Separating Matrix for PCA. Is it correct?

[MultiD Support]

Dear Doctor Friends

Thank you very much for you helps in my previous questions. I have followed your advices in my univariable experiments and found good and interesting results. However, now, I would like center me in multivariable experiment. I don’t sure if in you previous reply (to one of my questions that I put in managing data/data manager) is implicit the answer for the following question, however, I want to be more accurate in my question.

The data that I got are the product of the relativizations among the three plant varieties. In other words I did two matrixes of 5 x 9, each matrix is for one tissue (leaves and roots), and the number nine is for three varieties; I am relativizing with the average of expression of the three plants varieties. Now, I want get PCA for the four genes for EACH plant variety. My question is if I can use this relativized data separately in the PCA. In this way my idea is separate the results of data-preprocessing in three matrixes for each variety.

This is one scheme about the procedure

Marix for Leaves (result after data pre-processing, the relativization was made with average)

_______________Gene 1 Gene2 Gene3 Gene4 GeneHousk
Leaves Variety1
Leaves Variety1
Leaves Variety1
Leaves Variety2
Leaves Variety2
Leaves Variety2
Leaves Variety3
Leaves Variety3
Leaves Variety3

My idea is take the results from data pre-processed of this matrix in three separate matrixes for PCA. Is it correct?

_______________Gene 1 Gene2 Gene3 Gene4 GeneHousk
Leaves Variety1
Leaves Variety1
Leaves Variety1

_______________Gene 1 Gene2 Gene3 Gene4 GeneHousk
Leaves Variety2
Leaves Variety2
Leaves Variety2

________________Gene 1 Gene2 Gene3 Gene4 GeneHousk
Leaves Variety3
Leaves Variety3
Leaves Variety3

//Morgan

[MultiD Support]

Hello Morgan,
What you are proposing is known as a multiway design. In essence you can analyze the data by PCA for leaves and roots separately. Probably you should start doing this. However, in such analysis the two PC1 vs PC2 scatter plots will not be comparable, because the principal components will be different for the root and the leaf data. To obtain common principal components the matrices should be augmented, which is the same as joint. We just published a study presenting this approach:

Multiway real-time PCR gene expression profiling in yeast Saccharomyces cerevisiae reveals altered transcriptional response of ADH-genes to glucose stimuli. Anders Ståhlberg, Karin Elbing, José Manuel Andrade-Garda, Björn Sjögreen, Amin Forootan, Mikael Kubista, BMC Genomics 2008, 9:170

The paper including the data is available for download from MultiD website. You should be able to analyze your data analogously.
Good luck!