Analysis of Electroencephologram Data Using Time-Delay Embeddings to Reconstruct Phase Space

In this paper, the necessary embedding dimension for electroencephologram(EEG) data is calculated. The tools used include a 1981 theorem from Floris Takens, and a subsequent extension of that theorem in 1991 given by Casdagli, Sauer and Yorke. These theorems give a method of reconstructing the phase space of the original system up to diffeomorphism using time-delays. If d is the original dimension of the phase space, the theorems require that at least 2d + 1 time-delays are used in order to guarantee reconstruction of the phase space. This embedding dimension is calculated using false nearest neighbors.