Factor Analysis Causes of Data Structures

As a rule, the properties of objects are determined neither by only one feature nor by all the features equally. Instead the measured parameters influence variously the properties in a complex way because the variables are usually not independent from each other but are correlated to a certain degree. 

The goal of factor analysis (FA) and their essential variant principal component analysis (PCA) is to describe the structure of a data set by means of new uncorrelated variables, so-called common factors or principal components. These factors characterize frequently underlying real effects which can be interpreted in a meaningful way. 

The principle of FA and PCA consists in an orthogonal decomposition of the original n x m data matrix X into a product of two matrixes, F (nxk matrix of factor scores, common factors) and L (kxm matrix of factor loadings) 

This is the complete factor solution which admittedly contains uncorrelated variables but all the k factors are extracted completely and no reduction 

By means of this reduction of dimensions the information in the form of variance is subdivided into essential contributions (common and specific variance) on one hand and residual variance on the other  

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