4.1.1. Statistical Measures

The purpose of the statistical analysis was to better understand the relationship between the three classes of drugs of abuse and the class of negatives. First, the mean ATR-FTIR spectrum was calculated for each class for the qualitative assessment of the data. The results, illustrated in Figure 1, indicate that all the targeted classes have the main peak near 2800 cm−1. The strongest peak characterizes the amphetamines, followed by the cannabinoids, opioids, and negatives. Although the peak at 2800 cm−<sup>1</sup> of opioids and

negatives have nearly the same intensity, their mean spectra can be easily differentiated because the opioids have a second relatively strong peak at 2400 cm<sup>−</sup>1.

**Figure 1.** Mean ATR-FTIR spectrum calculated for the amphetamines (blue), opioids (orange), cannabinoids (green), and negatives (red) included in the database.

The statistical parameters calculated for the mean spectra are presented in Table 2. In terms of the central tendency of the spectra, the mean values vary only between 0.0338 and 0.0452. The data dispersion shows that the class of amphetamines stands out with a standard deviation of 0.0263, almost double of the next one, determined for the class of cannabinoids. The relatively large standard deviation of the class of amphetamines indicates that the spectra of these compounds are less similar than those included in the other classes. This is probably due to the fact that the class of hallucinogenic amphetamines is formed by three subclasses of compounds, i.e., 2C-x, DOx, and NBOMe amphetamines.

**Table 2.** Statistical parameters calculated based on the mean ATR-FTIR spectra of the targeted classes of compounds, between 1500 and 4000 cm<sup>−</sup>1, with a resolution of 1.92 cm−1.


The skewness of the spectra of each class indicates that none ranges between −0.5 and 0.5, so none of the analyzed classes of compounds has a symmetrical distribution. The class of negatives is a moderately skewed dataset, as its skewness ranges between 0.5 and 1. The sets formed by the spectra of the three modeled classes of positives have skewness values larger than 1, so they are highly skewed.

The distributions of the spectra of the three classes of positives are leptokurtic, as they have large excess kurtosis. The largest excess kurtosis is recorded for the cannabinoids. The negatives have a mesokurtic distribution. The excess kurtosis of this group being very small (close to zero), their distribution may be considered practically normal. The results obtained for the negatives are consistent with the fact that it contains the highest diversity of

substances, with the rest of the classes consisting of substances with very similar molecular structures and hence very similar ATR-FTIR spectra.

#### 4.1.2. Principal Component Analysis

A two-component PCA was then performed as a preliminary exploratory analysis. Figure 2 displays the score plot obtained for the first two PCs, which indicates that the amphetamines form the most compact cluster. The points associated with the opioid and cannabinoid compounds are much more spread out. Many of the points associated with the negatives are overlying the clusters formed by the positives, especially the cluster of opioids.

**Figure 2.** Score plot of the first two principal components of a two-component PCA displaying the class of amphetamines (red), opioids (green), cannabinoids (blue), and negatives (black).

#### 4.1.3. Independent Component Analysis

The score plot obtained with a three-component ICA is displayed in Figure 3. It indicates that ICA leads to better clustering, especially for the class of amphetamines. The opioids and the cannabinoids also show a better grouping than in the case of PCA. There is practically no improvement in the group of negatives, their associated points being scattered on nearly the whole plot.

#### 4.1.4. Transformers

The results obtained with 10 component transformers are presented in Figure 4. For the class of amphetamines, this method leads to results similar to those obtained with ICA. However, there is an improvement in the other three modeled classes: the opioid and cannabinoid classes are more clearly separated, and the negatives tend to be better discriminated as well.

**Figure 3.** Score plot of the first two components of a three-component ICA displaying the class of amphetamines (red), opioids (green), cannabinoids (blue), and negatives (black).

**Figure 4.** Score plot of the 3rd and 8th components of a ten-component transformed operation displaying the class of amphetamines (red), opioids (green), cannabinoids (blue), and negatives (black).
