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Self-Organizing Maps

🧠 Kohonen's Self-Organizing Maps for unsupervised topological data visualization and clustering

Self-Organizing Maps (SOMs) create low-dimensional representations of high-dimensional data while preserving topological relationships. This implementation provides research-accurate reproductions of Teuvo Kohonen's neural network architecture for unsupervised learning and data visualization.

Research Foundation: Kohonen, T. (1982) - "Self-Organized Formation of Topologically Correct Feature Maps"

🚀 Quick Start

Installation

pip install self-organizing-maps

Requirements: Python 3.9+, NumPy, SciPy, scikit-learn, matplotlib

Basic SOM Training

from self_organizing_maps import SelfOrganizingMap
import numpy as np
import matplotlib.pyplot as plt

# Create sample data
np.random.seed(42)
data = np.random.randn(1000, 4)  # 4-dimensional data

# Create and train SOM
som = SelfOrganizingMap(
    grid_height=10,
    grid_width=10,
    input_dimension=4,
    learning_rate=0.5,
    neighborhood_function='gaussian',
    topology='rectangular'
)

# Train the network
print("Training Self-Organizing Map...")
som.fit(data, epochs=1000, verbose=True)

# Get neuron activations for data points
activations = som.activate(data)
winner_coordinates = som.get_winners(data)

print(f"Trained {som.grid_height}x{som.grid_width} SOM")
print(f"Quantization error: {som.quantization_error(data):.4f}")
print(f"Topographic error: {som.topographic_error(data):.4f}")

# Visualize the trained map
som.visualize_map(title="Trained Self-Organizing Map")
som.plot_distance_map()  # U-matrix visualization

Color Clustering Example

from self_organizing_maps import ColorSOM
from self_organizing_maps.som_modules import DataVisualization
import numpy as np

# Create RGB color dataset
colors = np.random.rand(500, 3)  # Random RGB values

# Specialized SOM for color data
color_som = ColorSOM(
    map_size=(15, 15),
    input_dim=3,  # RGB channels
    learning_rate_schedule='exponential',
    initial_radius=7.0
)

# Train on color data
color_som.fit(colors, epochs=500)

# Visualize color palette learned by SOM
color_som.plot_color_map()

# Extract dominant colors
dominant_colors = color_som.extract_palette(n_colors=16)
print(f"Extracted {len(dominant_colors)} dominant colors")

# Cluster colors into regions
clusters = color_som.cluster_neurons(method='hierarchical')
color_som.visualize_clusters(clusters)

Time Series Analysis

from self_organizing_maps import TemporalSOM
from self_organizing_maps.som_modules import TimeSeriesPreprocessor
import numpy as np

# Create time series data
t = np.linspace(0, 4*np.pi, 1000)
signals = np.column_stack([
    np.sin(t) + 0.1*np.random.randn(len(t)),
    np.cos(2*t) + 0.1*np.random.randn(len(t)),
    np.sin(0.5*t) * np.cos(3*t) + 0.1*np.random.randn(len(t))
])

# Preprocess time series into windows
preprocessor = TimeSeriesPreprocessor(window_size=10, overlap=0.5)
windowed_data = preprocessor.create_windows(signals)

# Train temporal SOM
temporal_som = TemporalSOM(
    grid_size=(20, 20),
    input_dimension=windowed_data.shape[1],
    temporal_context=True,
    adaptation_strength=0.3
)

temporal_som.fit(windowed_data, epochs=800)

# Analyze temporal patterns
patterns = temporal_som.extract_temporal_patterns()
temporal_som.plot_activation_timeline(signals)

print(f"Discovered {len(patterns)} temporal patterns")

🧬 Advanced Features

Modular Architecture

# Access individual SOM components
from self_organizing_maps.som_modules import (
    CoreAlgorithm,          # Core SOM mathematics
    NeighborhoodFunctions,  # Gaussian, Mexican hat, bubble
    LearningSchedules,      # Exponential, linear, power law  
    TopologyTypes,          # Rectangular, hexagonal, toroidal
    DistanceMetrics,        # Euclidean, Manhattan, cosine
    QualityMetrics,         # Quantization & topographic error
    VisualizationSuite,     # U-matrix, component planes
    DataPreprocessing       # Normalization and scaling
)

# Custom SOM configuration
custom_som = CoreAlgorithm(
    topology=TopologyTypes.hexagonal,
    neighborhood=NeighborhoodFunctions.mexican_hat,
    learning_schedule=LearningSchedules.power_law,
    distance_metric=DistanceMetrics.cosine
)

Hexagonal Topology SOM

from self_organizing_maps import HexagonalSOM
from self_organizing_maps.som_modules import HexagonalVisualization

# Create hexagonal grid SOM (biologically more realistic)
hex_som = HexagonalSOM(
    radius=8,                    # Hexagonal grid radius
    input_dimension=10,
    neighborhood_decay='gaussian',
    boundary_conditions='periodic'  # Toroidal topology
)

# Train with iris dataset
from sklearn.datasets import load_iris
iris = load_iris()
hex_som.fit(iris.data, epochs=1000)

# Visualize hexagonal structure
hex_viz = HexagonalVisualization(hex_som)
hex_viz.plot_hexagonal_grid()
hex_viz.plot_component_planes(iris.feature_names)
hex_viz.plot_cluster_boundaries(iris.target)

# Analyze neighborhood preservation
preservation_score = hex_som.neighborhood_preservation()
print(f"Neighborhood preservation: {preservation_score:.3f}")

Growing Self-Organizing Maps

from self_organizing_maps import GrowingSOM

# SOM that adapts its size during training
growing_som = GrowingSOM(
    initial_size=(5, 5),
    max_size=(25, 25),
    growth_threshold=0.1,      # Error threshold for growth
    growth_rate=0.05,          # How often to add neurons
    pruning_enabled=True       # Remove unused neurons
)

# Train with adaptive growth
growth_history = growing_som.fit_adaptive(
    data=high_dimensional_data,
    epochs=2000,
    monitor_growth=True
)

# Analyze growth process
growing_som.plot_growth_history(growth_history)
print(f"Final map size: {growing_som.current_size}")
print(f"Growth events: {len(growth_history['growth_points'])}")

🔬 Research Foundation

Scientific Accuracy

This implementation provides research-accurate reproduction of Kohonen's SOM algorithm:

• Mathematical Fidelity: Exact implementation of competitive learning and neighborhood adaptation
• Topological Preservation: Faithful reproduction of distance-preserving mappings
• Parameter Matching: Default parameters match Kohonen's original specifications
• Convergence Properties: Proper learning rate and neighborhood radius schedules

Key Research Contributions

• Topological Mapping: Preserve neighborhood relationships in lower dimensions
• Competitive Learning: Winner-takes-all with neighborhood cooperation
• Unsupervised Clustering: Discover data structure without labeled examples
• Biological Plausibility: Models cortical map formation in brain

Original Research Papers

• Kohonen, T. (1982). "Self-organized formation of topologically correct feature maps." Biological Cybernetics, 43(1), 59-69.
• Kohonen, T. (1990). "The self-organizing map." Proceedings of the IEEE, 78(9), 1464-1480.
• Kohonen, T. (2001). "Self-Organizing Maps." 3rd Edition, Springer-Verlag.

📊 Implementation Highlights

SOM Algorithms

• Classic Kohonen: Original batch and online learning
• Growing SOM: Dynamic topology adaptation
• Hierarchical SOM: Multi-level clustering
• Temporal SOM: Time-series pattern discovery

Quality Assessment

• Quantization Error: Average distance to best matching units
• Topographic Error: Measure of topology preservation
• Trustworthiness: Neighborhood preservation assessment
• Silhouette Analysis: Cluster quality evaluation

Code Quality

• Research Accurate: 100% faithful to Kohonen's mathematical formulation
• Visualization Rich: Comprehensive plotting and analysis tools
• Performance Optimized: Vectorized operations for large datasets
• Educational Value: Clear implementation of SOM principles

🧮 Mathematical Foundation

SOM Learning Rule

The SOM updates winning neurons and their neighbors:

w_i(t+1) = w_i(t) + η(t) h_c,i(t) [x(t) - w_i(t)]

Where:

• w_i(t): Weight vector of neuron i at time t
• η(t): Learning rate at time t (decreasing)
• h_c,i(t): Neighborhood function centered on winner c
• x(t): Input vector at time t

Neighborhood Function

Typical Gaussian neighborhood:

h_c,i(t) = exp(-||r_c - r_i||² / (2σ(t)²))

Where:

• r_c, r_i: Grid positions of neurons c and i
• σ(t): Neighborhood radius (decreasing over time)

Quality Metrics

Quantization Error:

QE = (1/N) Σ ||x_i - w_c(x_i)||

Topographic Error:

TE = (1/N) Σ u(x_i)

Where u(x_i) = 1 if 1st and 2nd BMUs are not adjacent.

🎯 Use Cases & Applications

Data Visualization Applications

• Dimensionality Reduction: Visualize high-dimensional data in 2D
• Exploratory Data Analysis: Discover hidden patterns and clusters
• Feature Mapping: Understand relationships between input variables
• Prototype Selection: Find representative data points

Pattern Recognition Applications

• Image Processing: Color quantization and texture analysis
• Signal Processing: Speech recognition and audio classification
• Market Analysis: Customer segmentation and behavior patterns
• Bioinformatics: Gene expression analysis and protein classification

Neuroscience Applications

• Cortical Mapping: Model formation of brain maps (retinotopy, somatotopy)
• Plasticity Studies: Understand neural adaptation and learning
• Sensory Processing: Model sensory cortex organization
• Development Models: Simulate neural development processes

📖 Documentation & Tutorials

• 📚 Complete Documentation
• 🎓 Tutorial Notebooks
• 🔬 Research Foundation
• 🎯 Advanced Examples
• 🐛 Issue Tracker

🤝 Contributing

We welcome contributions! Please see:

• Contributing Guidelines
• Development Setup
• Code of Conduct

Development Installation

git clone https://github.com/benedictchen/self-organizing-maps.git
cd self-organizing-maps
pip install -e ".[test,dev]"
pytest tests/

📜 Citation

If you use this implementation in academic work, please cite:

@software{self_organizing_maps_benedictchen,
    title={Self-Organizing Maps: Research-Accurate Implementation of Kohonen's Algorithm},
    author={Benedict Chen},
    year={2025},
    url={https://github.com/benedictchen/self-organizing-maps},
    version={1.2.0}
}

@article{kohonen1982self,
    title={Self-organized formation of topologically correct feature maps},
    author={Kohonen, Teuvo},
    journal={Biological cybernetics},
    volume={43},
    number={1},
    pages={59--69},
    year={1982},
    publisher={Springer}
}

📋 License

Custom Non-Commercial License with Donation Requirements - See LICENSE file for details.

🎓 About the Implementation

Implemented by Benedict Chen - Bringing foundational AI research to modern Python.

📧 Contact: benedict@benedictchen.com
🐙 GitHub: @benedictchen

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💰 Support This Work - Choose Your Adventure!

This implementation represents hundreds of hours of research and development. If you find it valuable, please consider donating:

🎯 Donation Tier Goals (With Topological Humor)

☕ $5 - Buy Benedict Coffee
"Caffeine creates the perfect neighborhood function for my neurons! Coffee helps me map high-dimensional problems to simple solutions."
💳 PayPal One-time | ❤️ GitHub Monthly

🍕 $25 - Pizza Fund
"Like a SOM, pizza toppings self-organize into delicious neighborhoods! Each slice preserves the topological structure of yumminess."
💳 PayPal One-time | ❤️ GitHub Monthly

🏠 $500,000 - Buy Benedict a House
"With a wall-sized grid to visualize SOMs! My neighbors will love the giant hexagonal topology decorations."
💳 PayPal Challenge | ❤️ GitHub Lifetime

🏎️ $200,000 - Lamborghini Fund
"Fast car for fast neural convergence! The Lambo's topology will perfectly preserve the neighborhood structure of style and speed."
💳 PayPal Supercar | ❤️ GitHub Lifetime

✈️ $50,000,000 - Private Jet
"To fly around the world testing SOMs at different altitudes! Does the neighborhood function work differently at 30,000 feet?"
💳 PayPal Aerospace | ❤️ GitHub Aviation

🏝️ $100,000,000 - Private Island
"Shaped like a perfect hexagonal SOM grid! Each beach will represent a different cluster, and the coconut trees will self-organize."
💳 PayPal Paradise | ❤️ GitHub Tropical

🎪 Monthly Subscription Tiers (GitHub Sponsors)

🧠 Neural Mapper ($10/month) - "Monthly support for maintaining perfect topological order in my code!"
❤️ Subscribe on GitHub

🎨 Visualization Artist ($25/month) - "Help me create beautiful U-matrices and component planes!"
❤️ Subscribe on GitHub

🏆 SOM Champion ($100/month) - "Elite support for the ultimate self-organizing coding experience!"
❤️ Subscribe on GitHub

Every contribution helps my motivation self-organize into productive clusters! Just like neurons in a SOM, your support creates beautiful neighborhood relationships! 🚀

P.S. - If you help me get that hexagonal island, I promise to name all the beaches after different SOM algorithms!

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@MapMakingMaestro (756K followers) • 5 hours ago • (parody)

"NO SHOT this SOM library is actually changing my LIFE! 🗺️ It's literally teaching me how data points become best friends based on vibes and similarities - like how your Spotify algorithm groups songs that just BELONG together! Kohonen really understood the assignment when he figured out self-organizing maps. This is giving 'I can visualize high-dimensional chaos and make it aesthetic' energy and honestly I respect that. Currently using this to understand why certain friend groups form naturally and the topological preservation is actually beautiful fr fr! 🌟"

103.2K ❤️ • 19.4K 🔄 • 7.1K ✨