Project 1: Image Similarity Search Engine
Build a working image search engine that finds similar images using vector representations and cosine similarity. This project integrates everything you’ve learned about vectors, dot products, and similarity measures.Estimated Time: 3-4 hours (take your time to understand each concept!)
Difficulty: Beginner-Intermediate
Concepts Used: Vectors, dot product, cosine similarity, normalization
Dataset: Product images (we’ll simulate these)
Difficulty: Beginner-Intermediate
Concepts Used: Vectors, dot product, cosine similarity, normalization
Dataset: Product images (we’ll simulate these)
🎯 The Big Picture: What Are We Really Doing?
Before diving into code, let’s understand the core insight that makes image search possible:The Key Insight
Every image can be represented as a vector (list of numbers). Once images are vectors, finding “similar” images becomes finding “nearby” vectors. It’s just geometry!| Image Comparison | Vector Comparison |
|---|---|
| ”These shoes look alike” | Vectors point in similar directions |
| ”Cat ≠ Car” | Vectors point in very different directions |
| ”Same product, different angle” | Vectors are close together |
Why Does This Work?
Think about it: If two images are similar, they probably have:- Similar colors in similar places
- Similar shapes and patterns
- Similar brightness distributions
Project Overview
What You’ll Build
An image search engine that:- Converts images to vector representations (the magic transformation)
- Computes similarity between images (using cosine similarity)
- Returns the top-K most similar images to a query
- Visualizes results (so you can verify it works!)
Why This Matters
Real-World Applications (This is exactly what these companies do):| Company | Application | How It Works |
|---|---|---|
| Visual search | ”Find pins like this image” | |
| Google Images | Reverse search | ”Where else does this image appear?” |
| Amazon | Similar products | ”Customers who viewed this also viewed…” |
| Spotify | Cover art discovery | Audio → spectrogram → vector similarity |
| Face ID | Authentication | Face → embedding → compare to stored |
- Feature extraction (images → vectors)
- Similarity metrics (cosine similarity)
- Nearest neighbor search
- High-dimensional vector spaces
- Vectorized operations (matrix multiplication for speed!)
Part 1: Understanding the Problem (Deeply)
How Do We Represent Images as Vectors?
This is the crucial question. Let’s explore multiple methods and understand the tradeoffs.Method 2: Color Histogram (Better for Different Viewpoints)
The pixel method has a problem: if you rotate or shift an image slightly, the vector changes dramatically! Histograms solve this. The Idea: Instead of “where are the pixels?”, ask “what colors are present?”Histogram vs Pixels: When to Use Which?
For learning, we’ll use both! In production, companies use CNNs (neural networks) to extract “deep features.”
| Method | Pros | Cons | Best For |
|---|---|---|---|
| Raw Pixels | Simple, captures spatial info | Sensitive to rotation/shift | Exact duplicates, aligned images |
| Histogram | Rotation invariant, compact | Loses spatial info | Different viewpoints, color-based |
| Deep Learning (CNN) | Best of both worlds | Requires training | Production systems |
Part 2: Computing Similarity
This is where the linear algebra magic happens. We’ve turned images into vectors. Now we need to measure “how similar” two vectors are.The Core Insight: Similarity = Angle Between Vectors
Imagine two arrows (vectors) starting from the same point:- If they point in the same direction → very similar
- If they point in different directions → not similar
- If they’re perpendicular (90°) → completely unrelated
Cosine Similarity: The Math
Where:- is the dot product (sum of element-wise products)
- is the magnitude (length) of vector A
- The result is between -1 and 1
| Cosine Value | Angle | Meaning |
|---|---|---|
| 1.0 | 0° | Identical (same direction) |
| 0.7 | ~45° | Similar |
| 0.0 | 90° | Unrelated (perpendicular) |
| -1.0 | 180° | Opposite |
Implementation with Deep Understanding
Euclidean Distance: The Alternative
For completeness, here’s Euclidean distance. It measures “how far apart” vectors are in space:Which to Use?
- Cosine: When magnitude doesn’t matter (text, images with different brightness)
- Euclidean: When absolute values matter (coordinates, measurements)
Part 3: Building the Search Engine
Step 1: Create Image Database
Step 2: Use the Search Engine
Part 4: Visualizing Results
Part 5: Performance Analysis
Timing Comparison
Memory Usage
Part 6: Improvements & Extensions
1. Better Feature Extraction
2. Faster Search with Approximate Nearest Neighbors
3. Multi-Modal Search
Challenges & Exercises
Challenge 1: Batch Search
Modify the search engine to handle multiple queries at once:Challenge 2: Evaluation Metrics
Implement precision@K and recall@K:Challenge 3: Diversity
Modify search to return diverse results (not all similar to each other):Complete Code
Here’s the full working implementation:🚨 Real-World Challenge: Handling Messy Images
Key Takeaways
What You Built & Learned:
- ✅ Images as Vectors - Pixels, histograms, and deep features all work
- ✅ Cosine Similarity - Measure angular distance between high-dimensional vectors
- ✅ Vectorized Operations - Replace loops with matrix operations for 100x speedup
- ✅ Batch Processing - Matrix multiplication enables searching thousands of images instantly
- ✅ Real ML Pipeline - From raw data → vectors → similarity → results
- ✅ Production Robustness - Handle corrupted, malformed, and edge-case images
What’s Next?
You’ve built a working image search engine using linear algebra! Next, we’ll explore eigenvalues and eigenvectors to build even more powerful applications like face recognition and dimensionality reduction.Next: Eigenvalues & Eigenvectors
Learn the math behind PCA and face recognition