Eigen-Component Analysis

A Python package for Eigen-Component Analysis (ECA) and Unsupervised Eigen-Component Analysis (uECA) for classification and clustering tasks without data centralization or standardization. ECA is a quantum theory-inspired linear model that provides interpretable feature-to-class mappings through eigencomponents.

Features

• Scikit-learn Compatible: Implements the scikit-learn Estimator API with fit, transform, and predict methods
• Supervised & Unsupervised Learning: Supports both classification (ECA) and clustering (uECA) modes
• GPU Acceleration: PyTorch backend enables GPU acceleration when available
• Visualization Tools: Built-in methods to visualize eigenfeatures, mappings, and results
• Mathematical Foundation: Based on quantum theory principles with antisymmetric transformation matrices

Installation

From PyPI

pip install eigen-analysis

From Source

# Clone the repository
git clone https://github.com/lachlanchen/eigen_analysis.git
cd eigen_analysis
pip install .

# Install in development mode
pip install -e .

Requirements

• numpy >= 1.18.0
• torch >= 1.7.0
• matplotlib >= 3.3.0
• seaborn >= 0.11.0
• scikit-learn >= 0.24.0
• scipy >= 1.6.0

Usage

Unified API

The package provides a unified API that automatically selects between supervised and unsupervised modes:

from eigen_analysis import eigencomponent_analysis

# For classification (supervised)
model = eigencomponent_analysis(X, y, num_clusters=3)

# For clustering (unsupervised)
model = eigencomponent_analysis(X, num_clusters=3)

Classification Example

import numpy as np
from sklearn import datasets
from sklearn.model_selection import train_test_split
from eigen_analysis import ECA

# Load Iris dataset
iris = datasets.load_iris()
X = iris.data
y = iris.target

# Split data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)

# Create and train ECA model
eca = ECA(num_clusters=3, num_epochs=10000, learning_rate=0.001)
eca.fit(X_train, y_train)

# Make predictions
y_pred = eca.predict(X_test)

# Evaluate accuracy
from sklearn.metrics import accuracy_score
accuracy = accuracy_score(y_test, y_pred)
print(f"Test accuracy: {accuracy:.4f}")

# Get transformed data
X_transformed = eca.transform(X_test)

# Access model components
P_matrix = eca.P_numpy_  # Eigenfeatures
L_matrix = eca.L_numpy_  # Feature-to-class mapping

# Visualize results
from eigen_analysis.visualization import visualize_clustering_results
visualize_clustering_results(
    X_test, y_test, y_pred, 
    eca.loss_history_, 
    eca.transform(X_test),
    eca.num_epochs,
    eca.model_,
    (eca.L_numpy_ > 0.5).astype(float),
    eca.L_numpy_,
    eca.P_numpy_,
    "Iris",
    output_dir="eca_classification_results"
)

Clustering Example

import numpy as np
from sklearn.datasets import make_blobs
from eigen_analysis import UECA
from sklearn.metrics import adjusted_rand_score

# Generate synthetic data
X, y_true = make_blobs(n_samples=300, centers=3, random_state=42)

# Train UECA model
ueca = UECA(num_clusters=3, learning_rate=0.01, num_epochs=3000)
ueca.fit(X, y_true)  # y_true used only for evaluation

# Access clustering results
clusters = ueca.labels_
remapped_clusters = ueca.remapped_labels_  # Optimal mapping to ground truth

# Evaluate clustering quality
ari_score = adjusted_rand_score(y_true, clusters)
print(f"Adjusted Rand Index: {ari_score:.4f}")

# Visualize clustering results
from eigen_analysis.visualization import visualize_clustering_results
visualize_clustering_results(
    X, 
    y_true, 
    ueca.remapped_labels_, 
    ueca.loss_history_, 
    ueca.transform(X),
    ueca.num_epochs,
    ueca.model_,
    ueca.L_hard_numpy_,
    ueca.L_numpy_,
    ueca.P_numpy_,
    "Custom Dataset",
    output_dir="eca_clustering_results"
)

Advanced Usage

Customizing Visualizations

# Customize visualization with feature and class names
visualize_clustering_results(
    X, y, predictions,
    loss_history, projections, num_epochs,
    model, L_hard, L_soft, P_matrix,
    dataset_name="Iris",
    feature_names=["Sepal Length", "Sepal Width", "Petal Length", "Petal Width"],
    class_names=["Setosa", "Versicolor", "Virginica"],
    output_dir="custom_visualization"
)

Working with MNIST

For MNIST visualization, there's a specialized function:

from torchvision import datasets, transforms
from eigen_analysis import ECA
from eigen_analysis.visualization import visualize_mnist_eigenfeatures

# Load MNIST
mnist_train = datasets.MNIST('data', train=True, download=True)
X_train = mnist_train.data.reshape(-1, 784).float() / 255.0
y_train = mnist_train.targets

# Train ECA model
eca = ECA(num_clusters=10, num_epochs=1000)
eca.fit(X_train, y_train)

# Visualize MNIST eigenfeatures
visualize_mnist_eigenfeatures(eca.model_, output_dir='mnist_results')

Model Parameters

ECA Model (Supervised)

• num_clusters: Number of classes
• learning_rate: Learning rate for optimizer (default: 0.001)
• num_epochs: Number of training epochs (default: 1000)
• temp: Temperature parameter for sigmoid (default: 10.0)
• random_state: Random seed for reproducibility
• device: Device to use ('cpu' or 'cuda')

UECA Model (Unsupervised)

• num_clusters: Number of clusters
• learning_rate: Learning rate for optimizer (default: 0.01)
• num_epochs: Number of training epochs (default: 3000)
• random_state: Random seed for reproducibility
• device: Device to use ('cpu' or 'cuda')

Citation

If you use this package in your research, please cite:

@inproceedings{chen2025eigen,
  title={Eigen-Component Analysis: {A} Quantum Theory-Inspired Linear Model},
  author={Chen, Rongzhou and Zhao, Yaping and Liu, Hanghang and Xu, Haohan and Ma, Shaohua and Lam, Edmund Y.},
  booktitle={2025 IEEE International Symposium on Circuits and Systems (ISCAS)},
  pages={},
  year={2025},
  publisher={IEEE},
  doi={},
}

License

MIT