Dimensionality reduction in multivariable stochastic systems

Abstract

The transfer function mat.rj x of a large mult.i-m put.jrrmlt.i-out.put. linear st.ochnst.ic time-invariant control system may be computationally difficult to estimate und, further, may not provide a good interpretation of the underlying structure of the system. Priest.ley, Ran and Tong (\Ui3) have suggested a method, using information theoretic and statistical criteria, for reducing the dimensions of such a system, and thus. to some extent, overcoming these difficult.ics. The authors have undertaken a computational study of t.hc application of this t.hcory, illuminating the problems encountered, and demonstrating the feasibility of the method in practice.

Eigenvalue tests and distributions for small sample order determination for complex Wishart matrices

“…In particular, the principal component analysis approach is now considered classic. Priestley et al The authors point out that there may be an aliasing problem, as discussed by Haggan and Priestly [100] who successfully applied the method to a real system. The issue of order estimation was not discussed.…”

Identifying Patterns in Multiple Time Series Data

“…When this .understanding is not available, a method of analysing the multiple time series data with a view to discovering such sources of variation is desirable. Downloaded by [Northwestern University] at 11:25 25 March 2015 iDENTIFYING PATTERNS Principal Component Analysis c('uld be the answer and work has been done towards this direction mainly by researchers with focus on the frequency domain [3,6].…”

Dimensionality reduction in multivariable stochastic systems Application to a chemical engineering plant

“…The distillation column may be regarded as a stationary multi-input/ multi-output stochastic control system and may be described schematically thus: Haggan and Priestley (1975), that the reduction of the dimension of the output vector is based on the loss function L=E(Y(t)'QY(t)), where Y(t) is the observed output vector, Y(t)={Y1(t), ... , Yll(t)}', and Q is a positive definite (11 x 11) symmetric matrix (the' loss function matrix '). \,ye construct an orthogonal linear transformation on the output vector of the form .…”

“…To determine q, the dimension of the reduced output vector, we use the statistic Haggan and Priestley (1975)), and then we choose the reduced dimension as the smallest q for which A q ;;. 0·95.…”

“…In Haggan and Priestley (1975) we described how the' principal components ' method, introduced by Priestley et al (1973) for the reduction of the dimension of a multi-inputjmulti-output stationary stochastic system, was tested using simulated data. In that paper we reported that the results obtained on the simulated system were very satisfactory, and that the reduced dimensions obtained by this method were, in fact, correct for the given model.…”