Chapter 14 - Shannon entropy-based complexity quantification of nonlinear stochastic process: diagnostic and predictive spatiotemporal uncertainty of multiple sclerosis subgroups

Abstract

Complex dynamic characteristics of systems based on entropy entail a detailed specification and synthesis of the intricate elements, as the system gets more and more complex. The growth of complexity, in more nonlinear and complicated instances, evolves with increasing information and entropy in a monotonous way. Multilevel analyses are to be employed for the development of a quantitative understanding of complexity, which is among the information required for the description of a particular system. In that regard, to detect and quantify nonlinearity that is in question in a signal is realized through methods that employ complexity and entropy. Brain as a complex system, formed out of neurons and molecules formed out of atoms, with many elements being at interplay with one another requires a sophisticated analysis since uncertainty prevails. Multiple sclerosis (MS) is a neurodegenerative autoimmune disease affecting the central nervous system, particularly the brain, optic nerve, and spinal cord, within this complex system. The timely diagnosis of MS and prediction of the long-term course of disability is a highly complex process, necessitating a lot of time and effort. Robust model-driven decision-making is critical for the prognosis and diagnosis of MS whose course varies from individual to individual, displaying transient properties and a high level of uncertainty. Accordingly, the aim of this chapter is to facilitate the accurate classification of three MS subgroups (relapsing remitting MS, secondary progressive MS, primary progressive MS) as well as healthy individuals. For this particular purpose in our proposed method, the following steps were performed: (1) an entropy-based feature selection method (Shannon entropy and minimum redundancy maximum relevance [MRMR]) and linear transformation methods (principal component analysis [PCA] and linear discriminant analysis [LDA]) were administered on the MS dataset. (2) Based on the MS dataset, four new datasets (Shannon entropy-MS dataset, MRMR-MS dataset, PCA-MS dataset, and LDA-MS dataset) with the new significant attributes were obtained. Each new dataset obtained was addressed as input for the training procedure of k-nearest neighbor (k-NN) and decision tree algorithms. (3) The accuracy rates for the classification of the MS subgroups as obtained from the application of k-NN and decision tree algorithms on the new datasets obtained from (1) and (2) were compared. The optimized experimental results of our study demonstrate that Shannon entropy, as a distinctive entropy method, is proved to be higher in terms of accuracy compared with the other feature selection methods. Consequently, the proposed model of ours in the study manifests the reliability, accuracy and applicability of the integrated methods employed. Thus, our study aims at pointing out a new perspective for critical decision-making and toward manageable tracking in medicine and relevant fields that have to deal with the complex dynamic systems where uncertainty and heterogeneity prevail.