arXiv subjects
Publications and source records attributed to Ralph G. Andrzejak.
We demonstrate by means of a simple example that the arbitrariness of defining a phase from an aperiodic signal is not just an academic problem, but is more serious and fundamental. Decomposition of the signal into components with positive phase velocities is proposed as an old solution to this new problem.
Motivation: Clustering is a frequently used concept in variety of bioinformatical applications. We present a new method for hierarchical clustering of data called mutual information clustering (MIC) algorithm. It uses mutual information (MI) as a similarity measure and exploits its grouping property: The MI between three objects X, Y, and Z is equal to the sum of the MI between X and Y, plus the MI between Z and the combined object (XY). Results: We use this both in the Shannon (probabilistic) version of information theory, where the "objects" are probability distributions represented by random samples, and in the Kolmogorov (algorithmic) version, where the "objects" are symbol sequences. We apply our method to the construction of mammal phylogenetic trees from mitochondrial DNA sequences and we reconstruct the fetal ECG from the output of independent components analysis (ICA) applied to the ECG of a pregnant woman. Availability: The programs for estimation of MI and for clustering (probabilistic version) are available at http://www.fz-juelich.de/nic/cs/software
We present a method for hierarchical clustering of data called {\it mutual information clustering} (MIC) algorithm. It uses mutual information (MI) as a similarity measure and exploits its grouping property: The MI between three objects $X, Y,$ and $Z$ is equal to the sum of the MI between $X$ and $Y$, plus the MI between $Z$ and the combined object $(XY)$. We use this both in the Shannon (probabilistic) version of information theory and in the Kolmogorov (algorithmic) version. We apply our method to the construction of phylogenetic trees from mitochondrial DNA sequences and to the output of independent components analysis (ICA) as illustrated with the ECG of a pregnant woman.