The nonlinear correlation character of gene expression data on Alzheimer´s disease and hierarchy clustering of co-regulated gene

Alzheimer´s disease (AD) is the most common form of dementia. Possibly it is caused by some genes associated with co-regulation genes. With the development of DNA microarray technique, the identification of candidate co-regulated genes via computation becomes feasible. Co-regulated genes share similar biological character so that their expression levels are similar possibly. In this paper, the correlation on different variables of the AD expression data downloaded from [1], is analyzed using Principal Component Analysis (PCA), the following three features are observed: 1. Linear correlation is strong and nonlinear is weak. 2. Co-regulation information of genes is mapped into the compactness of clustering. 3. Nonlinear correlation causes the hierarchy of compact clustering. According these features, a hierarchical sorting of expression data is proposed, and its elementary framework is introduced in this paper.