## 3 Results
### Quantitative Analysis: Milk Identification
We cannot conclude, however, at present, that the difference is due to this fact, but an investigation in this sense can certainly constitute an interesting future development. As for the lactose-free milk samples, they have a higher capacity than the semi-skimmed milk, although they have the same amount of fat. Lactose is a disaccharide sugar, therefore complex, and it needs to be broken down into its two main monosaccharides components, glucose and galactose, to be digested correctly. Lactose-free milk has the lactose already divided into the glucose and galactose and these two monosaccharides have a higher dielectric constant [42] with respect to lactose; this fact should explain the higher capacitance values of the lactose-free milk. Although the distinction between the capacity values of the whole milk and lactose-free milk is evident from Figure 8, in order to validate measurement results more rigorously a statistical analysis was performed by means of a PCA (Principal Components Analysis, with XLSTAT software, by Addinsoft Inc., New York, NY, USA) with all of the variables obtained for the circuit parameters, and whose mean values are reported in Table 3. The analysis was performed for each brand, to distinguish all of the types of milk. The \(n\) parameter is not included in the analysis because it is a constant for each brand. The correlation matrix was calculated by [PERSON]'s method and the performed analysis, whose results are shown as an example for brand 3, in Figure 9, succeeded in obtaining two PCs (F1 and F2) with a variance large enough to successfully (94.27%) allow the clear separation of the three sample groups (whole, semi-skimmed, and lactose-free milk). The PC F1 is strictly correlated to the variables \(C\) and \(Q\), while a strong correlation results between the PC F2 and \(R\). This means that, in principle, only two variables, that are \(C\) (or \(Q\)) and \(R\), are needed in order to clearly distinguish the type of milk within a brand. It is probably preferable to use \(C\) instead of \(Q\) because the concept of capacitance is a little more familiar with respect to \(CPE\). The results shown in the figure refer to brand 3, but similar results were obtained for brand 2. For brand 1, on the other hand, the statistical analysis identifies with certainty the milk without lactose, while the only useful parameter to distinguish the whole milk from semi-skimmed milk appears to be \(R\). If, on the other hand, the PCA analysis is carried out on five variables, that is also adding to \(C\), \(Q\) and \(R\) the value of the susceptance at the peak frequency and the value of the high frequency conductance (for example, at 100 kHz), the results improve. For brand 1, for example, as can be seen from Figure 10, the success rate is of 92.23%. In this case, the PC F1 is strictly correlated to the variables \(Im(Y)\), \(Re(Y)\) and \(R\), while the PC F2 is mainly correlated to \(Q\). If the PCA analysis is performed with five variables for brand 2, as it is shown in Figure 11, a 95.12% of success is reached in the separation of the three sample groups. In this case, each type of milk occupies a different quadrant, a situation similar to the one shown in Figure 9, indicating that the five variables are redundant and therefore, for brands 2 and 3, only the values of the circuit components would be sufficient. As regards the interpretative doubt of the admittance curves relative to the semi-skimmed milk and fat-free, lactose-free milk (blue and light blue curves in Figures 4 and 6), it is evident from the table that the capacitance value helps to identify with certainty the type of milk. In fact, the capacitance associated with the LFFM sample is about 30% higher than the capacitance associated with the SSM sample. Figure 8: Comparison of capacitance values to distinguish whole milk from lactose-free milk for different brands (samples from brand 2 (**a**); from brand 1 (**b**) and from brand 3 (**c**)).