Vectorized ANFIS

High-performance ANFIS implementation using NumPy vectorization for 10-100x speedup. Combines fuzzy logic with neural networks through compact (~140 lines), production-ready code.

🎯 Overview

This repository provides a highly optimized, vectorized implementation of Adaptive Neuro-Fuzzy Inference System (ANFIS) that achieves 10-100x speedup over traditional loop-based approaches while maintaining a remarkably compact codebase (~140 lines of core implementation).

Why This Implementation?

• ⚡ Blazing Fast: Leverages NumPy broadcasting for parallel computation across all samples simultaneously
• 📦 Compact: Complete ANFIS in ~140 lines without sacrificing functionality
• 🎓 Well-Documented: Comprehensive mathematical theory and practical guides
• 🔧 Production-Ready: Clean API, early stopping, validation monitoring
• 🧪 Proven: Achieves R² > 0.98 on energy efficiency benchmarks

🚀 Quick Start

Installation

git clone https://github.com/yourusername/vectorized-anfis.git
cd vectorized-anfis
pip install -r Requirements.txt

Basic Usage

from src.anfis import ANFIS
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split

# Prepare your data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)
scaler = StandardScaler().fit(X_train)
X_train, X_test = scaler.transform(X_train), scaler.transform(X_test)
X_train, X_val, y_train, y_val = train_test_split(X_train, y_train, test_size=0.1)

# Train ANFIS
model = ANFIS(n_clusters=50, X=X_train)
model.fit(X_train, y_train, X_val, y_val, epochs=200, lr=0.01, patience=15)

# Evaluate
model.test(X_test, y_test)

Run the demo:

python main.py  # Simple example
python Data/Energy_demo.py  # Comprehensive demo with visualizations

📚 What is ANFIS?

Adaptive Neuro-Fuzzy Inference System (ANFIS) is a hybrid intelligent system that combines:

• Fuzzy Logic: Human-like reasoning with linguistic rules
• Neural Networks: Learning capability through gradient-based optimization

The Power of Hybrid Intelligence

ANFIS excels at modeling complex nonlinear relationships by using:

1. Fuzzy IF-THEN rules to partition the input space
2. Neural network learning to optimize parameters automatically
3. Interpretable structure unlike black-box neural networks

Perfect for: Time series prediction, system identification, control systems, regression problems with complex patterns.

🧮 Mathematical Foundation

Five-Layer Architecture

Our implementation follows the classical Takagi-Sugeno model:

Layer 1 (Input)        → Raw features [x₁, x₂, ..., xF]
Layer 2 (Fuzzify)      → Gaussian membership functions
Layer 3 (Product)      → Rule firing strengths (implicit)
Layer 4 (Normalize)    → Normalized firing strengths
Layer 5 (Defuzzify)    → Weighted linear combination

Key Equations

Gaussian Membership Function:

μⱼᵢ(xᵢ) = exp(-(xᵢ - cⱼᵢ)² / (2σⱼᵢ²))

Rule Firing Strength (product t-norm):

wⱼ(x) = ∏ᵢ μⱼᵢ(xᵢ) = exp(-∑ᵢ (xᵢ - cⱼᵢ)² / (2σⱼᵢ²))

Normalized Firing Strength:

w̄ⱼ(x) = wⱼ(x) / ∑ₖ wₖ(x)

Final Output:

y(x) = ∑ⱼ w̄ⱼ(x) · θⱼ

Hybrid Learning Algorithm

1. Forward Pass: Compute memberships and firing strengths
2. Least Squares: Optimize consequent parameters (θⱼ) with closed-form solution
3. Backpropagation: Update premise parameters (centers cⱼᵢ, stds σⱼᵢ) via gradient descent
4. Validation: Monitor validation loss for early stopping

See docs/theory.md for complete mathematical derivations.

⚡ Vectorization: The Secret Sauce

Traditional Approach (Slow)

# Nested loops: O(N × K × F) sequential operations
for n in range(N):              # Each sample
    for k in range(K):          # Each cluster
        for f in range(F):      # Each feature
            membership[n,k] *= gaussian(X[n,f], centers[k,f], stds[k,f])

Vectorized Approach (Fast)

# Broadcasting: O(N × K × F) parallel operations
diffs = X[:, None, :] - centers[None, :, :]  # (N,K,F) in one shot
sq = diffs**2 / (2 * stds[None, :, :]**2)
memberships = np.exp(-sq.sum(axis=2))  # All at once!

📊 Example: Energy Efficiency Prediction

Predicting building heating/cooling loads from architectural features:

Input Features (8):

• Relative Compactness
• Surface Area
• Wall Area
• Roof Area
• Overall Height
• Orientation
• Glazing Area
• Glazing Area Distribution

Performance:

Test MSE:  2.34
Test RMSE: 1.53
Test MAE:  1.18
Test R²:   0.982
Training:  ~30 seconds (200 epochs, early stopping at epoch 47)

Visualization:

Run python Data/Energy_demo.py to see:

• Actual vs Predicted scatter plots
• Residual analysis
• Error distributions
• Configuration comparisons

🛠️ API Reference

Class: ANFIS

Constructor

ANFIS(n_clusters, X)

Parameters:

• n_clusters (int): Number of fuzzy rules/clusters (typically 20-100)
• X (ndarray): Training data for k-means initialization, shape (N, F)

Methods

fit(X, y, Xv, yv, epochs=100, lr=1e-4, patience=20)

Train the ANFIS model using hybrid learning.

Parameters:

• X: Training features (N, F)
• y: Training targets (N,)
• Xv: Validation features
• yv: Validation targets
• epochs: Maximum training iterations (default: 100)
• lr: Learning rate for gradient descent (default: 1e-4)
• patience: Early stopping patience (default: 20)

predict(X)

Generate predictions for input data.

Parameters:

• X: Input features (N, F)

Returns:

• Predictions (N,)

test(X, y, plot=True)

Evaluate model performance on test data.

Parameters:

• X: Test features
• y: Test targets
• plot: Whether to display scatter plot (default: True)

Returns:

• Tuple: (MSE, RMSE, MAE, R²)

📁 Repository Structure

vectorized-anfis/
├── src/
│   ├── __init__.py          # Package initialization
│   └── anfis.py             # Core ANFIS implementation (~140 lines)
├── Data/
│   └── Energy_demo.py       # Comprehensive demo with visualizations
├── Example/
│   └── ENB2012_data.xlsx    # Sample dataset
├── docs/
│   └── theory.md            # Deep mathematical theory
├── main.py                  # Simple entry point
├── quickstart.md            # Step-by-step tutorial
├── Requirements.txt         # Dependencies
├── Setup.py                 # Package installation
└── README.md                # This file

🎓 Learning Resources

• Quick Start Guide: Step-by-step tutorial for beginners
• Mathematical Theory: Complete derivations and explanations
• Energy Demo: Working example with visualizations
• Dataset Info: Dataset information and preprocessing

🔧 Hyperparameter Guide

Parameter	Typical Range	Notes
n_clusters	20-100	More = higher capacity, slower training
lr	0.001-0.01	Start with 0.01, reduce if unstable
epochs	100-300	Early stopping handles this
patience	15-25	Balance between underfitting/overfitting

Pro Tips:

• Always standardize features (StandardScaler)
• Use ~10% of training data for validation
• Start with n_clusters = sqrt(N_samples) as baseline
• Monitor validation loss to detect overfitting

🤝 Contributing

We welcome contributions! Please open an issue or submit a pull request.

Areas for contribution:

• Unit tests with pytest
• Additional example datasets
• Alternative membership functions
• Performance benchmarking suite
• Extended documentation

📜 Citation

If you use this implementation in your research, please star this Repo.

🙏 Acknowledgments

• Dataset: Energy Efficiency dataset from UCI Machine Learning Repository
• Inspiration: Classical ANFIS by J.-S. Jang (1993) with modern NumPy optimization
• Community: Thanks to all contributors and users

📚 References

1. Jang, J.-S. R. (1993). "ANFIS: Adaptive-Network-Based Fuzzy Inference System". IEEE Transactions on Systems, Man, and Cybernetics, 23(3), 665-685.
2. Takagi, T., & Sugeno, M. (1985). "Fuzzy identification of systems and its applications to modeling and control". IEEE Transactions on Systems, Man, and Cybernetics.

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Made with ⚡ by combining the interpretability of fuzzy logic with the power of neural networks