Chapter 3 Materials and methods
11. Principal Component Analysis (PCA)
Principal Component Analysis (PCA) is a general method which uses underlying mathematical principles to transforms a number of possibly correlated variables into a smaller number of variables called principal components. PCA is one of the most important applied methods in the linear algebra and perhaps its most common use is as the first step in trying to analyse large data sets.
In general terms, PCA uses a vector space transform to reduce the dimensionality of large data sets. Using mathematical projection, the original data set, which may have involved many variables, can often be interpreted in just a few variables (the principal components). It is therefore often the case that an examination of the reduced dimension data set will allow the user to spot trends, patterns and outliers in the data, far more easily than would have been possible without performing the principal component analysis [39].
The method uses different lineal combinations of the observable variables. The graphic representation of the scores and loadings in the space of the components allow to interpret the relation between the different variables and the different samples.
The methodology applied in this Thesis is described in the work of Polo C. [40].
11. 1 Number of principal component required
As a practical rules to decide how many principal components are required and how are excluded with the object to reduce the quantity of data, it should be considered:
- To include the principal components that explain the 90% of the total variance
- To exclude all the components which their associated eigenvalues are lower than 1.5 )
- To choose the required principal component so that all the variables are properly represented (the sum of the square of the correlation coefficients of each variable, explain at least a high percentage of its variance (around 1)
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Chapter 4
Results