Statistical Monitoring of Complex Multivariate Processes: With Applications in Industrial Process Control

Chapter 9

Principal component analysis

This chapter introduces the PCA algorithm, including a discussion showing that the computed score and loading vectors maximize their contribution to the column and row space of a data matrix. A summary of PCA and the introduction of a preliminary PCA algorithm then follows in Section 9.2. A detailed summary of the properties of PCA is given in Section 9.3. Without attempting to give a complete review of the available research literature, further material concerning PCA may be found in Dunteman (1989); Jackson (2003); Jolliffe (1986); Wold (1978); Chapter 8 in Mardia et al. (1979) and Chapter 11 in Anderson (2003).

9.1 The core algorithm

PCA extracts sets of latent variables from a given data matrix , containing K mean-centered and appropriately scaled samples of a variable set

9.1

The scaling matrix is a diagonal matrix and often contains the reciprocal values of the estimated standard deviation of the recorded variables

9.2

Based on , PCA determines ...