Multifractional Gaussian Process Based on Self-similarity Modelling for MS Subgroups' Clustering with Fuzzy C-Means

Abstract

Multifractal analysis is a beneficial way to systematically characterize the heterogeneous nature of both theoretical and experimental patterns of fractal. Multifractal analysis tackles the singularity structure of functions or signals locally and globally. While Holder exponent at each point provides the local information, the global information is attained by characterization of the statistical or geometrical distribution of Holder exponents occurring, referred to as multifractal spectrum. This analysis is time-saving while dealing with irregular signals; hence, such analysis is used extensively. Multiple Sclerosis (MS), is an auto-immune disease that is chronic and characterized by the damage to the Central Nervous System (CNS), is a neurological disorder exhibiting dissimilar and irregular attributes varying among patients. In our study, the MS dataset consists of the Expanded Disability Status Scale (EDSS) scores and Magnetic Resonance Imaging (MRI) (taken in different years) of patients diagnosed with MS subgroups (relapsing remitting MS (RRMS), secondary progressive MS (SPMS) and primary progressive MS (PPMS)) while healthy individuals constitute the control group. This study aims to identify similar attributes in homogeneous MS clusters and dissimilar attributes in different MS subgroup clusters. Thus, it has been aimed to demonstrate the applicability and accuracy of the proposed method based on such cluster formation. Within this framework, the approach we propose follows these steps for the classification of the MS dataset. Firstly, Multifractal denoising with Gaussian process is employed for identifying the critical and significant self-similar attributes through the removal of MS dataset noise, by which, mFd MS dataset is generated. As another step, Fuzzy C-means algorithm is applied to the MS dataset for the classification purposes of both datasets. Based on the experimental results derived within the scheme of the applicable and efficient proposed method, it is shown that mFd MS dataset yielded a higher accuracy rate since the critical and significant self-similar attributes were identified in the process. This study can provide future direction in different fields such as medicine, natural sciences and engineering as a result of the model proposed and the application of alternative mathematical models. As obtained based on the model, the experimental results of the study confirm the efficiency, reliability and applicability of the proposed method. Thus, it is hoped that the derived results based on the thorough analyses and algorithmic applications will be assisting in terms of guidance for the related studies in the future.