**3.3 Case 3**

Another (forensic) case which involved a comparison between very similar samples was the comparison between a piece of a packing tape used on a case containing drugs with a roll of packing tape found during a house search, in order to establish whether the packing tape could have been ripped from the roll. Finding such evidence would have been of utmost importance in building a strong case against the suspect. Both exhibits, analyzed by FTIR in transmission, revealed an adhesive part of polybutylacrylate and a support of

Principal Component Analysis: A Powerful

Interpretative Tool at the Service of Analytical Methodology 63

SIMCA was then applied, considering a 95% confidence level to define class space and the unweighted augmented distance (Wold & Sjostrom, 1977). A cross validation with 10 cancellation groups was carried out and 8 components were used to build the mathematical model of each class. The boundaries were forced to include all the objects of the training set in each class, which provided a sensitivity of 100% for each class. With regard to the specificity, class 4 showed a specificity of 90% towards class 2, 80% for class 3 and 10%

For classes 1 and 4, the Cooman's plot is shown in figure 13. It can be seen that 9 samples of class 1 fall in the common area between classes 1 and 4 (the specificity of class 4 towards class 1 was in fact 10%). This kind of result indicates a significant similarity between classes 1 and 4, that is between the roll of packing tape found in the suspect's house and the piece of

From the Cooman's plot relative to classes 2 and 4 (figure 14), it can be deduced that only one sample from class 2 is classified in the common area between classes 2 and 4 (specificity of class 4 towards class 2 equal to 90%), while no samples from class 4 are classified also in class 2. The similarity between classes 2 and 4 can therefore be considered insignificant.

Finally, from the Cooman's plot relative to classes 3 and 4 (figure 15), it is clearly visible that only 2 samples of class 3 fall in the overlapping area with class 4 (the specificity of class 4 towards class 3 was in fact 80%), whilst there are no samples from class 4 that fall in the overlapping area with class 3. From this last figure it can be deduced that the similarity between classes 1 and 4 is significantly higher than the similarity between classes 3 and 4.

towards class 1. Such results can be visualized in the Cooman's plots.

packing tape stuck on the case containing drugs.

Fig. 13. Cooman's plot for the classes 1 and 4.

polypropylene. Both supports and adhesive parts showed significant similarity in IR absorptions. This similarity, though necessary, was not sufficient in itself to establish whether the packing tape had been ripped from the exact same roll seized at the suspect's home. The compatibility between the two exhibits was studied through a multivariate approach, analyzing, via FTIR, 10 independent portions of the adhesive part for each exhibit. 10 portions of the adhesive part (in polybutylacrylate) of two other rolls of packing tape (not linked to the case) were also analyzed. PCA was then applied to a data set relative to 40 samples and variables obtained from a data spacing of 16 cm-1 (with a smooth of 11, corresponding to 21.213 cm-1) of FT-IR transmittances. Six PCs were extracted, with eigenvalues greater than 1, explaining 98,15% of the total variance.

The score plot of the first three principal components is shown in figure 12, where samples taken from the seized roll are indicated as class 1, the other two rolls are indicated respectively as classes 2 and 3, while the piece of packing tape is indicated as class 4. From the score plot it can be seen that points of class 4 are fairly close to those of class 1, indicating a decent similarity between the two classes of interest. However, points of class 4 are also rather close to points of class 3, suggesting a similarity also between classes 4 and 3, while points of class 2 appear more distant, showing a lower similarity between classes 2 and 4. In this case, PCA gave a first display of data, but could not be used as definitive proof to establish the compatibility between classes 1 and 4 because class 4 appears also to be consistent with class 3.

Fig. 12. Score plot of PC3 versus PC2 versus PC1 relative to FT-IR data for 40 packing tape samples.

62 Principal Component Analysis

polypropylene. Both supports and adhesive parts showed significant similarity in IR absorptions. This similarity, though necessary, was not sufficient in itself to establish whether the packing tape had been ripped from the exact same roll seized at the suspect's home. The compatibility between the two exhibits was studied through a multivariate approach, analyzing, via FTIR, 10 independent portions of the adhesive part for each exhibit. 10 portions of the adhesive part (in polybutylacrylate) of two other rolls of packing tape (not linked to the case) were also analyzed. PCA was then applied to a data set relative to 40 samples and variables obtained from a data spacing of 16 cm-1 (with a smooth of 11, corresponding to 21.213 cm-1) of FT-IR transmittances. Six PCs were extracted, with

The score plot of the first three principal components is shown in figure 12, where samples taken from the seized roll are indicated as class 1, the other two rolls are indicated respectively as classes 2 and 3, while the piece of packing tape is indicated as class 4. From the score plot it can be seen that points of class 4 are fairly close to those of class 1, indicating a decent similarity between the two classes of interest. However, points of class 4 are also rather close to points of class 3, suggesting a similarity also between classes 4 and 3, while points of class 2 appear more distant, showing a lower similarity between classes 2 and 4. In this case, PCA gave a first display of data, but could not be used as definitive proof to establish the compatibility between classes 1 and 4 because class 4 appears also to be

Fig. 12. Score plot of PC3 versus PC2 versus PC1 relative to FT-IR data for 40 packing tape

eigenvalues greater than 1, explaining 98,15% of the total variance.

consistent with class 3.

samples.

SIMCA was then applied, considering a 95% confidence level to define class space and the unweighted augmented distance (Wold & Sjostrom, 1977). A cross validation with 10 cancellation groups was carried out and 8 components were used to build the mathematical model of each class. The boundaries were forced to include all the objects of the training set in each class, which provided a sensitivity of 100% for each class. With regard to the specificity, class 4 showed a specificity of 90% towards class 2, 80% for class 3 and 10% towards class 1. Such results can be visualized in the Cooman's plots.

For classes 1 and 4, the Cooman's plot is shown in figure 13. It can be seen that 9 samples of class 1 fall in the common area between classes 1 and 4 (the specificity of class 4 towards class 1 was in fact 10%). This kind of result indicates a significant similarity between classes 1 and 4, that is between the roll of packing tape found in the suspect's house and the piece of packing tape stuck on the case containing drugs.

Fig. 13. Cooman's plot for the classes 1 and 4.

From the Cooman's plot relative to classes 2 and 4 (figure 14), it can be deduced that only one sample from class 2 is classified in the common area between classes 2 and 4 (specificity of class 4 towards class 2 equal to 90%), while no samples from class 4 are classified also in class 2. The similarity between classes 2 and 4 can therefore be considered insignificant.

Finally, from the Cooman's plot relative to classes 3 and 4 (figure 15), it is clearly visible that only 2 samples of class 3 fall in the overlapping area with class 4 (the specificity of class 4 towards class 3 was in fact 80%), whilst there are no samples from class 4 that fall in the overlapping area with class 3. From this last figure it can be deduced that the similarity between classes 1 and 4 is significantly higher than the similarity between classes 3 and 4.

Principal Component Analysis: A Powerful

**4. Conclusions** 

be found.

the variability within each class.

developed in a specific context.

Interpretative Tool at the Service of Analytical Methodology 65

In conclusion, SIMCA analysis allowed the comparison between a piece of a packing tape and three rolls of packing tape that had the same chemical composition, finding the most significant similarity with the seized roll. Such a degree of similarity was measured in terms of specificity of the tape class (4) with the roll classes (1, 2 and 3): the lower the specificity is, the higher the similarity between the two classes under study is. SIMCA results are fairly consistent with PCA results, which gave a simple visualization of data. Both techniques found that class 4 had the lowest similarity with class 2. In addition, SIMCA, as a class

This study shows the importance of PCA in traceability studies which can be carried out on different kind of matrices. As the majority of products come about from a transformation of some raw material, traceability has components deriving from both the fingerprint geographical characteristics transfer to the raw material and the production techniques

Moreover, PCA is a very useful tool for dealing with some supervised problems, due to its capability of describe objects without altering their native structure. However, it must be noted that, especially in forensics, results originating from a multivariate statistical analysis need to be presented and considered in a court of law with great care. For these kinds of results, the probabilistic approach is different from the one generally adopted for analytical results. In fact, in univariate analytical chemistry, the result of a measurement is an estimate of its true value, with its uncertainty set at a stated level of confidence. On the other hand, the use of multivariate statistical analysis in a court of law would imply a comparison between an unknown sample and a data set of known samples belonging to a certain number of classes. However, there remains the real possibility that the unknown sample might belong to yet another class, different from those of the known samples. In case 1, for example, the unknown sample might have been produced in a refinery that had not been included in the data matrix used for the comparison, or in case 3, the piece of packing tape, might not have belonged to any of the rolls analyzed. (Case 2 appears to be different,

In these cases, an initial approach to the analytical problem by using PCA is fundamental because it allows the characteristics of the unknown sample to be compared with those of samples of which the origin is known. Depending on the results obtained at this step, a potential similarity between the unknown sample and samples from some specific classes may be excluded, or the class presenting the best similarity with the unknown sample might

Results derived from PCA present a real picture of the situation - without any data manipulation or system forcing - and as such can form the basis for further deduction and the application of any other multivariate statistical analysis. A second step might be the application of some discriminant analysis or class modeling tool and an attempt to classify the sample in one of the classes included in the data matrix. A good result is achieved when PCA results fit those of supervised analysis. However, in a court of law these results would only become compelling alongside other strong evidence from the investigation, because, as already stated, the sample would have been compared with samples belonging to some distinct classes (and not all existing ones) and the data matrix might not adequately show

modeling tool, gave better results than PCA with regards classes 1, 3 and 4.

because sample C was specifically required to be classified in class A or B).

Fig. 14. Cooman's plot for the classes 2 and 4.

Fig. 15. Cooman's plot for the classes 3 and 4.

In conclusion, SIMCA analysis allowed the comparison between a piece of a packing tape and three rolls of packing tape that had the same chemical composition, finding the most significant similarity with the seized roll. Such a degree of similarity was measured in terms of specificity of the tape class (4) with the roll classes (1, 2 and 3): the lower the specificity is, the higher the similarity between the two classes under study is. SIMCA results are fairly consistent with PCA results, which gave a simple visualization of data. Both techniques found that class 4 had the lowest similarity with class 2. In addition, SIMCA, as a class modeling tool, gave better results than PCA with regards classes 1, 3 and 4.
