

  8. "Python density plot color"

    • Description: This query likely seeks information on customizing the colors of density plots in Python, including kernel density estimates.
    • Code Implementation:
      import seaborn as sns import matplotlib.pyplot as plt import numpy as np # Generate sample data data = np.random.normal(size=1000) # Customizing color in density plot with Seaborn sns.histplot(data, kde=True, color='skyblue') plt.title('Density Plot with Custom Color') plt.show()

  9. "Kernel density estimation Python scikit-learn"

    • Description: This query indicates an interest in utilizing scikit-learn, a popular machine learning library, for kernel density estimation in Python.
    • Code Implementation:
      from sklearn.neighbors import KernelDensity import numpy as np import matplotlib.pyplot as plt # Generate sample data data = np.random.normal(size=1000)[:, np.newaxis] # Fit KDE using scikit-learn kde = KernelDensity(kernel='gaussian', bandwidth=0.5).fit(data) # Generate plot x_plot = np.linspace(-5, 5, 1000)[:, np.newaxis] log_dens = kde.score_samples(x_plot) plt.fill_between(x_plot[:, 0], np.exp(log_dens), alpha=0.5) plt.title('Kernel Density Estimation with scikit-learn') plt.show()

  10. "Python 2D KDE plot with seaborn hue"

    • Description: This query suggests an interest in creating a 2D kernel density plot with Seaborn while incorporating a hue parameter to visualize additional categorical information.
    • Code Implementation:
      import seaborn as sns import numpy as np # Generate sample data x = np.random.normal(size=1000) y = np.random.normal(size=1000) category = np.random.choice(['A', 'B'], size=1000) # Create 2D KDE plot with hue sns.kdeplot(x=x, y=y, hue=category) plt.title('2D KDE Plot with Seaborn Hue') plt.show()

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