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Clustering and Machine Learning

single-algebra provides powerful clustering and community detection algorithms that are particularly useful for analyzing complex networks, identifying patterns in high-dimensional data, and discovering communities in biological systems.

Community Detection​

Louvain Method​

The Louvain method is a hierarchical clustering algorithm that optimizes modularity in networks:

  • Multi-level Implementation: Recursively applies local optimization and community aggregation
  • Resolution Parameter: Configurable to control the granularity of detected communities
  • Fast Convergence: Efficient for large networks with millions of nodes
  • Deterministic Variant: Provides reproducible results with seed configuration

Leiden Algorithm​

An improved version of the Louvain method with guaranteed well-connected communities:

  • Enhanced Community Quality: Avoids the formation of badly connected communities
  • Refinement Phase: Includes extra refinement steps for improved results
  • Parallel Implementation: Optimized for multi-core processing

Network Analysis​

Network Construction​

  • Similarity Networks: Build networks based on data similarity with various metrics
  • K-Nearest Neighbors Graphs: Construct sparse networks connecting each node to its k nearest neighbors
  • Customizable Similarity Measures: Multiple metrics including:
    • Cosine similarity
    • Euclidean similarity
    • Pearson correlation
    • Manhattan distance
    • Jaccard similarity

Network Operations​

  • Network Reduction: Create reduced networks by aggregating communities
  • Subnetwork Extraction: Extract subnetworks based on community assignments
  • Network Metrics: Calculate various network properties and statistics

Local Moving Algorithm​

The fundamental component of community detection algorithms:

  • Standard Implementation: Sequential version for accurate results
  • Parallel Implementation: High-performance version for large networks
  • Quality Function Optimization: Designed to maximize modularity or other quality metrics
  • Random Initialization: Configurable for exploration of different solutions

Integration with Dimensionality Reduction​

Clustering algorithms can be easily combined with the dimensionality reduction techniques:

  • PCA + Clustering Pipeline: Reduce dimensions before applying clustering
  • Similarity Networks from Embeddings: Create networks based on dimensionality-reduced data
  • Community Analysis in Embedded Space: Identify communities in transformed data

Performance Optimization​

  • Sparse Data Structures: Optimized representations for large, sparse networks
  • Parallel Processing: Multi-threaded implementations of key algorithms
  • Memory-Efficient Algorithms: Designed for large biological datasets
  • Graph-optimized Data Structures: Custom implementations for network operations

Applications​

The clustering and network analysis capabilities in single-algebra are particularly valuable for:

  • Single-cell RNA-seq data analysis
  • Protein interaction network analysis
  • Metabolic pathway identification
  • Gene co-expression networks
  • Patient stratification in clinical data
  • Feature clustering in high-dimensional data

These methods help researchers identify meaningful structures and patterns in complex biological data, providing insights into functional relationships and system organization.

The implementation follows modular design principles, allowing components to be used independently or combined into more complex analytical pipelines.