quantile normalization 原理：
A quick illustration of such normalizing on a very small dataset:
Arrays 1 to 3, genes A to D
A 5 4 3 B 2 1 4 C 3 4 6 D 4 2 8
For each column determine a rank from lowest to highest and assign number i-iv
A iv iii i B i i ii C ii iii iii D iii ii iv
These rank values are set aside to use later. Go back to the first set of data. Rearrange that first set of column values so each column is in order going lowest to highest value. (First column consists of 5,2,3,4. This is rearranged to 2,3,4,5. Second Column 4,1,4,2 is rearranged to 1,2,4,4, and column 3 consisting of 3,4,6,8 stays the same because it is already in order from lowest to highest value.) The result is:
A 5 4 3 becomes A 2 1 3 B 2 1 4 becomes B 3 2 4 C 3 4 6 becomes C 4 4 6 D 4 2 8 becomes D 5 4 8
Now find the mean for each row to determine the ranks
A (2 1 3)/3 = 2.00 = rank i B (3 2 4)/3 = 3.00 = rank ii C (4 4 6)/3 = 4.67 = rank iii D (5 4 8)/3 = 5.67 = rank iv
Now take the ranking order and substitute in new values
A iv iii i B i i ii C ii iii iii D iii ii iv
becomes:
A 5.67 4.67 2.00 B 2.00 2.00 3.00 C 3.00 4.67 4.67 D 4.67 3.00 5.67
R實現方法： 實質上是針對array數據進行設置的，要求數據每一列是一個array，每一行是一個探針
針對分位數標准化，R中有多個包進行處理 1：affy 2: preprocessCore 其中preprocessCore 中的normalize.quantiles使用非常方便
> a<-matrix(1:6,3,2)
> a
[,1] [,2]
[1,] 1 4
[2,] 2 5
[3,] 3 6
> library(preprocessCore)
> b=normalize.quantiles(a)
> b
[,1] [,2]
[1,] 2.5 2.5
[2,] 3.5 3.5
[3,] 4.5 4.5