Matching sensor ontologies through siamese neural networks without using reference alignment

Sensor ontology and sensor ontology matching

Alignment’s evaluation metrics

Generally, precision (P), recall (R), and f-measure (F) are utilized to test the matching results’ quality (Xue, 2020; Xue et al., 2021b; Xue et al., 2021a): (4)${\displaystyle R=\frac{correct\text{\_}found\text{\_}correspondences}{all\text{\_}possible\text{\_}correspondences}}$ (5)${\displaystyle P=\frac{correct\text{\_}found\text{\_}correspondences}{all\text{\_}found\text{\_}correspondences}}$ (6)${\displaystyle F=\frac{2\times R\times P}{R+P}}$ where P and R respectively indicate the accuracy and completeness of the results. P equals 1 denoting all found correspondences are correct, while R equals 1 representing that all correct correspondences are found; F is the harmonic mean of P and R to balance them.

Concept similarity measure

CSM is the kernel technique in the ontology matching domain, which outputs a real number in [0,1] by considering the two input concepts’ information (Xue & Chen, 2019). Generally, CSM can be divided into three categories: string-based CSM, linguistics-based CSM, and structure-based CSM. Furthermore, string-based CSM computes the edit distance by using entities’ identifier, label or comment, linguistics-based CSM outputs the similar value through the external dictionaries or corpora, e.g., WordNet, and structure-based CSM outputs two concepts’ similarity value by taking their adjacent concepts into consideration.

In this work, the CSM is adopted to determine the anchor correspondences from two to-be-matched ontologies, which gets rid of the limitation that most NN-based OMTs rely on reference alignment. The anchor correspondences are utilized to build the training data for the model’s training. In particular, for the effectiveness and efficiency of matching process, the hybrid CSM is used that combines the n-gram similarity (string-based CSM), and the WordNet-based similarity (linguistics-based CSM), since they are greatly effective CSMs in the ontology matching field. The structure-based CSM often owns high time complexity, hence it is not advisable to employ it for building the training data, which could increase the time. Given two tokens t₁ and t₂, n-gram similarity and WordNet-based similarity are respectively defined as follows: (7)${\displaystyle n-gram\left(t_1,t_2\right)=\frac{|f\left(t_1,n\right)\cap f\left(t_2,n\right)|}{min\left(\left|t_1\right|,\left|t_2\right|\right)-n+1}}$ (8)${\displaystyle WordSim\left(t_1,t_2\right)=\underset{w_1\in sen\left(t_1\right),w_2\in sen\left(t_2\right)}{max}\left[sim\left(w_1,w_2\right)\right]}$ where |t₁| and |t₂| are respectively the length of t₁ and t₂, f(t₁, n) represents a set of substrings of t_i with length n.sen(t_i) denotes a set of possible meanings of the token t_i. Here, n is empirically set as 3.

For the quality of used training data, given two concepts c′ and c, theirs’ labels and comments are lowercased, replaced underlines with spaces, and stripped of stop-words, respectively. Finally, four token sets $T_{label}^{\prime }$, $T_{comment}^{\prime }$, T_label, and T_comment are generated for the similarity computing. As the diverse heterogeneity situation of the testing cases that some of the labels or comments are garbled or missed, so the designed CSM is as follows: (9)${\displaystyle sim\left(c^{\prime },c\right)=max\left(si{m}_{label}\left(c^{\prime },c\right),si{m}_{comment}\left(c^{\prime },c\right)\right)}$ where sim_label(c′, c) and sim_comment(c′, c) are respectively the label-based and comment-based similarity value by using concepts’ labels, and comments. To be specific, given two label token sets $T_{label}^{\prime }$ and T_label, represented by T₁ and T₂, then label-based CSM can be computed: (10)${\displaystyle si{m}_{label}\left(c^{\prime },c\right)=\frac{\sum _{i=1}^{\left|T_1\right|}max{\left\{n-gram\left(T_{1,i},T_{2,j}\right),WordSim\left(T_{1,i},T_{2,j}\right)\right\}}_{j=1}^{\left|T_2\right|}}{T_1}}$ where T_1,i and T_2,j respectively represent the |T₁|’s ith token and |T₂|’s jth token. The comment-based CSM is also calculated in this way only the input token sets is different.

The determination of representative concepts

The Degree Centrality (DC) is a measure to compute the significance of nodes in a graph, which is determined by the quantity of connections of the nodes (Bonacich, 2007; Bródka et al., 2011; Algergawy et al., 2015). A node with high DC is more significant than others (Algergawy et al., 2015; Pouriyeh et al., 2018). In order to build effective training data set and improve the matching efficiency, we extract representative concepts (nodes with the high numbers out-degree and int-degree in the class hierarchy graph) from the ontologies to be aligned. All concepts are first sorted using the DC and concepts with high rank will be selected to build the training data set. Empirically, we select the top 30% concepts, which is able to enhance the alignment’s quality and the matching efficiency. It can be seen in Fig. 4, the concepts “Device” and “Sensor”, whose DC are high, are more important than other concepts.

Training data set construction

In this work, the positive samples are build by determining anchor correspondences through the proposed CSM rather than using the reference alignment. The proposed CSM (see Eqs. (9) and (10)) is used to calculate the similarity value among representative concepts. The correspondence with the similarity score higher than the threshold 0.95 is regarded as candidate anchor correspondence and their set is denoted as C_c. However, the threshold based filtering strategy is not able to guarantee that all anchors are correct correspondences. Therefore, a logic reasoning based filtering method (see also ‘Alignment refinement’) is employed on the candidate anchors C_c to enhance the result’s confidence, then, the final anchor correspondence set C_f is obtained. The correspondence in C_f is the positive sample and the correspondence in C_c∖C_f is the negative sample. To balance the dataset to prevent biasing the training process, it is necessary to make the same number of positive and negative samples. Given an anchor correspondence Cor = (c′, c, s, t) ∈ C_f that c′ from ontologies O₁, the negative sample is produced by replacing c′ with a concept c^′′ randomly selected from O₁. Finally, the built data set is employed to train the SNN model.

Matching ontologies through siamese neural network

SNN is a type of NN that inputs two different vectors into two same structure and weights networks and it is used to find the similarity of the inputs by comparing its feature vectors. It can learn semantic similarity as it focuses on learning embedding, bringing the same concepts closely together (Melekhov, Kannala & Rahtu, 2016; Mueller & Thyagarajan, 2016). According to previous research (Bento, Zouaq & Gagnon, 2020; Iyer, Agarwal & Kumar, 2020; Jiang & Xue, 2020), the ancestry nodes are more suitable for ontology matching rather than other nodes. To capture the sensor concepts’ context information, two concepts and their two super-classes, respectively denoted by Concept₁ and Concept₂, are used as two the input. Figure 5 shows an example of the positive sample that semantically consistent concepts “ProcessInput” and “Input” and their two sup-classes are utilized to input. To feed the SNN the numeric representation vectors, the character embeddings (https://github.com/minimaxir/char-embeddings) is utilized whose possible character is a representation vector in 300 dimensions, and the value in each dimension is normalized in the interval [0,1]. In this work, the used structure of networks is an Attention-based Bidirectional Long Short-Term Memory Network (Zhou et al., 2016), which is able to connect future and past contexts of sensor concept pairs while catch the significant part to enhance the model’s performance, and capture the semantic relationships and features of input concept pairs.

Input two context vectors Concept₁ and Concept₂ of c′ and c to the trained SNN, the similarity value is calculated by the distance-based CSM, which is defined as follows: (11)${\displaystyle si{m}_{distance}\left(c^{\prime },c\right)=1-\frac{\left|\right|Featur{e}_1-Featur{e}_2\left|\right|}{\left|\right|Featur{e}_1\left|\right|+\left|\right|Featur{e}_2\left|\right|}}$ where ||⋅|| denotes the Euclidean norm, Feature₁ and Feature₂ are the output feature vectors, $\frac{\left|\right|Featur{e}_1-Featur{e}_2\left|\right|}{\left|\right|Featur{e}_1\left|\right|+\left|\right|Featur{e}_2\left|\right|}$ is the normalized distance, denoted as d. The similarity value can be obtained according to the principle that the smaller the distance, the greater the similarity score. In addition, an effective optimization algorithm, Adam optimizer (Kingma & Ba, 2014; Yi, Ahn & Ji, 2020; Ruder, 2016), and the most commonly used contrastive loss (Koch, Zemel & Salakhutdinov, 2015) for SNN are employed to optimize the weights of networks: (12)${\displaystyle L_{contrastive}=\sum _{i=0}^N\frac{y_i\times d_i+\left(1-y_i\right)\times max\left\{m-d_i,0\right\}}{2N}}$ where N is the number of samples; d is the distance of two output feature vectors; y_i is the sample type that y_i equals 0 denoting the negative sample and 1 representing the positive sample; m is a margin value.

Alignment refinement

By means of the trained SNN, the M × N similarity matrix can be obtained that M and N are the numbers of input concepts of O₁ and O₂, respectively. In particular, the concepts corresponding to the anchor are not inputted into the model for calculation, which decreases the matching time. Each element in the similarity matrix is the similarity score calculated through the (11). After that, an alignment refining method is proposed to enhance the quality of the alignment, which makes use of the sensor ontology’s concept hierarchy to remove the logically conflict correspondences. The alignment refinement method is shown in ?? and the detailed process is as follows: (1) the correspondences are sorted by descending, (2) to ensure the precision of the final alignment, a threshold is adopted to filter the correspondences (3) the correspondence with the greatest similarity is selected, (4) finally, the rest correspondences are chosen one by one if it does not conflict with previous correspondences. To be specific, in Fig. 6, two correspondences ($c_1^{\prime },c_1$) and ($c_2^{\prime },c_3$) conflict that $c_1^{\prime }$ is the subclass of $c_2^{\prime }$ and c₃ is the subclass of c₁, then the correspondence with the lower similarity score will be discarded. Finally, the anchor correspondences and the above correspondences without filtration form the final alignment.

 
_______________________ 
Algorithm 1 Alignment Refinement_______________________________________________________ 
  1:  Input:   The  similarity  matrix  with  row=  M,  column  =N;  the  corre- 
     spondences set Cs  =  {Cor1,Cor2,...,CorM×N},  Cork  =  (c′i,cj,s),  k ∈ 
  {1,2,...,M × N}, i ∈{1,2,...,M}, j ∈{1,2,...,N}; 
  2:  Output: the final alignment; 
  3:  Sort correspondences in descending order according to similarity score, then 
     the sorted correspondences set C′s = {Cor′1,Cor′2,...,Cor′M×N}; 
  4:  A threshold is adopted on C′s to remove a number of correspondences; 
  5:  for h = 1 : C′s.Length do 
 6:     if Cor′h then 
 7:         if h == 1 then 
 8:            Reserve the correspondence Cor′h = (c′i,cj,s); 
  9:            Remove the correspondences in C′s if its row or column is same with 
              the correspondence Cor′h = (c′i,cj,s); 
10:         else 
11:            if Correspondence Cor′h does not conflict with previous correspon- 
              dences then 
12:                Reserve the correspondence Cor′h = (c′i,cj,s); 
13:                Remove the correspondences in C′s if its row or column is same 
                 with the correspondence Cor′h = (c′i,cj,s); 
14:            else 
15:                Remove the correspondence Cor′h = (c′i,cj,s) in C′s; 
16:            end if 
17:         end if 
18:     end if 
19:  end for____________________________________________________________________________