To constrain the factor model we used Linear Discriminant Analysis, a technique used to classify a set of observa tions into categories. In particu lar, in the following we will describe the methodology and selleck bio the results obtained from applying FA to mRNA and miRNA data simultaneously, with the goal to identify information that is not obvious when the analysis is performed on the 2 datasets separately, or when using other approaches. In particular, the identification of a set of co localized miRNAs with possible relevance for the molecular description of gliosarcomas, appears to emerge from this analysis only, showing the potential FA in the identification of emergent properties. Besides LDA, other classifiers were also tested and performances are listed in Table S9 of the Additional file 1.

We only briefly mention here that most of the performances are identical for all the classifiers, and only for the Glioblastomas discrimination LDA shows slightly more accuracy. These results indicate that the clas sification analysis is robust and gives stable results inde pendently from the choice of the classification algorithm. Factor analysis proceeds from a matrix of pair wise corre lations to extract a small number of factors that describe the major patterns of common covariation. More formally, the common factor model is based on the equation D LF E, where D are the observed variables, L are the com mon factors, F are the coefficients or scores of the factors and E are the unique factors, under the assumptions that the unique factors are uncorrelated whith each other and that F and E are independent.

Since only common varia tion is analyzed, these individual factors describe the latent structure underlying the major patterns of molecular cov ariation. The sign and magnitude of the factors coefficients reflect the extent and direction of the correlation between each variable and individual factor and describe the rela tive contribution of each variable to a particular pattern of multivariate changes. FA derives a set of factor scores that gives the relative location of each item in the reduced latent variable subspace. The resultant factors, coefficients and scores are interpreted in light of biological knowledge about the specific data under study. FA can define a biolo gical model about the underlying nature of molecular cov ariation.

These models are evaluated both biologically and statistically and subsequently used to explain the structure and dynamics of complex biological systems. FA and Principal Component Analysis involve several of the same statistical components and are both useful for data reduction. Therefore few words on the rationale for Drug_discovery choosing FA instead of PCA are necessary. PCA is an exact mathematical method that returns a single solution where each component is ortho gonal and represents an element of variance in the sam ples.