# Identifying the Primary Odor Perception Descriptors by Multi-Output Linear Regression Models
## 3 Experimental Results
### Stability Analysis of the Identification Framework for POPDs and NPOPDs  
The stability analysis of the proposed identification framework's results is conducted. This framework comprises the disjunctive model based on clustering algorithms and the validation model based on multi-output regression models. The multi-regression model is one of the three classical regression models: Ridge, LASSO, ElasticNet model, so the results of the validation model is stable, and the stability of this framework only relies on the disjunctive model. The stability of the disjunctive model's results is affected by the random initialization of the clustering algorithms. To this end, the clustering algorithms are executed many times to obtain the candidate odor perception descriptors. The CCOPDs are obtained by an updating strategy based on CT and frequency constraints to ensure the disjunctive model results' stability, as described in Section 2.2.1.  
The fewer the number of clusters is, the greater the fluctuation of the selected CCOPDs are. A higher CT could lead to the greater flexibility of CCOPDs. Hence, the stability of 10 CCOPDs with a CT of 1.0 was investigated.  
Precisely, the clustering algorithms were executed for 100, 200, 300, 400, 500, 600, 700, 800, 900, and 1000 times to obtain the candidate CCOPDs. The CCOPDs were then derived by the updating strategy based on the constraints of CT and frequency. For each of the ten numbers of the execution times for the clustering algorithms, the disjunctive model was implemented 30 times. The results are shown in Figure 6.  
It can be observed that as the number of the execution times of the clustering algorithms increases, the results of CCOPDs converge, indicating the effectiveness and stability of the disjunctive model. When the number of execution times of clustering algorithms reaches up to 1000, the results of the 30 implementations of the disjunctive models are the same. That is, the same ten CCOPDs are selected with a probability of 1. Hence, in the rest of this paper, all the results are obtained under the 1000 executions of the clustering algorithms. It should be noticed that the clustering algorithm is only used to select out the CCOPDs. After 1000 executions of the clustering algorithm and the updating strategy, the disjunctive models' results are no longer the clustering algorithms' results.  
As shown in Figure 6, 14 odor descriptors were chosen as the CCOPDs for GMM-disjunctive and K-means-disjunctive models, and 13 out of these 14 descriptors were overlapped. The singular one was \"rancid\" for the K-means-disjunctive model and \"increase\" for the GMM-disjunctive model, respectively. Nine out of 10 CCOPDs obtained in these models are the same, i.e., \"fruity, citrus\", \"fruity, other than citrus\", \"floral\", \"fragrant\", \"rope\", \"disinfectant carbonic\", \"sharp pungent, acid\", \"light\", and \"warm\". The other odor descriptor is \"sweaty\" for GMM-disjunctive model and \"cool, cooling\" for K-means-disjunctive model. This subtle difference is due to the similarities between these two algorithms. K-means is a particular case of GMM with an isotropic covariance matrix. As the number of clustering centers increases, the results of these two algorithms are still different.