Alpha-cut implemented fuzzy clustering algorithms and switching regressions

Area of Science:

• Data Science
• Machine Learning
• Statistics

Background:

• Standard fuzzy c-means (FCM) clustering struggles with noise and outliers, as data points rarely achieve full membership (value of 1).
• FCM's limitations persist when embedded in switching regressions (FCRs), hindering accurate clustering in real-world, noisy datasets.

Purpose of the Study:

• To introduce FCMalpha, an enhanced fuzzy clustering algorithm that addresses FCM's drawbacks by enabling full data point membership.
• To develop FCRalpha, an improved switching regression model incorporating FCMalpha for superior performance in noisy environments.

Main Methods:

• Proposed FCMalpha algorithm utilizes alpha-cuts to form distinct cluster cores where data points have a membership value of 1.
• Investigated the role of the fuzziness index 'm' in both FCM and FCMalpha, analyzing its impact on clustering robustness.
• Integrated FCMalpha into switching regressions to create FCRalpha, comparing its performance against traditional FCR.

Main Results:

• FCMalpha successfully creates cluster cores, resolving the issue of incomplete data point membership inherent in FCM.
• FCMalpha demonstrates increased robustness to noise and outliers, especially with a higher fuzziness index 'm'.
• The proposed FCRalpha model significantly outperforms FCR in handling noisy data, showcasing improved clustering accuracy and reliability.

Conclusions:

• FCMalpha offers a robust solution for fuzzy clustering, effectively handling noise and outliers by establishing clear cluster cores.
• FCRalpha provides a more reliable approach for switching regression tasks in the presence of data imperfections.
• The developed methods offer a significant advancement in clustering and regression analysis for complex, real-world datasets.