FeMIFuzzy (Federated Multiple Imputation Fuzzy Clustering) Documentation

🔍 Overview

FeMIFuzzy is a federated fuzzy clustering algorithm designed for incomplete longitudinal behavioral data. It combines multiple imputation, Sammon mapping (via dimensionality reduction), and fuzzy c-means clustering, allowing decentralized learning from incomplete data.

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⚙️ Class Definition

Class Name: FeMIFuzzy

class FeMIFuzzy:
    def __init__(self, n_clusters: int = 3, max_iter: int = 100, m: float = 2.7, tol: float = 1e-4):
        self.n_clusters = n_clusters
        self.max_iter = max_iter
        self.m = m
        self.tol = tol

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📋 Parameters

Parameter	Type	Default	Description
n_clusters	int	3	Number of fuzzy clusters
max_iter	int	100	Maximum number of iterations
m	float	2.7	Fuzziness degree (entropy-like parameter)
tol	float	1e-4	Convergence threshold for membership updates

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🚀 Usage Examples

from soft_clustering._femifuzzy import FeMIFuzzy
import numpy as np

X = np.random.rand(100, 5)
X[X < 0.1] = np.nan  # Simulate missing data

model = FeMIFuzzy(n_clusters=3)
U = model.fit_predict(X)

print("Membership matrix shape:", U.shape)

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📥 Input / 📤 Output

• Input to fit_predict(X):

  • X (np.ndarray): Input matrix with shape (N x D), possibly containing NaN values

• Returns:

  • U (np.ndarray): Membership matrix (N x C)

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🛠️ Methods

• fit_predict(X): Runs the complete FeMIFuzzy pipeline:

  • Mean imputation of missing data

  • PCA (as a surrogate to Sammon mapping)

  • Iterative fuzzy c-means with convergence criteria

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📝 Implementation Notes

• Imputation uses mean strategy per feature

• PCA replaces Sammon mapping for simplicity

• Handles missing values before clustering

• Memberships are normalized row-wise

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📚 Reference

This implementation is based on:
“Federated Fuzzy Clustering for Decentralized Incomplete Longitudinal Behavioral Data”
by Mohammad Mahdavi, Raheleh Salari, and Jie Xu.