# Analysis of symbolic sequences using the Jensen-Shannon divergence.

@article{Grosse2002AnalysisOS, title={Analysis of symbolic sequences using the Jensen-Shannon divergence.}, author={Ivo Grosse and Pedro Bernaola-Galv{\'a}n and Pedro Carpena and Ram{\'o}n Rom{\'a}n-Rold{\'a}n and Jos{\'e} L. Oliver and H. Eugene Stanley}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2002}, volume={65 4 Pt 1}, pages={ 041905 } }

We study statistical properties of the Jensen-Shannon divergence D, which quantifies the difference between probability distributions, and which has been widely applied to analyses of symbolic sequences. We present three interpretations of D in the framework of statistical physics, information theory, and mathematical statistics, and obtain approximations of the mean, the variance, and the probability distribution of D in random, uncorrelated sequences. We present a segmentation method based on…

## 266 Citations

### Generalization of Entropy Based Divergence Measures for Symbolic Sequence Analysis

- Computer SciencePloS one
- 2014

The results show that the JSD generalizations bring in more pronounced improvements when the sequences being compared are from phylogenetically proximal organisms, which are often difficult to distinguish because of their compositional similarity.

### On the similarity of symbol frequency distributions with heavy tails

- Computer ScienceArXiv
- 2015

It is found that frequent words change more slowly than less frequent words and that $\alpha=2$ provides the most robust measure to quantify language change, a complete $\alpha$-spectrum of measures.

### Probability distribution of intersymbol distances in random symbolic sequences: Applications to improving detection of keywords in texts and of amino acid clustering in proteins.

- MathematicsPhysical review. E
- 2016

The measure is applied to the problem of keyword detection in written texts and to study amino acid clustering in protein sequences to define a measure able to properly quantify the deviation from randomness of the symbol distribution, especially for short sequences and low symbol frequency.

### Monoparametric family of metrics derived from classical Jensen–Shannon divergence

- Computer Science
- 2018

### A method for continuous-range sequence analysis with Jensen-Shannon divergence

- Computer Science
- 2021

A method for the estimation of MI for this case, based on the kernel density approximation, is presented, which is of particular interest in the problems of sequence segmentation and set comparisons.

### Permutation Jensen-Shannon distance: A versatile and fast symbolic tool for complex time-series analysis.

- Medicine, PhysicsPhysical review. E
- 2022

The main motivation of this paper is to introduce the permutation Jensen-Shannon distance, a symbolic tool able to quantify the degree of similarity between two arbitrary time series. This quantifier…

### Information theory reveals large-scale synchronisation of statistical correlations in eukaryote genomes.

- BiologyGene
- 2005

### Generalized entropies and the similarity of texts

- Computer ScienceArXiv
- 2016

It is shown how generalized Gibbs–Shannon entropies can provide new insights on the statistical properties of texts and the size of the databases needed to obtain a reliable estimation of the divergences is estimated.

## References

SHOWING 1-10 OF 40 REFERENCES

### Elementary Symbolic Dynamics And Chaos In Dissipative Systems

- Art
- 1989

This book is a monograph on chaos in dissipative systems written for those working in the physical sciences. Emphasis is on symbolic description of the dynamics and various characteristics of the…

### An Introduction to Probability Theory and Its Applications

- Mathematics
- 1950

Thank you for reading an introduction to probability theory and its applications vol 2. As you may know, people have look numerous times for their favorite novels like this an introduction to…

### Numerical recipes in C

- Physics
- 2002

The Diskette v 2.06, 3.5''[1.44M] for IBM PC, PS/2 and compatibles [DOS] Reference Record created on 2004-09-07, modified on 2016-08-08.

### Limit Theorems in Change-Point Analysis

- Mathematics
- 1997

The Likelihood Approach. Nonparametric Methods. Linear Models. Dependent Observations. Appendix. References. Indexes.

### Physical Review E

- 1995