Modeling and Multivariate Methods - SAS

Chapter 19 Analyzing Principal Components and Reducing Dimensionality 483
Principal Components
Principal Components
If you want to see the arrangement of points across many correlated variables, you can use principal
component analysis to show the most prominent directions of the high-dimensional data. Using principal
component analysis reduces the dimensionality of a set of data. Principal components is a way to picture the
structure of the data as completely as possible by using as few variables as possible.
For n original variables, n principal components are formed as follows:
• The first principal component is the linear combination of the standardized original variables that has
the greatest possible variance.
• Each subsequent principal component is the linear combination of the variables that has the greatest
possible variance and is uncorrelated with all previously defined components.
Each principal component is calculated by taking a linear combination of an eigenvector of the correlation
matrix (or covariance matrix or SSCP matrix) with a variable. The eigenvalues show the variance of each
component.
Principal components representation is important in visualizing multivariate data by reducing it to
dimensionalities that are graphable.
Launch the Platform
Select Analyze > Multivariate Methods > Principal Components to launch the platform. JMP presents
you with a dialog box to specify the variables involved in the analysis. In this example, we use all the
continuous variables from the Solubility.jmp data set.
The Estimation Method list provides different methods for calculating the correlations. For details on the
methods, see the “Correlations and Multivariate Techniques” chapter on page 441.
Principal components analysis is also available in the Multivariate and Scatterplot 3D platforms.