The aim of performing Hierarchical cluster analysis (HCA) is to separate data into specific groups by considering similarity criterion, a distance metric such as Euclidean distance, as follows: (2) d ij = ( ∑ k = 1 K ( r ik − r jk ) 2 ) 1 / 2where K is the number of variables (in this case K is equal to 32 that is the number of sensors in the Cyranose), while i and j are the indices for groups of samples. Hence, a parameter to measure the level of similarity, S_ij, is defined as [8]: (3) S ij = 1 − d ij / max { d ij }

The computational process of S_ij using MATLAB gives a dendrogram as shown in Figure 5. The figure proved the capability of HCA to differentiate between G12, G22, and G33.

Principal component analysis (PCA) is an unsupervised statistical method that generates a new set of variables, called principal components. Each principal component is a linear combination of the original variables (r_s,n) defined by [9]: (4) PC p , n = α p , 1 γ 1 , n + α p , 2 γ 2 , n + ⋯ + α p , s γ s , nwhere PC_p,n is the notation for the p-th order principal component for the overall n number of data and is termed as scores. Coefficients transformations (α_p,s), referred as loadings, are obtained by taking elements of the eigenvectors from the covariant of the original data. The eigenvalue represents the variance associated with each principal component. By using MATLAB software, the two principal components {PC_1,n, PC_2,n} are obtained and have the two greatest variances: 88.096% and 11.202% (or total cumulative variance of 99.298%). The results of the PCA analysis are shown in Figure 6. The scores of the three groups of oils are plotted for principal component 2 (PC2) versus principal component 1 (PC1). The discrimination between the different types of oils can be clearly seen from the figure.

The previous two statistical approaches, HCA and PCA, successfully showed their capabilities to distinguish different types of agarwood oils. Both are typically used for exploratory data analysis to see how the multivariate data is clustered and to assess the linear separability of the odour classes. However, in cases where prediction is required (e.g., when implementing an automated classifier), the ANN is the more appropriate tool [7]. This section presents the use of ANN as an alternative choice to solve the classification problem in this work.

In this experiment, the backpropagation ANN with the Levenberg-Marquardt training algorithm was applied. The training used all the 32 sensors as inputs, 20 neurons in the single hidden layer, and three neurons at the output layer. The activation functions used are sigmoid and identity functions at the hidden and output layer, respectively. Figure 7 illustrates the structure of the ANN and how the input and output data were organised and indexed.

The same experimental procedure was carried out for the training as well as the testing data. The 200 raw data points were collected by experiments for each of the oil types G12, G22, and G32. This resulted in 600 data points for use in training and validation. After performing baseline manipulation and auto-scaling, the data were organised in one matrix to be fed as input. The testing data was collected on a different day, by sniffing the odour of the oils in nine vials that were assigned for testing only. The total of 1,800 data points was used as the testing data.

As shown in Table 3, the ANN performed very well in discriminating the three types of oils with 5.713345 × 10⁻⁸ mean square error (MSE) and 100% prediction performance. The prediction performance was defined as: (number of correct classification/number of total data) × 100%.

The use of too many sensors may increase noise, redundant information and provides no real benefit, whereas minimizing the number of sensors can result in the loss of some useful input information [10,11]. Thus, optimization for a specific application can be achieved by observing the sensors which provide high contribution to the system and eliminating the lower ones.

In this work, PCA is used to reduce high dimensionality data and to improve ANN training [12]. Table 4 is the list of loadings for PC1 that was sorted in descending order. The summation of the correlation coefficient from the matrix response data for each sensor is also provided in Table 4 as a comparison with the PCA results. It is evident that the higher loading values of PC1 for all sensors correspond to the less correlated sensors.

From Table 4, the data from the five least correlated sensors (sensor number 23, 31, 1, 2, and 4) are selected as input for the ANN training. The result shows an improvement where the ANN has a lower MSE, 8.20279 × 10⁻⁹ and 100% successful prediction of unknown data. The time spent for training and identification also decrease. For specific application, in this case to discriminate the three different types of agarwood oils G12, G22, and G32, the five selected sensors (from the 32 total sensors in the Cyranose) is an effective choice in terms of speed of detection and high accuracy. Attempts to further reduce the number of sensors was not successful. Table 5 compares the results of the ANN training for the case of using reduced number of sensors.