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

✍ Scribed by WENTIAN LI; YANING YANG

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 264 KB
• Volume: 219
• Category: Article
• ISSN: 0022-5193
• DOI: 10.1006/jtbi.2002.3145

✦ Synopsis

Using a measure of how differentially expressed a gene is in two biochemically/phenotypically different conditions, we can rank all genes in a microarray dataset. We have shown that the falling-off of this measure (normalized maximum likelihood in a classification model such as logistic regression) as a function of the rank is typically a power-law function. This power-law function in other similar ranked plots are known as the Zipf's law, observed in many natural and social phenomena. The presence of this power-law function prevents an intrinsic cutoff point between the "important" genes and "irrelevant" genes. We have shown that similar power-law functions are also present in permuted dataset, and provide an explanation from the well-known chi(2) distribution of likelihood ratios. We discuss the implication of this Zipf's law on gene selection in a microarray data analysis, as well as other characterizations of the ranked likelihood plots such as the rate of fall-off of the likelihood.