3-way analysis
(This feature is only available in GenEx Enterprise)
Theory
Recently, very powerful methods have been developed to compare sets of data. The most fundamental is called Procrustes rotation. It compares two data sets, which can e.g. be dose-response studies of a wild-type and a mutant. In essence, Procrustes rotation identifies underlying expression patterns and sample patterns, in this case dose response patterns, which can be thought of as modified principal components, and compares their importance in the two data sets. For example, the expression pattern and the dose response described by the first component may be more important in the mutant, while the expression and dose-response patterns of the second component are more important in the wild-type. Form the patterns, the underlying genes can be identified. 3-way decomposition is a generalization of Procrustes rotation for the comparison of larger number of data sets.
How to
Open the 3-way tab among the analysis tabs in the top of the main window, and press the 3-way button to load the analysis into the Control panel.
Here the number of trilinear components to be calculated can be selected. Select Auto to uses statistical indicators to choose the number of components. Press the Run button to see the results.
The data is analyzed by trilinear decomposition which assumes that there is a limited number (n) of underlying factorizable expression patterns.
3-way decomposition calculates three sets of responses: one for data columns, one for rows, and one for the variable that distinguishes the data files (e.g. strain, drug load, age, treatment). If the data set is not transposed, rows reflect changes over samples, columns are changes over genes, and the third graph shows variation over the data files in the order they were loaded into the Control panel. The order is available under the Data file tab in the Control panel, and also in the drop-down list in the top of the main window. The lines in the graphs represent the underlying components. The lines are colored so that one color represents the same underlying component in all three graphs.
Inspecting the underlying components, we see three main profiles: one represented by the blue and red curves that essentially overlap in both the Rows and Columns plot, the green and black curves that are quite similar in the Columns plot, and finally the yellow curve. Looking in the Data files plot, the blue and red curves show extreme values for strain 1 and 3, and we conclude from the Rows plot that a maximum response after 10 minutes is characteristic for these strains. We also find that genes 4, 10 and 12 are important in these strains by looking in the Columns plot.
The underlying assumption behind trilinear decomposition as described by the equation above, is usually not valid in a strict sense in expression profiling, and trilinear decomposition should be viewed as an approach to reveal patterns and correlations in the data similar to principal component analyses. In fact, an alternative to trilinear decomposition is augmented PCA. In augmented PCA the data sets are either catenated or laminated before PCA. The genes in the different sets can be distinguished by both color and symbol which is defined in the Data manager.
References
R.A Harshman (1970). Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multimodal factor analysis. UCLA working papers in phonetics, 16, pp 1-84.
J.D Carroll and J.J Chang (1970). Analysis of individual differences in multidimensional scaling via an n-way generalization of "Eckart-Young" decomposition. Psychometrika, 35:3, pp 283-319.
M. Kubista (1990). A New Method for the Analysis of Correlated Data Using Procrustes Rotation which is Suitable for Spectral Analysis. Chemometrics and intelligent laboratory systems, vol 7, pp 273-279.
A. Smilde, R. Bro and P. Geladi (2004). Multi-Way Analysis with Applications in the Chemical Sciences. John Wiley & Sons Ltd. (ISBN:9780471986911).