Zipf定律在基因对癌症分类的重要性中的应用
Zipf's Law in Importance of Genes for Cancer Classification Using Microarray Data
摘要：
微阵列数据由特定条件下数千个基因的mRNA表达水平组成。基因在两种不同状况/表型下的表达水平的差异，例如癌性与非癌性、一种癌症亚型与另一种癌症亚型、药物治疗之前与之后，指示该基因与高水平表型的差异的相关性。每个基因可以根据其区分这两种情况的能力进行排名。我们研究了单基因分类能力如何随其等级而降低（Zipf图）。从各种癌症研究中获得的四个微阵列数据集在Zipf图中观察到幂律函数。齐普夫图中的这种幂律行为让人想起其他自然和社会现象中类似的幂律曲线（齐普夫定律）。然而，由于我们选择了分类能力的重要性度量，即，在逻辑回归中的最大似然，幂律函数的指数是样本大小的函数，而不是Zipf定律的典型示例中接近1的固定值。这种幂律行为的存在对于决定用于判别式微阵列数据分析的基因数量是重要的。
英文摘要：
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.
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