Classification Approaches in Neuroscience: A Geometrical Point of View

Functional magnetic resonance images (fMRI) are brain scan images by MRI machine which are taken functionally cross the time. Several studies have investigated methods analyzing such images (or actually the drawn data from them) and is interestingly growing up. For examples models can predict the behaviours and actions of people based on their brain pattern, which can be useful in many fields. We do the classification study and prediction of fMRI data and we develop some approaches and some modifications on them which have not been used in such classification problems. The proposed approaches were assessed by comparing the classification error rates in a real fMRI data study. In addition, many programming codes for reading from fMRI scans and codes for using classification approaches are provided to manipulate fMRI data in practice. The codes, can be gathered later as a package in R. Also, there is a steadily growing interest in analyzing functional data which can often exploit Riemannian geometry. As a prototypical example of these kind of data, we will consider the functional data rising from an electroencephalography (EEG) signal in Brain-Computer interface (BCI) which translates the brain signals to the commands in the machine. It can be used for people with physical inability and movement problems or even in video games, which has had increased interest. To do that, a classification study on EEG signals has been proposed, while, the data in hand to be classified are matrices. A multiplicative algorithm (MPM), which is a fast and efficient algorithm, was developed to compute the power means for matrices which is the crucial step in our proposed approaches for classification. In addition, some simulation studies were used to examine the performance of MPM against existing algorithms. We will compare the behavior of different power means in terms of accuracy in our classifications, which had not been discovered previously. We will show that it is hard to have a guess to find the optimal power mean to have higher accuracy depending on the multivariate distribution of data available. Then, we also develop an approach, combination of power means, to have the benefit of all to improve the classification performance. All the codes related to the fast MPM algorithms and the codes for manipulating EEG signals in classification are written in MATLAB and can be developed later as a package