Zipf's Law in Importance of Genes for Cancer Classification Using Microarray Data

Abstract

Microarray data consists of mRNA expression levels of thousands of genes under certain conditions. A difference in the expression level of a gene at two different conditions/phenotypes, such as cancerous versus non-cancerous, one subtype of cancer versus another, before versus after a drug treatment, is indicative of the relevance of that gene to the difference of the high-level phenotype. Each gene can be ranked by its ability to distinguish the two conditions. We study how the single-gene classification ability decreases with its rank (a Zipf's plot). Power-law function in the Zipf's plot is observed for the four microarray datasets obtained from various cancer studies. This power-law behavior in the Zipf's plot is reminiscent of similar power-law curves in other natural and social phenomena (Zipf's law). However, due to our choice of the measure of importance in classification ability, i.e., the maximized likelihood in a logistic regression, the exponent of the power-law function is a function of the sample size, instead of a fixed value close to 1 for a typical example of Zipf's law. The presence of this power-law behavior is important for deciding the number of genes to be used for a discriminant microarray data analysis.

11 pages, 5 figures. submitted

Cited by in corpus (9)

• Distance Is Not Dead: Social Interaction and Geographical Distance in the Internet Era
• A joint text mining-rank size investigation of the rhetoric structures of the US Presidents' speeches
• Universality and Shannon entropy of codon usage
• Extreme Value Distribution Based Gene Selection Criteria for Discriminant Microarray Data Analysis Using Logistic Regression
• Statistical Outliers and Dragon-Kings as Bose-Condensed Droplets
• Generalized (m,k)-Zipf law for fractional Brownian motion-like time series with or without effect of an additional linear trend
• A Constructive Approach to Gene Expression Dynamics
• Earthquakes economic costs through rank-size laws
• A stochastic approach to multi-gene expression dynamics