Statistical and Machine Learning models for Neurosciences

This thesis addresses several problems encountered in the field of statistical and machine learning methods for data analysis in neurosciences. The thesis is divided into three parts. The first part of the thesis is related to classification tree models. In the research field of polarization measures, a new polarization measure is defined. The function is incorporated in the decision tree algorithm as a splitting function in order to tackle some weaknesses of classical impurity measures. The new algorithm is called Polarized Classification Tree model. The model is tested on simulated and real data sets and compared with decision tree models where the classical impurity measures are deployed. In the second part of the thesis a new index for assessing and selecting the best model in a classification task when the target variable is ordinal is developed. The index proposed is compared to the traditional measures on simulated data sets and it is applied in a real case study related to Attenuated Psychosis Syndrome. The third part covers the topic of smoothing methods for quaternion time series data in the context of motion data classification. Different proper methods to smoothing time series in quaternion algebra are reviewed and a new method is proposed. The new method is compared with a method proposed in the literature in terms of classification performances on a real data set and five data sets obtained introducing different degrees of noise. The results confirmed the hypothesis made on the basis of the theoretical information available from the two methods, i.e. the logarithm is smoother and generally provides better results than the existing method in terms of classification performances.