Combination of Tucker3 model with cluster analysis for the assessment of the microbiological activity on benzimidazolium salts Gyula Oros a , Tibor Cserháti b, ⁎ a Plant Protection Institute, Hungarian Academy of Sciences, 1022 Herman O. 15, Budapest, Hungary b Research Institute of Materials and Environmental Chemistry, Chemical Research Center, Hungarian Academy of Sciences, P.O. Box 17,1525 Budapest, Hungary abstract article info Article history: Received 15 July 2008 Received in revised form 15 September 2008 Accepted 7 October 2008 Available online 1 November 2008 Keywords: Benzimidazolium salts Microbiological effect Tucker3 model Cluster analysis The antimicrobial effect of 7 benzimidazolium salts (base, chloride, sulfate, phosphate and nitrate forms) was determined on 15 microorganisms. The similarities and dissimilarities among the data consisting of the benzimidazolium salts and microorganisms were elucidated by using the Tucker model combined with cluster analysis. The calculations demonstrated that the combined method can be successfully employed for the separation of the impact of the molecular structure and cation type on the antimicrobial activity of the base and benzimidazolium salts. © 2008 Elsevier B.V. All rights reserved. 1. Introduction Principal component analysis (PCA), a versatile and easy-to-use multivariate mathematical–statistical method, has been developed to contribute to the extraction of maximal information from large data matrices containing numerous columns and rows [1]. As PCA is only suitable for the elucidation of the similarities and dissimilarities among the columns and rows of two-dimensional data matrices it cannot be employed for the evaluation of arrays of higher dimensions. A consider- able number of multiway mathematical statistical methods was devel- oped and successfully applied for the analysis of multi-dimensional arrays. The application of parallel factor analysis [2–4], direct fitting algorithm [5], and canonical decomposition analysis [6] was previously reported. The Tucker3 model or three-way PCA [7,8] and its improved version [9] have also been developed for the analysis of the similarities and dissimilarities among N-dimensional data arrays. The basic mathe- matical construction of the method is discussed in detail in refs [7–9]. The Tucker3 model computes three ortogonal matrices with lower dimensions than the original data arrays such a manner that the variance explained by the reduced matrices being as high as possible. The usefulness of these calculation methods have been proven in many fields of up-to-date data evaluation such as in the analysis of retention data in normal phase high-performance liquid chromatography [10], environmental analysis [11], person perception analysis in phsychology [12], medium-rank second order calibration [13], and enzyme produc- tion [14,15]. Similarly to 2-dimensional PCA traditional significant tests cannot be employed for the determination of the reliability of the results. As the resulting computed matrices of Tucker3 model are generally multidimensional they cannot be reliably evaluated by visual methods except in the cases when the first two elements of the data array explain the overwhelming majority of variance. Cluster analysis [16] has been developed for the reduction of the dimensionality of multidimensional arrays. Cluster analysis projects the points scattered in the multidimensional space on a plane such a manner that the distances among the points in the multidimensional space on the plane are as similar as possible. The objectives of the study were the measurement of the microbiological effect of benzimidazolium salts containing various cations, the application of the combination of Tucker3 model and cluster analysis for the evaluation of the dependence of the microbiological effect on the type of test organism, chemical structure of the free benzimidazolium base and the type of cation. To the best of our knowledge a Tucker3 model combined with cluster analysis has never been used in pesticide science and management. 2. Experimental The IUPAC and common names of benzimidazole derivatives are compiled in Table 1 . The free base and the salts formed with Cl - , SO 4 2- , PO 4 3- and NO 3 - were included in the experiments (altogether 5 × 7 elements). The data in Table 1 do not show the core elements with the corresponding explained variance. Species tested for the microbiolo- gical activity are listed in Table 2. (altogether 15 species) The fungi tested were taken from the collection of the Plant Protection Institute of the Hungarian Academy of Sciences (Budapest, Hungary). The test species represent various taxonomic groups as well as modes of habitation (saprotrophes, species parasitizing predominantly Chemometrics and Intelligent Laboratory Systems 96 (2009) 1–5 ⁎ Corresponding author. Tel.: +36 1 325 7900; fax: +36 1 325 7554. E-mail address: tevi@chemres.hu (T. Cserháti). 0169-7439/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.chemolab.2008.10.003 Contents lists available at ScienceDirect Chemometrics and Intelligent Laboratory Systems journal homepage: www.elsevier.com/locate/chemolab