# Identifying the Primary Odor Perception Descriptors by Multi-Output Linear Regression Models
## 1 Introduction  
The process of odor perception is more complicated than visual and auditory perception [1]. It is the result of the aggregate activations of 300 to 400 different types of olfactory receptors (ORs) [2], expressed in millions of olfactory sensory neurons (OSNs) [3, 4]. These OSNs send signals to the olfactory bulb, then further to structures in the brain [5, 6]. The olfactory signals are ultimately transformed into verbal descriptors, such as \"musky\" and \"sweet\". Compared with visual and auditory perception, odor perception is quite difficult to describe. The odor impression of human beings is affected by culture background [7], gender [8], and aging [9]. There are variabilities between people in the evaluation of odor perception. Besides, the relationships between odorants and odor perception remain elusive. Although some work has revealed some physicochemical features of the odorants, such as the carbon chain length [10] and molecular size [11], are related to human odor perception, the odorant molecules with similar structures could smell quite different. In contrast, the molecules with distinct structures could be described in an identical way [12]. In summary, odor perception is an exciting but challenging issue in the field of odor research. Currently, semantic methods are the most widely used approaches to qualify odor perceptions in practice [13, 14, 15]. Each odor perception descriptor corresponds to one odor perception, so they are considered equal in this paper. Semantic odor perception descriptors have played an important role in food [16, 17], beverage [18, 19], and fragrance engineering [20] for product quality assessment and othercommercial environments [21]. Therefore, numerous domain-specific sets of verbal descriptors for qualifying odor perception have been derived [19; 22; 23; 24]. [PERSON] et al. revealed a list of 146 wine-specific terms used in wine reviews [19]. The American Society for Testing and Materials (ASTM) Sensory Evaluation Committee reviewed literature and industrial sources and collected over 830 odor descriptors in use. Different from the traditional manual design approaches, [PERSON] et al. developed a standardized odor vocabulary in an automatic way [25]. They proposed a data-driven approach that could identify odor descriptors in English and used a distributed semantic word embedding model to derive its semantic organization. In summary, the odor vocabulary is a colossal family, which increases the difficulty of odor sensory assessment in the industries. The previous odor perception works have focused on deriving more and more verbal descriptors relating to odor perception, leading to redundancy in these odor perception descriptors. The identification of the redundant odor perception descriptors is a \"blank\" area. In the paper, we aim to fill this gap. Using these odor perception vocabularies, a lot of odorant-psychophysical datasets were developed [26; 27; 28]. The well-known Dravnieks dataset [29] contains 144 mono-molecular odorants, and their expert-labeled perceptual ratings of 146 odor descriptors range from 0 to 5. The DREAM dataset [30] involves 476 molecules and their perceptual ratings of 21 odor perception descriptors labeled by 49 untrained panelists, ranging from 0 to 100. These psychological odor datasets contain exuberant information on the relations between different odor perceptions. Base on these odorant-psychophysical datasets, Substantial efforts have focused on the odor perception space and the relations among different odor perceptions. There are two main viewpoints on the dimensions of the odor perception space: low dimension and high dimension. For the low dimension viewpoint, [PERSON] et al. found that pleasantness was the primary dimension of the odor perceptual space by principal component analysis (PCA) [31], and this finding was validated by a series of studies [32; 33; 34]. However, the degree of pleasantness is too coarse to describe the details of odor perception.