ANALYTICA CHIMICA zyxwvutsr ACTA zyxwvutsrqponml ELSEVIER Analytica Chimica Acta 331 (1996) 187-193 Application of Radial Basis Functions - Partial Least Squares to non-linear pattern recognition problems: diagnosis of process faults B. Walczak”‘“, D.L. Massartb %stitute of Chemistry, Silesian Vniversi@, 9 Szkolna Street, 40-006 Katowice, Poland bPharmaceurical Institute, Vrije Vniversiteit Brussel, Luarbeeklaan 103, B-1090 Brussels, Belgium Received 9 November 1995; revised 29 April 1996; accepted 29 April 1996 Abstract Performance and robustness of a newly proposed approach (based on the Radial Basis Function and PLS2) in the non-linear pattern recognition problem is studied and compared with those of Radial Basis Function Network (RBFN) and multilayer feed-forward network (MLP). An example concerns classification of process faults. The presented results show that the RBF- PLS2 method can be treated as an alternative for the RBFJN and MLP approaches, with an additional advantage over MLP as a linear method. Keywords: Pattern recognition; Radial Basis Functions Networks (RF3FN); Process control 1. Introduction Except for the typical pattern recognition techni- ques such as, e.g., k-Nearest Neighbours, Linear Discriminant Analysis, SIMCA etc., the standard regression methods with O/l class variables can also be used in the pattern recognition problems. Let us concentrate on the Partial Least Squares method [1,2]. This is a linear regression method allowing to deal with ill-posed data (i.e. with data containing more variables than objects). The PLS2 version allows to deal simultaneously with a number of dependent variables. Although little is known about * Corresponding author. Fax: 48 32 599 978. #03-2670/96/$!5.00 0 1996 Elsevier Science B.V. All rights reserved PII SOOO3-2670(96)00206- 1 the PLS model [2] from a statistical point of view, its popularity is growing, which gives evidence of its usefulness in data modelling. PLS2 is often compared with the statistically well known canonical correla- tion analysis [2,3]. The main difference is that maximization of the X-Y covariance in PLS2 has replaced maximization of the correlation in the latter and that PLS2 does not require a full column rank in X and Y. After allowing modifications to deal with non-linear problems, its usefulness can be extended to the pattern recognition area. As demonstrated in our previous paper [4], this can be done employing the idea of the Radial Basis Function Networks [5-71. Simplicity of the proposed algorithm and its guaran- teed convergence can make the RBF-PLS2 approach competitive with other neural network approaches. In