分位数标准化

 

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实现方法：
实质上是针对array数据进行设置的，要求数据每一列是一个array，每一行是一个探针

针对分位数标准化，R中有多个包进行处理
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