bh: Fuzzy Linear Discriminant Analysis

bh is a Python library implementing Fuzzy Linear Discriminant Analysis (FLDA), an extension of traditional Linear Discriminant Analysis that handles fuzzy or probabilistic class memberships.

Installation

pip install bh

Features

• Fuzzy Linear Discriminant Analysis: Extends traditional LDA to work with fuzzy class memberships
• scikit-learn compatible: Implements scikit-learn's estimator interface
• Dimensionality reduction: Transform high-dimensional data into a lower-dimensional space while preserving class separability
• Classification: Predict class probabilities and labels for new data points
• Data preprocessing: Includes utilities like sphericize to transform data to have spherical covariance

Usage

Basic Example

import numpy as np
from bh import FuzzyLDA

# Create some sample data
X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
# Fuzzy class membership: each point can partially belong to multiple classes
y = [
    {'class1': 0.8, 'class2': 0.2},
    {'class1': 0.9, 'class2': 0.1},
    {'class1': 1.0, 'class2': 0.0},
    {'class1': 0.1, 'class2': 0.9},
    {'class1': 0.0, 'class2': 1.0},
    {'class1': 0.2, 'class2': 0.8},
]

# Fit model
flda = FuzzyLDA()
flda.fit(X, y)

# Transform data
X_transformed = flda.transform(X)

# Predict on new data
new_data = np.array([[0.8, 1]])
probabilities = flda.predict_proba(new_data)
predicted_class = flda.predict(new_data)

Using with Hard Labels

FLDA also works with traditional hard labels:

from bh import FuzzyLDA

X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
y = [0, 0, 0, 1, 1, 1]  # Hard labels are automatically converted to fuzzy format

flda = FuzzyLDA()
flda.fit(X, y)

Data Preprocessing

from bh import sphericize

X_spherical = sphericize(X, y)

Theory

Fuzzy Linear Discriminant Analysis extends traditional LDA by allowing samples to partially belong to multiple classes. This is particularly useful in scenarios where:

• Class membership is inherently probabilistic
• There is uncertainty in class assignments
• Data points can naturally belong to multiple categories

The algorithm finds a linear transformation that maximizes the ratio of between-class scatter to within-class scatter, while accounting for fuzzy memberships.

License

[License information goes here]

Citation

If you use this software in your research, please cite it.