We demonstrate that projecting data points into hyperplanes is good strategy for general-purpose kernel design. We used three different hyperplanes generation schemes, random, convex hull and α-shape, and evaluated the results on two synthetic and three well known image-based datasets. The results showed considerable improvement in the classification performance in almost all scenarios, corroborating the claim that such an approach can be used as a general-purpose kernel transformation. Also, we discuss some connection with Convolutional Neural Networks and how such an approach could be used to understand such networks better.

For a long time, EEG has been used for diagnosing mental disorders, for the EEG is an easy technique to acquire such signals. Time series methods are used to study the data since EEG records can be seem as time series. Such methods can be divided into two categories, stochastic and deterministic. Several methods in both categories require the signal to be stationary. Although many works acknowledge the importance of stationarity, they do not check it in the data, or discuss why this is a valid assumption. The lack of stationarity in methods that require it can twist the meaning of the results, so this is an important property to check. Since the literature has not definitively answered the question of how to determine the stationarity of a signal, we investigated how two different approaches handle it. The stochastic approach performs a hypothesis test based on the Chi-Squared statistic to check if two consecutive windows have the same probability distribution function. On the other hand, the deterministic one makes use of dynamical closeness computed over the reconstructed phase space on each window of the signal. Based on this measure, it infers the underlying dynamics of each window and tries to find recurrence in these dynamics, clustering the similar windows together. Three different datasets were used, two synthetic, from a Gaussian distribution, and from the Lorenz system, and one real epileptic EEG signal dataset. The results showed a sensitivity in the window size parameter, and an upper limit for the embedding dimension. It was possible to narrow the range of the parameters. In the stochastic scenario, significance level should not be too stringent, and window size have displayed some sensitivity.