Matching sensor ontologies with unsupervised neural network with competitive learning

Sensor ontology matching

The sensor ontology normatively describes the core concepts and their relationships in the sensor domain (Xue & Chen, 2019), which can be defined as a 3-tuple (C, OP, DP), where C represents the set of classes, that is, the core concepts of the knowledge domain; OP is the set of object properties and DP is the set of data properties, both of which describe the relationships that exist between concepts (Xue & Wang, 2015). Figure 1 illustrates the classes and properties between the different concept modules of the SOSA (Sensor, Observation, Sample and Actuator) ontology, a lightweight core ontology designed for a pervasive target audience and sensor domain. More specifically, the rounded rectangles indicate classes and the dotted arrows indicate properties that describe the relationships between classes. The dotted boxes represent several conceptual modules covering key sensor, actuation and sampling concepts.

Sensor ontology matching is about constructing relationships between sensors, bridging the semantic gap between them, and finding the same sensor entities (Xue & Liu, 2017). The ontology matching process is a function: A = ϕ(O₁, O₂, P, RA), where A is the final alignment; O₁ and O₂ are two ontologies to be matched; P is the experimental parameter; RA is the reference alignment (Chu et al., 2020; Xue, 2020). In general, the final alignment between sensor ontologies’ concepts are dichotomized into disjointness and equivalence. Figure 2 depicts an example of the alignment on two sensor ontologies. Furthermore, the rounded rectangle represents the entities in the sensor ontology. The connections between entities on the same side represent structured information, that is, superclass relationships between entities. The bidirectional arrows represent the mapping between the two entities, that is, equivalence correspondence, and all mappings between the two sensor ontologies are called sensor ontology alignment.

Similarity measure

The similarity measure is a function that takes the entities of two ontologies as input and outputs a real number between (0, 1) to represent their similarity. Since no single similarity measure can guarantee robustness in any matching test, in general, to improve the accuracy of alignment results, sensor ontology matching systems aggregate multiple similarity measures. The subsequent sections describe the similarity measures used in this work.

Lexical-based similarity measure calculates the morphological similarity of two words. Four lexical-based similarity measures are adopted, that is, Jaro distance which uses the number and position of characters needed to convert two strings, Levenshtein distance which calculates the number of operations such as modification, deletion and insertion of characters, n-gram similarity which calculates the distance between two strings using the number of common substrings, and Dice coefficient which measures the similarity of strings. Given two strings s₁ and s₂, formulas are defined as follows:

(1) $$Jaro(s_1,s_2)={\displaystyle \frac{1}{3}\times \left({\displaystyle \frac{com(s_1,s_2)}{|s_1|}+{\displaystyle \frac{com(s_1,s_2)}{|s_2|}+{\displaystyle \frac{com(s_1,s_2)-diff(s_1,s_2)}{com(s_1,s_2)}}}}\right),}$$

(2) $$Levenstein(s_1,s_2)=max\{0,{\displaystyle \frac{min\{|s_1|,|s_2|\}-trans(s_1,s_2)}{min\{|s_1|,|s_2|\}}}\},$$

(3) $$n\text{-}gram(s_1,s_2)={\displaystyle \frac{|f(s_1,n)\cap f(s_2,n)|}{min\{|s_1|,|s_2|\}-n+1},}$$

(4) $$Dice(s_1,s_2)={\displaystyle \frac{2\ast com(s_1,s_2)}{|s_1|+|s_2|},}$$where |s₁| and |s₂| are the lengths of string s₁ and s₂, respectively; com(s₁, s₂) is the number of common characters of s₁ and s₂; diff(s₁, s₂) is the edit distance between s₁ and s₂; trans(s₁, s₂) is the number of common character pairs in different positions; f(s_i, n) represents several substrings of s_i with length n. Based on empirical values, in this work, n is 2.

In addition to measuring the similarity of entities by lexical-based approaches, the semantic similarity between them can also be calculated by linguistics-based measures of similarity values, which determine two words’ similarity by considering their synonym or hypernym relationship. Given two words w₁ and w₂, their similarity is calculated using the WordNet electronic vocabulary database. The definition is as follows:

(5) $$WordNet(w_1,w_2)=\{\begin{array}{cc}1,\hfill & \mathrm{i}\mathrm{f}\mathrm{t}\mathrm{w}\mathrm{o}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{d}\mathrm{s}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{y}\mathrm{n}\mathrm{o}\mathrm{n}\mathrm{y}\mathrm{m}\mathrm{o}\mathrm{u}\mathrm{s},\hfill \\ 0.5,\hfill & \mathrm{i}\mathrm{f}\mathrm{t}\mathrm{w}\mathrm{o}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{d}\mathrm{s}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{h}\mathrm{y}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{n}\mathrm{y}\mathrm{m},\hfill \\ 0,\hfill & \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}.\end{array}$$

Since this work utilizes neural networks as a classification model, as many similarity measure techniques as possible are chosen. Meanwhile, to ensure the quality of matching at different semantic levels, two types of measures are chosen, that is, lexical-based measures and linguistics-based measure.

Ontology matching problem

The semantic correspondence between similar entities in two ontologies is called ontology alignment. According to the literature (Xue et al., 2021b), the ontology alignment can be defined as follows: Given two ontologies O₁ and O₂, the alignment between them is a set of correspondence: $⟨e1,e2,r⟩$, where e₁ ∈ O₁, e₂ ∈ O₂ are matched entity pairs and r denotes the relationship between e₁ and e₂. The relationship is dichotomized into disjointness and equivalence, therefore the ontology matching problem can be transformed as a binary classification problem.

In this work, we construct a binary classification process for the ontology matching problem. First determine a similarity matrix M = [m_ij] _{|O1| * |O2|}, where |O₁| and |O₂| represent the cardinalities of two ontologies O₁ and O₂ respectively. For each pair of potentially aligned entities e₁ and e₂, their similarity is calculated by the multiple similarity measures mentioned above. In order to map the similarity to a binary decision, m_ij denotes the relationship between entities e₁ and e₂, corresponding to values 0 or 1, that is, m_ij = {0, 1}. Furthermore, the ontology matching problem is to investigate whether the two entities to be aligned are equivalent and evaluate the quality of the final alignment based on the reference alignment. For the best quality of the ontology alignment, the objective function is to maximize f-measure (M).

Neural networks are a multi-input connection model that has a widely application in classification problems (Chen, 2020). For the above mathematical model, in this work, we use unsupervised neural networks based on competitive learning to solve this binary classification problem.

Competitive learning mechanism

Traditional neural network models require back propagation algorithms to adjust the network weights when dealing with classification problems, which inevitably requires a large number of labelled training samples to calculate the error. For the sensor ontology, the labelled training samples are matching pairs that have determined the relationship between them. To reduce the reliance on labeled samples and achieve the goal of unsupervised learning, we train the network using the competitive learning strategy, where the output neurons of the network compete with each other and only the winner neuron adjusts the weight vector, while the state of the other neurons is suppressed. The process does not require the expectation value to calculate the error and adjust the weights, therefore unsupervised learning can be achieved. In the next, the pseudo-code for competitive learning is shown by Algorithm 1.

First, the training sample X is input to the network, and each similarity vector X_i is a p-dimensional real vector. The weight vectors corresponding to all neurons in the competitive layer are compared with X. The weight vector that is more similar to X is the winner neuron, and its weight is noted as W_j*. Second, the winner neuron adjusts its weight, and the weights of other neurons remain unchanged. The weight vector adjustment strategy is as follows:

(6) $$\{\begin{array}{c}{\mathbf{W}}_{j^{\ast }}(t+1)={\hat{\mathbf{W}}}_{j^{\ast }}(t)+\eta \left(\hat{\mathbf{X}}-{\hat{\mathbf{W}}}_{j^{\ast }}\right)j=j^{\ast },\hfill \\ {\mathbf{W}}_j(t+1)={\hat{\mathbf{W}}}_j(t)j\ne j^{\ast },\hfill \end{array}$$where η is the learning rate, which is used to adjust the weights and generally decreases with the iteration of the algorithm. j* represents the winner neuron and t represents the generation of the algorithm. After normalization of the weight vector, the algorithm enters the next generation. When the algorithm terminates, the network training ends and the network connected weights are determined.

The framework of unsupervised neural networks

This section demonstrates the framework of the proposal, as shown in Fig. 3. First, extract representative entities from the ontologies to be aligned as the training samples and generate input using the similarity measures, which does not require manual labelling of training samples. In the hierarchy diagram of the ontology, all entities are sorted by the sum of their in-degree and out-degree, and then the entities among them are selected to construct the dataset. In this paper, 30% entities are randomly selected as the dataset. Then, train the network using competitive learning strategy and optimize the network weights. When the training of the network is finished, the remaining entity pairs to be matched are input to the network for classification to complete the ontology alignment. Finally, evaluate the final matching results using the reference alignment.

Experimental configuration

In the experiments, the performance of our approach was tested using the benchmark track provided by the Ontology Alignment Evaluation Initiative (OAEI), as well as real sensor ontologies. Table 1 shows a detailed description of the benchmark test cases, where different series of test cases represent ontologies of different scales and domains. Select a representative case as the training dataset and the remaining cases of the same series are used as the test dataset. Table 2 presents a summary of the real sensor ontologies. Between the two sensor ontologies to be matched, thirty percent of the reference alignment is taken as the train dataset, and the remaining pairs are used as the test dataset. The recall and precision metrics are commonly used to evaluate the performance of matching systems in ontology alignment tasks, and the metrics are defined as follows:

(7) $$precision={\displaystyle \frac{correct\mathrm{\_}found\mathrm{\_}correspondences}{all\mathrm{\_}found\mathrm{\_}correspondences},}$$

(8) $$recall={\displaystyle \frac{correct\mathrm{\_}found\mathrm{\_}correspondences}{all\mathrm{\_}possible\mathrm{\_}correspondences}.}$$

To harmonize precision and recall, we further use the f-measure, which is defined as follows:

(9) $$f\text{-}measure={\displaystyle \frac{2\ast recall\ast precision}{recall+precision}.}$$

Comparison with OAEI’s participants

Figure 4 depicts the comparison between our approach and OAEI’s participants in terms of precision, recall and f-measure. The relevant data are available from OAEI. The figure is divided into four sections corresponding to the experimental results for different series of test cases. In the figure, the vertical axis represents the alignment results, the horizontal axis represents the three evaluation metrics, and the legends represent the different matching systems. As can be seen from the figure, in the four series of test sets, our approach obtains better experimental results than the other matchers. Based on the experimental results, it can be concluded that our proposal is both effective and efficient. It is worth mentioning that the training cases do not need to be manually labelled with positive or negative samples, reducing a significant amount of work regarding pre-processing. In this respect, our approach outperforms other supervised matchers.

Comparison with state-of-the-art ontology matchers

To verify the effectiveness of our approach in matching sensor ontologies, four popular ontology matching strategies were used as comparison groups, based on similarity flooding (SF) similarity (Boukhadra, Benatchba & Balla, 2015), Jaro–Winkler distance (Wang, Qin & Wang, 2017), Levenshtein distance (Behara, Bhaskar & Chung, 2020) and WordNet similarity (Beckwith et al., 2021), respectively. Table 3 exhibits the experimental results of our approach in terms of four sets of real sensor ontology alignment tasks and compares them with the results obtained by other strategies. As can be seen from the table, our approach outperforms the other matching strategies for most of the alignment tasks. In the “SSN-OSSN” task, our method is slightly lower than the Levenshtein distance and Jaro–Winkler distance. The reason is that individual alignment tasks can get better results using only a single similarity measure, and multiple measures become noisy. In addition, our strategy assumes that the alignment is one-to-one. Specifically, an entity in one ontology uniquely maps to another entity in another ontology. However, in some practical tasks, ontology mapping may be one-to-many or many-to-many. This can also explain that our strategy is lower than other strategies in terms of recall.