Approach to block entropy modeling and optimization

Abstract

This paper introduces an approach to the block entropy modeling of stationary signals. The block entropies, constructed according to the Tsallis generalized formalism, are optimized with respect to the block length and the partition of the signal value domain, to appropriately measure the complexity of the signal. The optimal partition is known to be addressed by the Euclidean mean, expressing the signal optimized level based on the least squares fitting method. However, this is valid only for random signal values following a symmetric distribution. Alternatively, and within the framework of fitting methods based on non-Euclidean metrics, we implement the q th order means to consistently describe the optimal signal level, and to clearly present the difference between the optimal signal level and the optimal partition. The signal optimization is utilized for detecting the distribution modes, developing a technique, being resistant to the noise corruption, that can be useful for detecting the optimal partition. Moreover, the mechanisms that affect the optimal partition are identified and thoroughly investigated. We first consider random signals following an arbitrary distribution, where the block entropy modeling reveals that the optimal partition is located at the median. Thereafter, we consider persistent signals, specifying a degree of determinism, where the optimal partition is found to be driven far from the median and close to the persistent mode. The existence of persistent modes of small hitting time is the key point of this dissertation, highlighting their implications on the block entropy modeling. Finally, efforts towards block entropy modeling of non-stationary signals are discussed.