NBCS 1.3

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.

NBCS (Nested barycentric coordinate system)

Version: 1.2
License: MIT License
Author: Amit Ronen Email: [e-mail]

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:

pip install nbcs

Usage

Classification Example

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

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:

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

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

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 [e-mail]