This paper aims at assessing spino-cerebellar type 2 ataxia by classifying electrooculography records into registers corresponding to healthy, presymptomatic and ill individuals. The primary used technique is the convolutional neural network applied to the time series of eye movements, called saccades. The problem is exceptionally hard, though, because the recorded saccadic movements for presymptomatic cases often do not substantially differ from those of healthy individuals. Precisely this distinction is of the utmost clinical importance, since early intervention on presymptomatic patients can ameliorate symptoms or at least slow their progression. Yet, each register contains a number of saccades that, although not consistent with the current label, have not been considered indicative of another class by the examining physicians. As a consequence, an unsupervised learning mechanism may be more suitable to handle this form of misclassification. Thus, our proposal introduces the k-means approach and the SOM method, as complementary techniques to analyse the time series. The three techniques operating in tandem lead to a well performing solution to this diagnosis problem.