(62) The learning rate (58) is determined according to the selection of the parameters. 5. Experiments 3-Methyladenine dissolve solubility To show the effectiveness of our new ontology algorithms, two experiments concerning ontology measure and ontology mapping are designed below. 5.1. Ontology Similarity Measure Experiment on Plant Data In the first experiment, we use plant “PO” ontology O1 which was constructed in the website http://www.plantontology.org/.

The structure of O1 is presented in Figure 1. P@N (precision ratio; see Craswell and Hawking [24]) is used to measure the quality of the experiment data. Here, we take k = 2, t = 3, ηt = 1, and λ = 0.1. Figure 1 The structure of “PO” ontology. We first give the closest N concepts for every vertex on the ontology graph by experts in plant field, and then we obtain the first N concepts for every vertex on ontology graph by Algorithm 3 and compute the precision ratio. Specifically, for vertex v and given integer N > 0. Let SimvN,expert be the set of vertices determined by experts and it contains N vertices having the most similarity of v. Let  vv1=arg min⁡v’∈V(G)−vfv−fv’, vv2=arg min⁡v’∈V(G)−v,vv1fv−fv’,  ⋮ vvN=arg min⁡v’∈V(G)−v,vv1,…,vvN−1fv−fv’, SimvN,algorithm=vv1,vv2,…,vvN.

(63) Then the precision ratio for vertex v is denoted by PrevN=SimvN,algorithm∩SimvN,expertN. (64) The P@N average precision ratio for ontology graph G is then stated as PreGN=∑v∈V(G)PrevNVG. (65) At the same time, we apply ontology methods in [11–13] to the “PO” ontology. Calculating the average precision ratio by these three algorithms

and comparing the results to Algorithm 3 rose in our paper, part of the data is referred to in Table 1. Table 1 The experiment results of ontology similarity measure. When N = 3, 5, or 10, the precision ratio by virtue of our gradient computation based algorithm is higher than the precision ratio determined by algorithms proposed in [11–13]. In particular, when N increases, such precision ratios are increasing apparently. Therefore, the gradient learning based ontology Algorithm 3 described in our paper is superior to the method proposed by [11–13]. 5.2. Ontology Mapping Experiment on Humanoid Robotics Data For the second experiment, we use “humanoid robotics” ontologies O2 and O3. The structure of O2 and O3 is shown in Figures ​Figures22 and ​and3,3, respectively. The ontology O2 presents the leg joint Anacetrapib structure of bionic walking device for six-legged robot, while the ontology O3 presents the exoskeleton frame of a robot with wearable and power-assisted lower extremities. In this experiment, we take k = 2, t = 4, ηt = 1, and λ = 0.05. Figure 2 “Humanoid robotics” ontology O2. Figure 3 “Humanoid robotics” ontology O3. The goal of this experiment is to give ontology mapping between O2 and O3. We also use P@N precision ratio to measure the quality of experiment.