algorithm-visualizations

SPTAG (Space Partition Tree And Graph) Visualization 🎯

中文文档

Algorithm Introduction

SPTAG (Space Partition Tree And Graph) is a high-performance vector similarity search algorithm that combines space partition trees with a navigable small world graph. It was developed by Microsoft and is particularly effective for large-scale, high-dimensional nearest neighbor search problems.

Core Features

1. Hybrid Structure
   • Space partition trees (KD-trees/BKT)
   • Navigable small world graph
   • Multiple tree combination
2. Search Strategy
   • Tree-based coarse search
   • Graph-based refinement
   • Parallel search paths

Performance Analysis

• Build Time: O(n log n)
• Query Time: O(log n) average case
• Space Complexity: O(n)
• Scalability: Excellent for high dimensions

Application Scenarios

1. Vector Search
   • Image retrieval
   • Document embedding search
   • Feature matching
2. Machine Learning
   • Recommendation systems
   • Pattern recognition
   • Clustering
3. Information Retrieval
   • Semantic search
   • Content-based retrieval
   • Similar item search

Visualization Features

This demonstration implements:

1. Structure Display
   • Space partition visualization
   • Graph connectivity
   • Search path tracking
2. Interactive Operations
   • Vector insertion
   • Nearest neighbor search
   • Parameter tuning
3. Performance Metrics
   • Search time statistics
   • Recall rate monitoring
   • Memory usage tracking

Code Structure

sptag/
├── index.html      # Main page
├── sptag.js        # SPTAG implementation
└── style.css       # Styling

Usage Instructions

1. Data Operations
   • Add vectors
   • Search nearest neighbors
   • Adjust search parameters
2. Visualization Control
   • View tree structure
   • Observe graph connections
   • Track search process

Implementation Details

1. Node Structure

   class SPTAGNode {
       constructor(vector, id) {
           this.vector = vector;
           this.id = id;
           this.neighbors = new Set();
           this.treeChildren = [null, null];
       }
   }
   

2. Tree Building

   function buildKDTree(points, depth = 0) {
       if (points.length === 0) return null;
          
       const axis = depth % dimension;
       points.sort((a, b) => a.vector[axis] - b.vector[axis]);
          
       const median = Math.floor(points.length / 2);
       const node = points[median];
          
       node.treeChildren[0] = buildKDTree(points.slice(0, median), depth + 1);
       node.treeChildren[1] = buildKDTree(points.slice(median + 1), depth + 1);
          
       return node;
   }
   

3. Graph Construction

   function buildGraph(nodes, k) {
       for (const node of nodes) {
           const neighbors = findApproximateNN(node, nodes, k);
           for (const neighbor of neighbors) {
               node.neighbors.add(neighbor);
               neighbor.neighbors.add(node);
           }
       }
   }
   

Optimization Strategies

1. Build-time Optimization
   • Balanced tree construction
   • Efficient neighbor selection
   • Parallel processing
2. Search Optimization
   • Early termination
   • Priority queue
   • Distance caching
3. Memory Management
   • Vector quantization
   • Compact storage
   • Batch processing

Key Parameters

1. Tree Parameters
   • Leaf size
   • Tree number
   • Split strategy
2. Graph Parameters
   • Neighbor count
   • Build factor
   • Search factor

Advanced Features

1. Multi-threading Support
   • Parallel tree building
   • Concurrent search
   • Load balancing
2. Quality Control
   • Recall rate monitoring
   • Precision tracking
   • Performance profiling

References

• SPTAG: A library for fast approximate nearest neighbor search
• Space Partition Tree And Graph Algorithm for Approximate Nearest Neighbor Search
• Microsoft’s Vector Search Solution

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