Target transform fitting: a new method for the non-linear fitting of multivariate data with separable parameters Porn Jandanklang, Marcel Maeder* and Andrew C. Whitson Department of Chemistry, The University of Newcastle, Callaghan, NSW 2308, Australia SUMMARY Data fitting is an important technique in chemistry. The number of parameters to be fitted is a most significant aspect: the larger the number, the more difficult the task. A unique combination of target factor analysis with non- linear data fitting can result in complete or partial separation of the parameters, which can then be fitted independently. Thus, instead of one multiparameter fit, several fits are performed with only one or a few parameters. The procedure can also support model development. Applications in kinetics and chromatography are presented. Copyright  2001 John Wiley & Sons, Ltd. KEY WORDS: target transformation; data fitting; separation of parameters; minimization; optimization; kinetics; chromatography; multivariate curve resolution; reaction mechanism INTRODUCTION Target transformation factor analysis (TTFA) is a well-known technique which can be applied to check whether the spectrum of a particular compound can be found in a series of spectra [1]. A typical example would be the detection of the existence of a particular component or rather its spectrum in an overlapping chromatographic peak cluster (measured with a multivariate detector, e.g. DAD, GC– MS, GC–FTIR) [2,3]. The simplicity of TTFA lends itself to more elaborate applications. Iterative target transform factor analysis (ITTFA) is one of the earliest examples [4]. In ITTFA a test vector is iteratively refined and convergence to the true result can often be achieved. ITTFA has many similarities with the alternating least squares (ALS) approach [5,6] and thus is a member of the family of soft modeling methods. An interesting variation on TTFA has been proposed recently by Furusjo ¨ and Danielsson [7]. Their method has many similarities with the technique proposed in this contribution and we will discuss the relationship between these two extensions of classical TTFA in more detail later. The first prerequisite for TTFA is a bilinear matrix of data, typically a series of absorption spectra measured as a function of an independent parameter such as time. The spectra are collected as rows in a matrix Y, and according to Beer–Lambert’s law, such a data matrix can be decomposed into the product of a concentration matrix C and a matrix A of absorption spectra: JOURNAL OF CHEMOMETRICS J. Chemometrics 2001; 15: 511–522 DOI: 10.1002/cem.640 * Correspondence to: Marcel Maeder, Department of Chemistry, The University of Newcastle, Callaghan, NSW 2308, Australia. E-mail: chmm@newcastle.edu.au Contract/grant sponsor: Australian Research Council. Contract/grant sponsor: The Rajaphat Institute, Thailand. Copyright  2001 John Wiley & Sons, Ltd. Received 3 January 2000 Accepted 27 April 2000