An important problem in physics concerns the analysis of audio time series generated by transduced acoustic phenomena. Here, we develop a new method to quantify the scaling properties of the local variance of nonstationary time series. We apply this technique to analyze audio signals obtained from selected genres of music. We find quantitative differences in the correlation properties of high art music, popular music, and dance music. We discuss the relevance of these objective findings in relation to the subjective experience of music.

Abstract-This paper develops a new understanding of mean shift algorithms from an information theoretic perspective. We show that the Gaussian Blurring Mean Shift (GBMS) directly minimizes the Renyi's quadratic entropy of the dataset and hence is unstable by definition. Further, its stable counterpart, the Gaussian Mean Shift (GMS), minimizes the Renyi's "cross" entropy where the local stationary solutions are modes of the dataset. By doing so, we aptly answer the question "What does mean shift algorithms optimize?", thus highlighting naturally the properties of these algorithms. A consequence of this new understanding is the superior performance of GMS over GBMS which we show in a wide variety of applications ranging from mode finding to clustering and image segmentation.Index Terms-Mean shift, information theoretic learning, Renyi's entropy.

Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher-order statistical moments in nonGaussian noise environments.Although correntropy has been used with complex data, no theoretical study was pursued to elucidate its properties, nor how to best use it for optimization . This paper presents a probabilistic interpretation for correntropy using complex-valued data called complex correntropy. A recursive solution for the maximum complex correntropy criterion (MCCC) is introduced based on a fixedpoint solution. This technique is applied to a simple system identification case study, and the results demonstrate prominent advantages when compared to the complex recursive least squares (RLS) algorithm. By using such probabilistic interpretation, correntropy can be applied to solve several problems involving complex data in a more straightforward way.

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