NBCS 1.4
Python package that implements an adaptive classification and regression system using simplicial complexes. The package provides a novel approach to handling both binary and multi-class classification problems, as well as regression tasks, by adaptively creating a simplicial decomposition of the feature space.
Requires Python: >=3.6

# NBCS (Nested barycentric coordinate system)

**Version:** 1.2  
**License:** MIT License  
**Author:** Amit Ronen
**Email:** erankfmn@gmail.com  

## Overview

NBCS (Non-Binary Classification System) is a Python package that implements an adaptive classification and regression system using simplicial complexes. The package provides a novel approach to handling both binary and multi-class classification problems, as well as regression tasks, by adaptively creating a simplicial decomposition of the feature space.

The package extends scikit-learn's base estimator and transformer interfaces, making it compatible with scikit-learn's ecosystem while providing unique capabilities for handling complex classification boundaries and non-linear regression problems.

## Features

- **Adaptive Classification:** Automatically adjusts the complexity of the decision boundary based on the data
- **Simplicial Complex Construction:** Creates an optimal decomposition of the feature space
- **Multiple Learning Modes:**
  - Barry fitting mode for general purpose learning
  - Adaptive fitting mode for classification tasks
- **Regression Support:** Handles complex regression problems with piece-wise linear approximations
- **Visualization Tools:** Built-in functions for plotting decision boundaries and regression results
- **Scikit-learn Compatible:** Implements scikit-learn's BaseEstimator and TransformerMixin interfaces

## Installation

You can install the package directly from PyPI using pip:

```bash
pip install nbcs
```

## Usage

### Classification Example

```python
import numpy as np
from nbcs import NBCS
from sklearn.svm import SVC

# Create and fit the NBCS model
model = NBCS(C=1000, k=4)
embedder = model.fit(X, y)

# Transform the data
points = embedder.transform(X)

# Use with any sklearn classifier
clf = SVC(kernel='linear')
clf.fit(points, y)
```

### Regression Example

```python
from nbcs import NBCS
from sklearn.linear_model import LinearRegression

# Create and fit the NBCS model
model = NBCS(k=3)
embedder = model.fit_barry(X)

# Transform the data
points = embedder.transform(X)

# Use with any sklearn regressor
reg = LinearRegression()
reg.fit(points, y)
```

## Parameters

- **C:** Regularization parameter (default=1)
- **k:** Number of refinement steps (default=1)

## Available Methods

- `fit(X, y)`: Fits the model using adaptive mode
- `fit_barry(X, y)`: Fits the model using barry mode
- `add_point(point)`: Adds a new point to the simplicial complex


## Visualization

The package includes several visualization tools:

```python
from nbcs.utils import make_meshgrid, plot_contours

# Create mesh grid for visualization
xx, yy = make_meshgrid(X[:, 0], X[:, 1])

# Plot decision boundaries
plot_contours(ax, clf, xx, yy, xy)
```

## Dependencies

- numpy
- scipy
- scikit-learn
- matplotlib

## Examples

### Classification with Regular Polytope

```python
import numpy as np
from nbcs import NBCS
from sklearn.svm import SVC

# Generate synthetic data
N = 1000
D = 2  # dimension
X = np.random.normal(0, 1, (N, D))
y = np.ones(N)

# Create and fit model
model = NBCS(C=1000, k=4)
embedder = model.fit(X, y)
```

### Regression with Multiple Lines

```python
import numpy as np
from nbcs import NBCS
from sklearn.linear_model import LinearRegression

# Generate synthetic data
x = np.linspace(0, 30, 60).reshape(-1, 1)
y = np.sin(x/10) + np.random.normal(0, 0.1, x.shape)

# Create and fit model
model = NBCS(k=3)
embedder = model.fit_barry(x)
```

## License

This project is licensed under the MIT License - see the LICENSE file for details.

## Acknowledgements

- scikit-learn for providing the foundational tools for machine learning in Python
- numpy and scipy for numerical computations
- matplotlib for data visualization

## Contact

If you have any questions or suggestions, feel free to reach out at erankfmn@gmail.com