Matplotlib and Seaborn: Data Visualization

The Grammar of Graphics

Data visualization is the graphical representation of information and data. A good visualization tells a story and reveals patterns that numbers alone cannot.

Matplotlib: The Foundation

Basic Plot Structure

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

# Figure anatomy â€” object-oriented interface
x = np.linspace(0, 10, 100)
y = np.sin(x)

fig, ax = plt.subplots(figsize=(10, 6))
ax.plot(x, y, label='sin(x)', color='blue', linewidth=2)
ax.set_xlabel('X Axis', fontsize=12)
ax.set_ylabel('Y Axis', fontsize=12)
ax.set_title('Basic Line Plot', fontsize=14)
ax.legend()
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()

Essential Plot Types

# Line Plot (trends over time)
dates = pd.date_range('2024-01-01', periods=12)
values = np.random.randn(12).cumsum() + 100

fig, ax = plt.subplots(figsize=(12, 6))
ax.plot(dates, values, marker='o', linestyle='-', color='#2196F3')
ax.fill_between(dates, values - 10, values + 10, alpha=0.2)
ax.set_title('Stock Price Trend')
plt.xticks(rotation=45)
plt.tight_layout()
plt.show()

# Bar Plot (comparisons)
categories = ['A', 'B', 'C', 'D', 'E']
values = [23, 45, 56, 78, 32]

fig, axes = plt.subplots(1, 2, figsize=(12, 5))
axes[0].bar(categories, values, color=['#FF6B6B', '#4ECDC4', '#45B7D1', '#96CEB4', '#FFEAA7'])
axes[0].set_title('Vertical Bar Plot')
axes[1].barh(categories, values, color=['#FF6B6B', '#4ECDC4', '#45B7D1', '#96CEB4', '#FFEAA7'])
axes[1].set_title('Horizontal Bar Plot')
plt.tight_layout()
plt.show()

# Scatter Plot (relationships)
x = np.random.randn(100)
y = x * 2 + np.random.randn(100) * 0.5
colors = np.random.rand(100)
sizes = np.random.rand(100) * 200

plt.figure(figsize=(10, 6))
scatter = plt.scatter(x, y, c=colors, s=sizes, alpha=0.6, cmap='viridis')
plt.colorbar(scatter)
plt.title('Scatter Plot with Color and Size')
plt.show()

Choosing the Right Plot

Line: Trends over continuous variables (time series)
Bar: Comparing discrete categories
Histogram: Distribution of a single numerical variable
Scatter: Relationship between two numerical variables
Box: Distribution summary with outliers (five-number summary)
Pie: Parts of a whole (use sparingly â€” bar charts are usually better)

Subplots and Layouts

# Complex layout with GridSpec
import matplotlib.gridspec as gridspec

fig = plt.figure(figsize=(14, 10))
gs = gridspec.GridSpec(3, 3, figure=fig)

# Large plot spanning 2 rows, 2 columns
ax_main = fig.add_subplot(gs[0:2, 0:2])
ax_main.plot(x, y, 'b-')
ax_main.set_title('Main Plot')

# Side plots
ax_right1 = fig.add_subplot(gs[0, 2])
ax_right1.barh(categories[:3], values[:3])

ax_right2 = fig.add_subplot(gs[1, 2])
ax_right2.pie(sizes[:3], labels=labels[:3])

# Bottom plot
ax_bottom = fig.add_subplot(gs[2, :])
ax_bottom.plot(x, np.sin(x) * 100, 'r-')
ax_bottom.set_title('Bottom Plot')

plt.tight_layout()
plt.show()

Seaborn: Statistical Visualization

Distribution Plots

import seaborn as sns

sns.set_theme(style="whitegrid")
tips = sns.load_dataset('tips')

# Histogram with KDE
fig, axes = plt.subplots(1, 2, figsize=(12, 5))
sns.histplot(data=tips, x='total_bill', kde=True, ax=axes[0])
axes[0].set_title('Histogram with KDE')
sns.histplot(data=tips, x='total_bill', hue='time', kde=True, ax=axes[1])
axes[1].set_title('Histogram by Time')
plt.tight_layout()
plt.show()

# KDE Plot
fig, axes = plt.subplots(1, 2, figsize=(12, 5))
sns.kdeplot(data=tips, x='total_bill', fill=True, ax=axes[0])
axes[0].set_title('KDE Plot')
sns.kdeplot(data=tips, x='total_bill', hue='day', fill=True, ax=axes[1])
axes[1].set_title('KDE by Day')
plt.tight_layout()
plt.show()

Kernel Density Estimation (KDE)

\hat{f}(x) = \frac{1}{nh} \sum_{i=1}^{n} K\left(\frac{x - x_i}{h}\right)

Here,

$K$ =kernel function (typically Gaussian)
$h$ =bandwidth (smoothing parameter)
$n$ =number of data points
$x_i$ =individual data points

Categorical Plots

# Box Plot
plt.figure(figsize=(12, 6))
sns.boxplot(data=tips, x='day', y='total_bill', hue='sex')
plt.title('Total Bill by Day and Gender')
plt.show()

# Violin Plot
plt.figure(figsize=(12, 6))
sns.violinplot(data=tips, x='day', y='total_bill', hue='sex', split=True)
plt.title('Violin Plot')
plt.show()

# Swarm Plot
plt.figure(figsize=(12, 6))
sns.swarmplot(data=tips, x='day', y='total_bill', hue='sex', size=4)
plt.title('Swarm Plot')
plt.show()

Box vs Violin vs Swarm

Box plot: Compact summary (median, quartiles, outliers). Best for comparing distributions across groups.
Violin plot: Combines box plot with KDE. Reveals multimodal distributions that box plots hide.
Swarm plot: Shows every data point without overlap. Best for small datasets (< 1000 points).

Relationship Plots

# Scatter Plot with Regression
fig, axes = plt.subplots(1, 2, figsize=(12, 5))
sns.scatterplot(data=tips, x='total_bill', y='tip', ax=axes[0])
axes[0].set_title('Basic Scatter')
sns.regplot(data=tips, x='total_bill', y='tip', ax=axes[1])
axes[1].set_title('Scatter with Regression')
plt.tight_layout()
plt.show()

# Joint Plot
g = sns.jointplot(data=tips, x='total_bill', y='tip', kind='scatter')
plt.show()

# Pair Plot (matrix of relationships)
iris = sns.load_dataset('iris')
g = sns.pairplot(iris, hue='species')
plt.show()

# Heatmap (correlation matrix)
plt.figure(figsize=(10, 8))
corr = tips.select_dtypes(include=[np.number]).corr()
sns.heatmap(corr, annot=True, cmap='coolwarm', center=0,
            square=True, linewidths=0.5)
plt.title('Correlation Heatmap')
plt.show()

Pearson Correlation Coefficient

r = \frac{\sum_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i - \bar{x})^2 \cdot \sum_{i=1}^{n}(y_i - \bar{y})^2}}

Here,

$r$ =Pearson correlation coefficient (-1 to 1)
$\bar{x}, \bar{y}$ =Sample means of x and y
$n$ =Number of data points

Matrix Plots

# FacetGrid for complex layouts
g = sns.FacetGrid(tips, col='time', row='sex', height=4, aspect=1.2)
g.map_dataframe(sns.histplot, x='total_bill', bins=15)
g.set_titles('{row_name} - {col_name}')
plt.show()

# PairGrid
g = sns.PairGrid(iris, hue='species')
g.map_upper(sns.scatterplot)
g.map_lower(sns.kdeplot)
g.map_diag(sns.histplot)
g.add_legend()
plt.show()

Customization and Themes

# Set theme
sns.set_theme(style="whitegrid", palette="muted")

# Custom color palettes
palette = sns.color_palette("husl", 10)
sns.set_palette(palette)

# Custom styling
plt.rcParams.update({
    'figure.figsize': (10, 6),
    'font.size': 12,
    'axes.titlesize': 14,
    'axes.labelsize': 12,
    'figure.dpi': 100,
    'savefig.dpi': 300,
    'savefig.bbox': 'tight'
})

Publication-Quality Visualizations

def create_publication_plot(data, x, y, hue=None, title="", filename=None):
    sns.set_theme(style="whitegrid", context="paper")
    fig, ax = plt.subplots(figsize=(8, 6))

    if hue:
        sns.scatterplot(data=data, x=x, y=y, hue=hue, s=100, alpha=0.7, ax=ax)
    else:
        sns.scatterplot(data=data, x=x, y=y, s=100, alpha=0.7, ax=ax)

    ax.set_title(title, fontsize=14, fontweight='bold', pad=20)
    ax.spines['top'].set_visible(False)
    ax.spines['right'].set_visible(False)
    ax.grid(True, alpha=0.3, linestyle='--')
    plt.tight_layout()

    if filename:
        plt.savefig(f'{filename}.png', dpi=300, bbox_inches='tight')
        plt.savefig(f'{filename}.pdf', bbox_inches='tight')
    plt.show()

Data-Ink Ratio (Tufte)

\text{Data-Ink Ratio} = \frac{\text{Ink used for data}}{\text{Total ink used in graphic}}

Tufte's Principles for Publication Figures

Edward Tufte's principles: (1) Maximize the data-ink ratio â€” remove chartjunk, (2) Avoid redundant data representations, (3) Small multiples over 3D effects, (4) Labels directly on data rather than legends when possible.

Practical Example: Sales Dashboard

np.random.seed(42)
dates = pd.date_range('2024-01-01', '2024-12-31', freq='D')
products = ['Product A', 'Product B', 'Product C']
regions = ['North', 'South', 'East', 'West']

data = {
    'date': np.random.choice(dates, 500),
    'product': np.random.choice(products, 500),
    'region': np.random.choice(regions, 500),
    'sales': np.random.randint(100, 1000, 500),
    'quantity': np.random.randint(1, 50, 500)
}
df = pd.DataFrame(data)
df['revenue'] = df['sales'] * df['quantity']

# Create dashboard
fig = plt.figure(figsize=(16, 12))
gs = fig.add_gridspec(3, 3, hspace=0.3, wspace=0.3)

ax1 = fig.add_subplot(gs[0, :2])
daily_sales = df.groupby('date')['revenue'].sum()
ax1.plot(daily_sales.index, daily_sales.values, color='#2196F3', linewidth=1)
ax1.fill_between(daily_sales.index, daily_sales.values, alpha=0.2)
ax1.set_title('Daily Revenue Trend', fontweight='bold')

ax2 = fig.add_subplot(gs[0, 2])
product_revenue = df.groupby('product')['revenue'].sum()
ax2.pie(product_revenue, labels=product_revenue.index, autopct='%1.1f%%',
        colors=['#FF6B6B', '#4ECDC4', '#45B7D1'])
ax2.set_title('Revenue by Product')

ax3 = fig.add_subplot(gs[1, :2])
region_product = df.groupby(['region', 'product'])['revenue'].sum().unstack()
region_product.plot(kind='bar', ax=ax3, colormap='Set2')
ax3.set_title('Revenue by Region & Product')

ax4 = fig.add_subplot(gs[1, 2])
sns.histplot(data=df, x='sales', kde=True, ax=ax4, color='#45B7D1')
ax4.set_title('Sales Distribution')

plt.suptitle('Sales Dashboard 2024', fontsize=16, fontweight='bold', y=1.02)
plt.show()

Key Takeaways

Summary: Matplotlib and Seaborn Visualization

Matplotlib provides full control via the object-oriented interface (fig, ax); prefer it over plt.plot() for production code
Seaborn is built on Matplotlib and excels at statistical plots â€” it handles grouping, aggregation, and estimation automatically
Grammar of Graphics teaches you to decompose any plot into data, aesthetics, geometries, statistics, coordinates, facets, and themes
KDE provides a smooth estimate of the probability density function; bandwidth selection is critical
Choose the right plot for your data type and question (see the plot selection guide above)
Publication quality: maximize data-ink ratio, remove chartjunk, use direct labels, save at 300+ DPI
Customization: themes (sns.set_theme), palettes (sns.color_palette), and plt.rcParams give full control over appearance

Practice Exercise

Create a multi-panel figure with 4 different plot types using plt.subplots(2, 2)
Customize colors, fonts, and layout using sns.set_theme and plt.rcParams
Build a Seaborn FacetGrid that facets a dataset by two categorical variables
Compute and visualize a correlation heatmap with annotations
Create a publication-quality scatter plot with regression line, removing top/right spines
Export your final figure in both PNG (300 DPI) and PDF formats
Build a mini-dashboard with at least 5 panels summarizing a dataset