zero to ten (zero for unpleasant and/or no odor and 10 for pleasant and/or intense odor).PCA analysis: To reduce the dimensionality of perceptual descriptors and physiochemical descriptors, we used the principal component (PC) function in the Statistics Toolbox of Matlab. Principal component analysis (PCA) takes a data set consisting of N points in an M-dimensional space (for example, 12 odorants in the 24-dimensional odor descriptor space) and finds a rotation matrix which rotates the N points onto a new M-dimensional space with certain special properties. These are such that (1) the new dimensions are orthogonal and (2) the new dimensions, called principal components (e.g., PC1, PC2, ..., PCM), are ordered so that each successive PC has the maximal possible variance. Thus, PC1 explains the most variance of any linear transform of the original data, PC2 explains the next biggest amount of variance, and so on. Because the PCs are orthogonal, they explain sets of data that are not necessarily mutually inclusive.Spanning analysis: To measure the span of the mixtures components, we analyzed the average minimum distance between the Dravniekss odorants and the mixtures components. For this procedure, we used the Statistics Toolbox of Matlab to generate 10,000 random possibilities of mixtures and compute the prevalence of the minimum distance between the odorants in all 146 dimensions (each one corresponding to one verbal descriptor). In general, the lower the average minimum distance, the greater the span across the perceptual space. ResultsMixtures whose components spanning the space and are in equated intensity are expected to have a similar smell. While there are many colorful shades of brown, there may be an even greater variety of olfactory browns. The similarity test intends to measure the similarity between those olfactory browns which are not necessarily indistinguishable. Above 15 components there is a similar perception Mixtures P-value Mixtures P-value4 vs 15 0.001 15 vs 25 0.194 vs 20 <0.001 15 vs 30 0.94 vs 25 <0.001 20 vs 25 0.284 vs 30 0.0013 20 vs 30 0.9515 vs 20 0.96 25 vs 30 0.25Table1. Comparison between the similarity of mixtures (T-test). Similarity between mixtures of four components and each of the other mixtures are significantly different. Furthermore, the similarity between all of the other odorant mixtures is not significantly different (Table 1).Two-dimensional perceptual spaceThe results from the psychophysics test in which participants were asked to rate the intensity and pleasantness of various odorant mixtures is shown below. In this graph, one can see the stark differences between mixture 4A and the rest of the mixtures, as that particular mixture was significantly intense and unpleasant. Other mixtures that showed similar levels of odor intensity were mixtures 4B and 25A. All the other mixtures are not significantly different in their pleasantness and intensity. (Figure is missing) The perception matrix of the mixture and evaluation of the spanning:As explained before, we used PCA to reduce the number of dimensions. The effective dimensionality of the odor profile space was much smaller than 24, with the first two PCs accounting for 80% of the total variance. The mixtures 4C, 15A, 20A and