Feature Overlap Measures

Feature-level measures analyze how well individual features separate classes.

F1 - Maximum Fisher's Discriminant Ratio

Measures the maximum discriminative power across all features.

cm = ComplexityMeasures(X, y)
f1 = cm.calculate_F1()
print(f"F1: {f1:.4f}")

Interpretation: - Higher values indicate better feature separability - Low F1 suggests poor feature discrimination

F1v - Directional-Vector Maximum Fisher's Discriminant Ratio

Extends F1 by considering feature combinations.

f1v = cm.calculate_F1v()

Interpretation: - Higher values indicate better separability in feature space

F2 - Volume of Overlapping Region

Measures the volume of the region where classes overlap.

f2 = cm.calculate_F2()

Interpretation: - Lower values indicate less overlap - 0.0: No overlap - 1.0: Complete overlap

F3 - Maximum Individual Feature Efficiency

Measures the efficiency of the best single feature.

f3 = cm.calculate_F3()

Interpretation: - Higher values indicate at least one feature separates classes well

F4 - Collective Feature Efficiency

Measures how well features collectively separate classes.

f4 = cm.calculate_F4()

Interpretation: - Higher values indicate good collective discrimination

Input Noise

Estimates the amount of noise in input features.

noise = cm.calculate_input_noise()

Interpretation: - Lower values indicate cleaner data - Higher values suggest noisy features

Example: Analyze All Feature Measures

from fairsample.complexity import ComplexityMeasures

cm = ComplexityMeasures(X, y)
feature_measures = cm.get_all_complexity_measures(measures='feature')

for measure, value in feature_measures.items():
    print(f"{measure}: {value:.4f}")