## 3 Methodology
### Steps in Pattern Recognition  
The multivariate response of an array of chemical gases with broad and partially overlapping selectivity created \"electronic fingerprints\" for a wide range of odour which can be characterized using pattern-recognition. The process of pattern recognition may be split into four sequential stages: data pre-processing, dimensionality reduction, classification and decision making. Figure 5 illustrates the pattern recognition process. Each stage is described in detail in the following sections. Figure 4: (**a**) Ambient environment; (**b**) Chemical presence; (**c**) Food and beverages; (**d**) Fragrance presence; and (**e**) Combustion activity. Figure 5: Steps in pattern recognition. The first stage of the pattern recognition process, after collecting raw data, is data pre-processing. Data pre-processing is a procedure that involves extracting certain significant characteristics from the sensor response curves or transient response in order to produce a set of numerical data or feature for further processing [42]. Choosing the correct pre-processing technique is important because it may aid in the success of subsequent analysis and affect the performance of pattern recognition [43]. Most data pre-processing techniques are basically derived from a typical sensor response as shown in Figure 6. _Vo_ is a measured value in clean ambient air or an initial value called the baseline, while _Vs_ is the response value to odour or smell. Basically, data pre-processing techniques can be divided into three major categories: baseline manipulation, normalization and compression. Every category has their own formula which was transformed from the sensor response. In this study, only five data pre-processing techniques have been selected which are frequently used in odour pattern recognition as summarized in Table 5. These five techniques, called features of pattern recognition and raw data, are also chosen as one of the features. The feature output from the pre-processing stage are often not suitable to be processed by the classifier due to data redundancy and high-dimensionality that can cause the problem of dimensionality [44]. On the other hand, if too many features are used for the classification, there is a risk that the model becomes too complex and the capability of the model to classify can be very poor. For this reason, a dimensionality reduction stage is required to eliminate the curse of dimensionality in classification and improve the accuracy or performance of classification [45]. Where, \(X_{ij}\) represents feature matrix for the \(i\)th sample of \(j\)th sensor, \(V_{ij}\) represents sensor's response value, and \(V_{bj}\) represents baseline value of \(V_{ij}\). A feature extraction technique based on principal component analysis (PCA), which is widely used in in machine learning for dimensionality reduction, is chosen for this study [22; 48; 49]. PCA is  
Figure 6: Typical sensor response. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Technique** & **Abbreviation** & **Formula** & **References** \\ \hline Raw & RW & \(X_{ij}=~{}V_{ij}\) & [46] \\ \hline Differential & DIFF & \(X_{ij}=~{}V_{ij}-V_{bj}\) & [43; 46; 47] \\ \hline Relative & REL & \(X_{ij}=~{}\frac{V_{ij}}{V_{bj}}\) & \\ \hline Fractional & FRACT & \(X_{ij}=\frac{V_{ij}-V_{bj}}{V_{bj}}\) & \\ \hline Sensor Normalization & SN & \(X_{ij}=\frac{V_{ij}-V_{ij}^{min}}{V_{ij}^{min}-V_{ij}^{min}}\) & [43; 46; 47] \\ \hline Vector Array Normalization & VAN & \(X_{ij}=\frac{V_{ij}}{\sqrt{\sum_{i=1}^{N}(V_{ij})^{2}}}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Data pre-processing techniques selected. defined by a matrix having as rows the eigenvectors of the feature space covariance matrix.