Factor analysis applied to Py-MS data

Attempting to find a smaller number of variables (dimensions) that retain most of the information in the original data matrix is very useful for a better and easier understanding of results. This approach of multivariate data treatment is known as factor analysis. 

There are several factor analysis procedures that result in a reduction in dimensionality. One such procedure simply eliminates some of the variables, which in Py-MS case would be the peaks for certain m/Zi values. To prevent the loss of valuable information in this procedure, an appropriate rule for this procedure must be established. Dedicated computer programs are available to perform such procedures, and commonly they have the following steps  

The above described procedure can be combined with moving points in a certain dimension to maintain the order of the distances. For example, if dij dm but dm, the coordinates Xij of a point j can be corrected (in dimension i ) to achieve dij dki. This type of technique was extensively used for processing Py-MS data for the classification of microorganisms and bioorganic samples [76, 76b], 

Another common method in factor analysis is principal component analysis. Principal component method can be considered a development of the previous procedure and commonly proceeds in a sequence of steps [74] as follows  

The first factor, defined as the linear combination of the original variables, obtained by the above described procedure will account for more of the variance in the data set than any other combination of variables. The second factor will be the linear combination of variables that accounts for most of the residual variance after the effect of the first factor has been removed from the data. Subsequent factors are defined similarly until all variance in the data is exhausted. In case the original variables are uncorrelated, the factor analysis solution requires as many factors as there are variables. However, in most data sets, many variables are more or less correlated and the variance in the data can be described by a smaller set of factors than there are variables. Therefore the data reduction is applicable. 

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