Self-Organisation Maps (SOM)

Definition

Self-Organising Maps (SOM), also known as Kohonen maps, are a type of artificial neural network introduced by Teuvo Kohonen. SOMs are used for unsupervised learning and are particularly effective for dimensionality reduction, clustering, and visualization of high-dimensional data by mapping it onto a low-dimensional (usually 2D) grid while preserving the topological relationships of the data.

Key Concepts

• Unsupervised LearningUnsupervised LearningUnsupervised Learning Definition Unsupervised Learning is a type of machine learning where the algorithm is trained on unlabeled data. The goal is to infer the natural structure present within a set of data points. Unlike supervised learning, there are no predefined labels or outcomes, and the system tries to learn the patterns and the structure from the data. Key Concepts Unlabeled Data:** Data that does not have associated labels or target values. Clustering:** Grouping a set of objects in: SOMs learn to organize and cluster data without labeled inputs.
• Topology Preservation: The SOM preserves the spatial relationships of the input data in the mapping process.
• Neighbourhood Function: Determines the region around a winning neuron that gets updated during training.
• Dimensionality Reduction: High-dimensional data is mapped onto a lower-dimensional space for visualization and analysis.

Detailed Explanation

Unsupervised Learning

• Learning Process: SOMs use competitive learning where neurons compete to respond to input patterns, with only the winning neuron and its neighbors getting updated.
• No Labels Needed: SOMs do not require labeled training data, making them suitable for exploratory data analysis.

Topology Preservation

• Mapping Input to Grid: The SOM maps high-dimensional input vectors to nodes on a lower-dimensional grid (typically 2D), ensuring that similar input vectors are mapped to nearby nodes on the grid.
• Preserving Relationships: The relative distances between data points in the input space are preserved in the SOM, allowing for meaningful clustering and visualization.

Neighborhood Function

• Updating Neurons: When a neuron (node) wins the competition, not only its weights are updated, but also those of its neighboring neurons. The degree of update decreases with distance from the winning neuron.
• Neighborhood Radius: The size of the neighborhood decreases over time, allowing the network to converge and fine-tune the mapping.

Dimensionality Reduction

• Visualizing High-Dimensional Data: By reducing the dimensionality, SOMs make it easier to visualize and interpret complex data sets.
• Clustering: Similar data points are grouped together on the map, aiding in identifying clusters and patterns in the data.

Diagrams

Basic Structure of a Self-Organizing Map

Training Process in SOM

Links to Resources

• Self-Organizing Maps by Teuvo Kohonen: Comprehensive resource on SOMs, authored by the creator of the method.
• Introduction to Self-Organizing Maps: An accessible introduction to SOMs with examples and applications.
• Neural Networks and Learning Machines by Simon Haykin: Textbook providing in-depth coverage of SOMs and other neural network models.

Notes and Annotations

• Summary of Key Points:
  • SOMs are effective for clustering, visualization, and dimensionality reduction of high-dimensional data.
  • They preserve the topological relationships of the input data in a lower-dimensional space.
  • The neighborhood function is crucial for the training process, allowing smooth transitions and convergence.
• Personal Annotations and Insights:
  • SOMs are particularly useful for exploratory data analysis and can reveal hidden patterns in complex datasets.
  • The ability to visualize high-dimensional data in a 2D map makes SOMs a powerful tool for data scientists and analysts.

Backlinks

• Pattern Clustering and Feature Mapping Network: Refer to notes on pattern clustering and feature mapping for a broader understanding of unsupervised learning networks.
• Unsupervised Learning Techniques: Connect to discussions on various unsupervised learning methods and their applications.
• Neural Network Models Overview: Link to an overview of different neural network models to see where SOMs fit in the landscape of machine learning techniques.