## 3 Materials and Methods
### Datasets  
In this work, we collected multiple free and public olfactory perception databases, including odor datasets from OdorRactor, TGSC, Sigma Aldrich, Pubchem, Flavorbase, AromaDB, SuperScent, and Flavornet. There are mainly two types of databases: (a) databases based on individual perception estimates; (b) chemical databases encoded by one or several odor perception descriptors. Databases based on individual perception estimates include the Arctander dataset (3102 odor perceptions estimated by perfumers), the DREAM dataset (DREAM Olfactory Prediction Challenge dataset, 476 odor molecules with 19 odor descriptors evaluated by 49 participants), Dravnieks Atlas of Odor Character Profiles (138 single molecules and 16 mixtures/oils estimated by 150 participants to obtain olfactory perception described by 146 odor descriptors), Boelens Atlas, etc. The odor databases encoded by one or more odor perception descriptors include the Goods Scents Company Web Page (TGSC) ([[http://www.thegoodscentscompany.com/](http://www.thegoodscentscompany.com/)]([http://www.thegoodscentscompany.com/](http://www.thegoodscentscompany.com/))) (accessed on 1 August 2021), the Flavor-Base (FLB)-10 th Edition database ([[http://www.leffingwell.com/flavbase.htm](http://www.leffingwell.com/flavbase.htm)]([http://www.leffingwell.com/flavbase.htm](http://www.leffingwell.com/flavbase.htm))) (accessed on 1 August 2021), Flavornet website ([[http://www.flavornet.org](http://www.flavornet.org)]([http://www.flavornet.org](http://www.flavornet.org))) (accessed on 1 August 2021), Sigma-Aldrich spice catalog, SuperScent database, OdorRactor database ([[http://mdl.shsmu.edu.cn/ODORactor/](http://mdl.shsmu.edu.cn/ODORactor/)]([http://mdl.shsmu.edu.cn/ODORactor/](http://mdl.shsmu.edu.cn/ODORactor/))) (accessed on 1 August 2021), AromaDB, PubChem ([[https://PubChem.ncbi.nlm.nih.gov/](https://PubChem.ncbi.nlm.nih.gov/)]([https://PubChem.ncbi.nlm.nih.gov/](https://PubChem.ncbi.nlm.nih.gov/))) (accessed on 1 August 2021), etc. There is significant homogeneity among the various data sources with respect to olfactory perception, olfactory characteristics, and evaluator expertise. After removing overlapping and redundant chemical molecules and removing odorless molecules, a total of 4032 expert-labeled odor molecules were obtained. At the same time, odor descriptors were homogenized to convert odors with the same core meaning or derivation into root odors. To ensure that there are enough samples for experimental predictions, we kept odor perception descriptors that appeared in at least 50 chemical molecules, and others were excluded from this study. After processing, we obtained a total of 3553 odor molecules and 105 odor descriptors, as shown in Figures 2 and 3. Each odor molecule can have multiple odor descriptors, and each odor descriptor can correspond to multiple odor molecules. Furthermore, some odor descriptors are very common, such as \"fruity\" and \"sweet\", while others are rare, such as \"potato\" or \"cedar\". The co-occurrence matrix of odor descriptors is shown in Figure 4. The color range of the heatmap is log-scaled and normalized so that each row and column can sum to 1. Figure 1: The overall architecture of the proposed olfactory perception model HGAFMN. PubChem [38] is a public database of chemical substances built by the National Institutes of Health (NIH). The database contains chemical properties and biological activity data for small organic molecules, including SMILES numbers (Simplified Molecular Linear Input Specification Numbers) for odor molecules. By querying the CID numbers of the collected 3553 molecules in batches on this website, the corresponding SMILES number dataset can be obtained. PaDEL-descriptor [14] is a free software application for computing chemical molecular feature descriptors.