# Identifying the Primary Odor Perception Descriptors by Multi-Output Linear Regression Models
## 4 Discussion  
A large number of odor perception descriptors applied in industries and academic literature is a challenging issue in the odor research community, and it hampers the odor sensory assessment in food, beverage, and fragrance industries. To tackle this issue, we propose the task of reducing the amount of odor perception descriptors, and we contrive a novel selection mechanism based on machine learning to identify the POPDs and NPOPDs. The selection mechanism aims to minimize the number of POPDs by maximizing the number of NPOPDs. The validation model in this selection mechanism builds mapping functions from the CCOPDs to the NPOPDs, revealing their relationship. Moreover, it demonstrates that the sparsity and correlation between every two odor perception descriptors dramatically impact predicting performance. Compared with the expansion of odor vocabulary in the previous work [19; 23; 24; 25], we propose a shrinkage strategy in this paper. Our findings demonstrate the feasibility of reducing the size of the odor vocabulary. Although the odor perception is complicated, it could be represented by a subset of odor domain-specific semantic attributes, namely, POPDs. Just like the three primary color descriptors \"red\", \"blue\", and \"green\" for visual perception. Moreover, the NPOPDs could be recovered from a weighted linear combination of the CCOPDs, just as any color can be formed by combining three primary colors. The framework proposed in this work is based on the assumption that there are inherent links among different odor perceptions. The identification framework proposed in this paper reveals the complicated relations between POPDs and NPOPDs to some extent. It demonstrates that some odor perception descriptors could be inferred from others, and this finding is consistent with the work in [42]. However, how to derive the general odor perception descriptors is not mentioned in [42], while we propose a disjunctive model with an updating strategy to identifying these general odor perception descriptors that could be used to infer the NPOPDs. Therefore, our work could be taken as the prequel to work in [42]. Moreover, it seems that the odor perceptions are not uniformly distributed in the odor perception space. Some of them are clustered together, while some of them are isolated points. That is, they have little to do with other odor perceptions. These findings are consistent with those in [41; 44]. However, the work in [44] focuses on the relations between the missing odor perception and the known ones, and [41] aims to predict the odor perception from the mass spectrum of mono-molecular odorants. Different from the approaches based on transformation, such as the work in [31; 36; 38], a selection mechanism based on machine learning is proposed in this paper. The transformation approaches mainly concentrate on exploring odor perception space, and the axes are the mixtures of several elementary odor perception descriptors. The meanings of these axes are different from any of the elementary ones. For instance, the work in [38] reveals ten axes of the odor perception space, which are the linear combination of several elementary descriptors. There are mainly six odor perception descriptors for the first basis vector, i.e., fragment, floral, perfumery, sweet, rose, and aromatic. Any existing word could not denote the exact meaning of the mixture of the six odor perception descriptors. These axes could not be used directly for odor assessment. If we want to obtain the perceptual ratings of these axes, The perceptual ratings of its elementary odor perception descriptors must be obtained first. Therefore, the findings of these transformation-based approaches could not simplify the odor assessment. Moreover, there is overlap among the ten axes identified in [38]. For example, \"fragrant\" is elementary of the first three axes, and it indicates that there is redundant information among these axes. By contrast, our work focuses on reducing the odor vocabulary, and a selection strategy is adopted.