Principal Component AnalysisΒΆ

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 \(N \times p\) None

Output Parameters

Parameter Type Constraint Description Remarks
\(\text{COEFF}\) \(\text{COEFF} \in \mathbb R^{p \times p}\) None 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.

Single Steps using the Algorithm

References

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