Technical Paper
New Trivial Principal Component Method: System Modeling
2015-04-14
2015-01-0448
Principal Component Analysis (PCA) is a powerful statistical technique used for understanding variation in the observed data and decomposing variation along eigenvectors, known as Principal Components (PCs), by considering variance-covariance structure of the data. Traditionally, eigenvectors that contain most of the variation or information are selected to reduce variables in data reduction. Eigenvalues of low magnitude are considered to be noise and often, not included in the dataset to accomplish dimensional reduction. Analogously, in Principal Component Regression (PCR), PCs with large eigenvalues are selected without considering correlation between the source variables and the dependent response. This inherent deficiency may lead to inferior regression modelling. While addressing this issue, an alternative to PCR is developed and proposed in this paper. In this method, a principal component associated with zero eigenvalue is termed Trivial Principal Component (TPC).