Principal Component Analysis

Global Algorithm - Multi-Dimensional algorithm

Principal Component Analysis algorithm is a well-known statistical procedure that can identify patterns in data and express the data using a small number of principal components.

For details refer to the online document A tutorial on Principal Components Analysis.

Input Parameters

Parameter	Type	Constraint	Description	Remarks
\(Y\)	\(Y \in \mathbb R^{N \times p}\)	\(N \in \mathbb{N}, N \geq p\)	Normalized input data of size \(N \times p\)

Output Parameters

Parameter	Type	Constraint	Description	Remarks
\(\text{COEFF}\)	\(\text{COEFF} \in \mathbb R^{p \times p}\)		The computed principal component coefficients	The columns are summarized by following the decreasing order of component variance. Each column contains coefficients for one principal component.

Tool Support

• Maple

  For details refer to the online documentation of the function g03aac(nag_mv_prin_comp).

• Matlab

  For details refer to the online documentation of the function ‘princomp’.

Single Steps using the Algorithm

• Data Reduction with Principal Component Analysis (PCA)

References

• I.T. Jolliffe, Principal Component Analysis, 2nd edition, Springer, 2002.