Exploiting Spatial Information to Enhance DTI Segmentations via Spatial Fuzzy c-Means with Covariance Matrix Data and Non-Euclidean Metrics

A diffusion tensor models the covariance of the Brownian motion of water at a voxel and is required to be symmetric and positive semi-definite. Therefore, image processing approaches, designed for linear entities, are not effective for diffusion tensor data manipulation, and the existence of artefacts in diffusion tensor imaging acquisition makes diffusion tensor data segmentation even more challenging. In this study, we develop a spatial fuzzy c-means clustering method for diffusion tensor data that effectively segments diffusion tensor images by accounting for the noise, partial voluming, magnetic field inhomogeneity, and other imaging artefacts. To retain the symmetry and positive semi-definiteness of diffusion tensors, the log and root Euclidean metrics are used to estimate the mean diffusion tensor for each cluster. The method exploits spatial contextual information and provides uncertainty information in segmentation decisions by calculating the membership values for assigning a diffusion tensor at one voxel to different clusters. A regularisation model that allows the user to integrate their prior knowledge into the segmentation scheme or to highlight and segment local structures is also proposed. Experiments on simulated images and real brain datasets from healthy and Spinocerebellar ataxia 2 subjects showed that the new method was more effective than conventional segmentation methods.

Neuroclusterization method of stabilometric data

Stabilometry is a modern method for assessing the functional state of a person by the ability to maintain a stable balance of an upright posture. Technically, the implementation of the stabilometry method consists in measuring, with the help of specialized devices, the values that make up the support reaction, with the subsequent determination, according to these measurements, of the coordinates of the center of body pressure on the support. The nature of the migrations of the center of pressure during the stabilometric study is a source of information about the features of the processes of postural regulation. At the same time, up to the present time, there is a problem of the correct interpretation of the results of stabilometry. The adequacy of the conclusions is largely determined by the human factor, i.e. qualification of a specialist analyzing stabilometry data. Thus, in our opinion, the task of objectifying the assessment of stabilometry results is urgent. The aim of this work is to study the possibility of applying the neurocluster method using self-organizing neural networks to objectify the analysis of stabilometry data. The authors proposed a technique for analyzing the structure of individual and group stabilometric data by clustering them using selforganizing Kohonen neural maps with Euclidean metrics. Neuroclusterization of stabilometric data allows in automatic mode (without human intervention) to identify the type of group of subjects corresponding to the norm or pathology, various types of pathologies, as well as individual biometric characteristics of the subjects. The subsequent analysis of the individual characteristics of the data of the subjects, grouped in this way, makes it possible to detect deviations indicating the presence of abnormalities or the formation of various pathological conditions, which can be useful for the early diagnosis of diseases.

CONVERGENCE/DIVERGENCE ANALYSIS AND DIFFERENTIATION IN MACROECONOMIC VARIABLES IN THE DEVELOPMENT OF THE RUSSIAN FEDERATION

The purpose of this paper is to analyze the economic development and the diversification of the individual regions of the Russian Federation (RF) on the basis of taxonomic indices and a convergence/divergence analysis of five macroeconomic variables, namely registered unemployment rate, investment per capita, gross domestic product (GDP) per capita, wages, and the number of organizations conducting research and development (R&D) per million inhabitants, for the period between 2000 and 2012 (the period was chosen due to lack of data for years 2014, 2015 and 2016 for few regions). The study covers 79 regions, and the data used for the analyses comes from the Russian Statistical. The principal method of analysis is the taxonomic index based on Euclidean metrics. The spatial differentiation in the development of RF regions demonstrates the specific character of the individual regions of Russia. The analysis made leads to the conclusion that the most developed regions in terms of the analyzed variables are of industrial and mining character, while the least developed ones are agricultural in character. The structure of this paper is as follows: the spatial differentiation of macroeconomic variables in RF regions, registered unemployment rate, per capita investment, per capita GDP, wages, and number of organizations conducting R&D activities per million inhabitants is discussed in section 2; the definition of a taxonomic index based on Euclidean metrics is presented in section 3; the analysis of the diversified development of RF regions based on taxonomic indicators is given in section 4, a preliminary convergence/divergence analysis is presented in section 5, while section 6 provides a key conclusions.