On-line adaptive principal component extraction algorithms using iteration approach

Two new on-line algorithms for adaptive principal component analysis (APCA) are proposed and discussed in order to solve the problem of on-line industrial process monitoring in this paper. Both the algorithms have the capability of extracting principal component eigenvectors on-line in a fixed size sliding data window with high dimensional input data. The first algorithm is based on the steepest gradient descent approach, which updates the covariance matrix with deflation transformation and on-line iteration. Based on neural networks, the second algorithm constructs the input data sequence with an on-line iteration method and trains the neural network in every data frame. The convergence of the two algorithms is then analyzed and the simulations are given to illustrate the effectiveness of the two algorithms. At last, the applications of the two algorithms are discussed.

► We propose two new online algorithms for APCA.
► Algorithms are applied to the online industrial process monitoring.
► Both of the algorithms can extract principal component on-line.
► Both of the algorithms can deal with high-dimensional input data.