### Abstract

Finding relations among gene expressions involves the definition of the similarity between experimental data. A simplest similarity measure is the Correlation Coefficient. It is able to identify linear dependences only; moreover, is sensitive to experimental errors. An alternative measure, the Shannon Mutual Information (MI), is free from the above mentioned weaknesses. However, the calculation of MI for continuous variables from the finite number of experimental points, N, involves an ambiguity arising when one divides the range of values of the continuous variable into boxes. Then the distribution of experimental points among the boxes (and, therefore, MI) depends on the box size. An algorithm for the calculation of MI for continuous variables is proposed. We find the optimum box sizes for a given N from the condition of minimum entropy variation with respect to the change of the box sizes. We have applied this technique to the gene expression dataset from Stanford, containing microarray data at 18 time points from yeast Saccharomyces cerevisiae cultures (Spellman et al.,). We calculated MI for all of the pairs of time points. The MI analysis allowed us to identify time patterns related to different biological processes in the cell.

Original language | English (US) |
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Title of host publication | AIP Conference Proceedings |

Pages | 25-30 |

Number of pages | 6 |

Volume | 854 |

DOIs | |

State | Published - 2006 |

Externally published | Yes |

Event | 9h Mexican Symposium on Medical Physics - Guadalajara, Jalisco, Mexico Duration: Mar 18 2006 → Mar 23 2006 |

### Other

Other | 9h Mexican Symposium on Medical Physics |
---|---|

Country | Mexico |

City | Guadalajara, Jalisco |

Period | 3/18/06 → 3/23/06 |

### Fingerprint

### Keywords

- Gene expression
- Mutual information

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*AIP Conference Proceedings*(Vol. 854, pp. 25-30) https://doi.org/10.1063/1.2356392

**Using mutual information to discover temporal patterns in gene expression data.** / Chumakov, Sergei; Ballesteros, Efren; Rodriguez Sanchez, Jorge E.; Chavez, Arturo; Zhang, Meizhuo; Pettitt, Bernard; Fofanov, Yuriy.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*AIP Conference Proceedings.*vol. 854, pp. 25-30, 9h Mexican Symposium on Medical Physics, Guadalajara, Jalisco, Mexico, 3/18/06. https://doi.org/10.1063/1.2356392

}

TY - GEN

T1 - Using mutual information to discover temporal patterns in gene expression data

AU - Chumakov, Sergei

AU - Ballesteros, Efren

AU - Rodriguez Sanchez, Jorge E.

AU - Chavez, Arturo

AU - Zhang, Meizhuo

AU - Pettitt, Bernard

AU - Fofanov, Yuriy

PY - 2006

Y1 - 2006

N2 - Finding relations among gene expressions involves the definition of the similarity between experimental data. A simplest similarity measure is the Correlation Coefficient. It is able to identify linear dependences only; moreover, is sensitive to experimental errors. An alternative measure, the Shannon Mutual Information (MI), is free from the above mentioned weaknesses. However, the calculation of MI for continuous variables from the finite number of experimental points, N, involves an ambiguity arising when one divides the range of values of the continuous variable into boxes. Then the distribution of experimental points among the boxes (and, therefore, MI) depends on the box size. An algorithm for the calculation of MI for continuous variables is proposed. We find the optimum box sizes for a given N from the condition of minimum entropy variation with respect to the change of the box sizes. We have applied this technique to the gene expression dataset from Stanford, containing microarray data at 18 time points from yeast Saccharomyces cerevisiae cultures (Spellman et al.,). We calculated MI for all of the pairs of time points. The MI analysis allowed us to identify time patterns related to different biological processes in the cell.

AB - Finding relations among gene expressions involves the definition of the similarity between experimental data. A simplest similarity measure is the Correlation Coefficient. It is able to identify linear dependences only; moreover, is sensitive to experimental errors. An alternative measure, the Shannon Mutual Information (MI), is free from the above mentioned weaknesses. However, the calculation of MI for continuous variables from the finite number of experimental points, N, involves an ambiguity arising when one divides the range of values of the continuous variable into boxes. Then the distribution of experimental points among the boxes (and, therefore, MI) depends on the box size. An algorithm for the calculation of MI for continuous variables is proposed. We find the optimum box sizes for a given N from the condition of minimum entropy variation with respect to the change of the box sizes. We have applied this technique to the gene expression dataset from Stanford, containing microarray data at 18 time points from yeast Saccharomyces cerevisiae cultures (Spellman et al.,). We calculated MI for all of the pairs of time points. The MI analysis allowed us to identify time patterns related to different biological processes in the cell.

KW - Gene expression

KW - Mutual information

UR - http://www.scopus.com/inward/record.url?scp=33846527894&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846527894&partnerID=8YFLogxK

U2 - 10.1063/1.2356392

DO - 10.1063/1.2356392

M3 - Conference contribution

VL - 854

SP - 25

EP - 30

BT - AIP Conference Proceedings

ER -