# Identifying the Primary Odor Perception Descriptors by Multi-Output Linear Regression Models
## 1 Introduction
[PERSON] developed an olfactory representation referred to as odor effects diagram with two fundamental polarities: ergogenous versus antiergoneous (refreshing) and narcotic versus stimulating [35]. [PERSON] and [PERSON] obtained similar results to the odor effects diagram by applying PCA to two public databases [20]. For the high dimension viewpoint, [PERSON] and [PERSON] reported that an upper bound of 68 dimensions and a lower bound of at least 32 Euclidean dimensions for the odor space was revealed by applying multidimensional scaling (MDS) on a 171 \(\times\) 171 dissimilarity matrix derived from Chee-Ruiter data originated from Aldrich Chemical Company's catalog [36]. [PERSON] et al. implemented the Isomap algorithm to reduce the dimensions of human odor perceptions for predicting odor perceptions [37]. [PERSON] et al. identified ten primary dimension axes of the odor perception space by using non-negative matrix factorization (NMF), in which each axis was a meta-descriptor consisting of a linear combination of a handful of the elementary descriptors [38]. In short, there is no consistency in the structure of the odor perception space. Moreover, all of these works are based on the transformation approaches, and each dimension comprises multiple-element odor perceptions. Different from that, We propose a selection mechanism to narrow down the numbers of odor perception descriptors. Based on this selection mechanism, every odor perception descriptors' meaning remains, whose meaning is easily understood. Hence, the odor experts only need to rate much fewer odor perception descriptors so that the odor assessment workload is alleviated dramatically. For the relations between different odor perceptions, due to the linguistic nature of odor perception descriptors, natural language processing (NLP)-based approaches have been introduced [25; 39; 40; 41; 42]. [PERSON] and [PERSON] implemented a hierarchical clustering based on the cosine similarity matrix, which was calculated from the 300-dimensional word vectors of 38 odor descriptors [43]. However, it mainly focuses on the prediction of odor perceptions. The reduced outputs are more intangible and harsher than the originals, and the details of the original perception information were lost. [PERSON] et al. investigated the internal relationship between the 21 odor perceptual descriptors of the DREAM dataset and found that pleasantness was inferred from \"sweet\" precisely, which implied that some of the odor perceptions overlapped with others. Nonetheless, 21 descriptors are insufficient to describe the entire odor perception [44]. In summary, the relationship between these odor perceptions has not been thoroughly investigated. To address the issues of reducing the odor vocabulary, inspired by the conception of primary odorants [45], the chemicals which the specific anosmias are mapped, we proposed the definition of primary odor perceptual descriptors (POPDs), defining as the smallest set of odor perception descriptors. The perceptual ratings of the other odor perception descriptors, namely non-primary odor perception descriptors (NPOPDs), could be inferred or predicted precisely from those of the POPDs. It should be noted that the POPDs only relate to human odor perception and have no relation with the odorants. To identify the POPDs and NPOPDs, we proposed a novel selection mechanism based on machine learning, as described in Figure 1.  
The identification framework of POPDs comprises the disjunctive and validation models. The disjunctive model is employed to identify the Clustering-Center Odor Perception Descriptors (CCOPDs) and Non-Clustering-Center Odor Perception Descriptor (NCCOPDs). The NCCOPDs are the undetermined descriptors. The validation model is applied to divide the undetermined descriptors into predictable and unpredictable odor perception descriptors. The CCOPDs and unpredictable odor perception descriptors are identified as the POPDs, and the predictable odor perception descriptors as the NPOPDs.