**1. Introduction**

14 Multivariate Analysis in Management, Engineering and the Sciences

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First of all, what is multivariate data analysis and why is it useful in waste management?

Methods dealing with only one variable are called univariate methods. Methods dealing with more than one variable at once are called multivariate methods. Using univariate methods natural systems cannot be described satisfactorily. Nature is multivariate. That means that any particular phenomenon studied in detail usually depends on several factors. For example, the weather depends on the variables: wind, air pressure, temperature, dew point and seasonal variations. If these factors are collected every day a multivariate data matrix is generated. For interpretation of such data sets multivariate data analysis is useful. Multivariate data analysis can be used to process information in a meaningful fashion. These methods can afford hidden data structures. On the one hand the elements of measurements often do not contribute to the relevant property and on the other hand hidden phenomena are unwittingly recorded. Multivariate data analysis allows us to handle huge data sets in order to discover such hidden data structures which contributes to a better understanding and easier interpretation. There are many multivariate data analysis techniques available. It depends on the question to be answered which method to choose.

Due to the requirement of representative sampling number of samples and analyses in waste management lead to huge data sets to obtain reliable results. In many cases extensive data sets are generated by the analytical method itself. Spectroscopic or chromatographic methods for instance provide more than 1000 data points for one sample. Evaluation tools can be developed to support interpretation of such analytical methods for practical applications. For specific questions and problems different evaluation tools are necessary. Calculation and interpretation are carried out by the provided evaluation tool.

© 2012 Böhm et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Böhm et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In this study an overview of multivariate data analysis methods and their application in waste management research and practice is given.

Application of Multivariate Data Analyses in Waste Management 17

PCA is mathematically defined as an orthogonal linear transformation that arranges the data to a new coordinate system in that the greatest variance by any projection of the data takes place along the first coordinate (called the first principal component), the second greatest variance along the second coordinate, and so on. Theoretically the PCA is the optimum transformation for a given data set in least square terms. That means PCA is used for dimensionality reduction of variables in a data set by retaining those characteristics of the data set that contribute most to its variance. The transformation to the new coordinate system is described by scores (T), loadings (P) and errors (E). In matrix terms, this can be written as X = T \* P + E. Fig. 1 illustrates the mathematical transformation using PCA. The matrices can be displayed graphically. The scores matrix illustrates the data structure and the loading matrix displays the influence of the different variables on the data structure.

PCA displays hidden structures of huge data sets. PCA is applied in different fields of waste management to find out the relevant parameters of a large parameter set. So we can see which properties of a sample are significant and important to answer a particular question. Due to the results obtained time and money can be saved in further research activities.

J

I

Errors E

J

Loadings P

\* +

A

I A

Scores T

Many applications can be found in compost science. Zbytniewski and Buszewski [1] applied PCA to reveal the significant parameters and possible groupings of chemical parameters, absorption band ratios and NMR data. Campitelli and Ceppi [3] investigated the quality of different composts and vermicomposts. The collected data were evaluated by means of PCA to extract the significant differences between the two compost types. Gil et al. [4] used PCA to show effects of cattle manure compost applied on different soils. Termorshuizen et al. [13] carried out a PCA based on disease suppression data determined by bioassays in different compost/peat mixtures and pure composts. PCA was applied by Planquart et al. [10] to examine the interactions between nutrients and trace metals in colza (Brassica napus) when sewage sludge compost was applied to soils. LaMontagne et al. [7] applied PCA on terminal restriction fragment length polymorphisms (TRFLP) patterns of different composts to reveal their characteristics with respect to microbial communities. Malley et al. [8] recorded near infrared spectra from cattle manure during composting. The collected spectral data were

**2.1. Pattern recognition** 

I

*2.1.1. Exploratory data analysis* 

Principal Componant Analysis (PCA)

**Figure 1.** Principle of the PCA (according to Esbensen [85])

Data matrix X

J

PCA
