Explain Principle Component Analysis (PCA) in data analysis.

• PCA is a method used to reduce number of variables in dataset by extracting important one from a large dataset.

• It reduces the dimension of our data with the aim of retaining as much information as possible.

• In other words, this method combines highly correlated variables together to form a smaller number of an artificial set of variables which is called principal components (PC) that account for most variance in the data.

• A principal component can be defined as a linear combination of optimally-weighted observed variables.

• The first principal component retains maximum variation that was present in the original components.

• The principal components are the eigenvectors of a covariance matrix, and hence they are orthogonal.

• The output of PCA are these principal components, the number of which is less than or equal to the number of original variables.

• The PCs possess some useful properties which are listed below :-

  • The PCs are essentially the linear combinations of the original variables and the weights vector.

  • The PCs are orthogonal.

  • The variation present in the PC decrease as we move from the 1st PC to the last one.