Is Symbolic Dynamics the Most Efficient Data Compression Tool for Chaotic Time Series?

摘要

Symbolic dynamics represents each data point by a symbol. Typically, the set of symbols is small and less than a dozen. For instance in a chaotic time series, the symbol at time step might be S_n = (L)ow, if the state xn is less than a given threshold m_1. If the state xn is greater or equal to m1, the symbol Sn 5(H)igh. Table 1 shows a chaotic logistic map dynamics x_(n+1)= 4 x_n (1-x_n) and the corresponding symbol sequence. Figure 1 shows a plot of a chaotic logistic map time series and the corresponding symbols. Symbolic dynamics is a very course grained description of the dynamics and a data compression technique. For instance in Table 1, each original data value x_n can assume 10,000 different values, because it is a four digit decimal, whereas each symbol value can have only two different values: L and H. Therefore, the memory requirements to store the data are reduced by a factor of 5000 if they are stored as a symbol sequence.