Concept2vec: Metrics for Evaluating Quality of Embeddings for Ontological Concepts
Although there is an emerging trend towards generating embeddings for primarily unstructured data, and recently for structured data, there is not yet any systematic suite for measuring the quality of embeddings. This deficiency is further sensed with respect to embeddings generated for structured data because there are no concrete evaluation metrics measuring the quality of encoded structure as well as semantic patterns in the embedding space. In this paper, we introduce a framework containing three distinct tasks concerned with the individual aspects of ontological concepts: (i) the categorization aspect, (ii) the hierarchical aspect, and (iii) the relational aspect. Then, in the scope of each task, a number of intrinsic metrics are proposed for evaluating the quality of the embeddings. Furthermore, w.r.t. this framework multiple experimental studies were run to compare the quality of the available embedding models. Employing this framework in future research can reduce misjudgment and provide greater insight about quality comparisons of embeddings for ontological concepts.
Although the Web of Data is growing enormously
Ontological concepts play a crucial role in (i) capturing the semantics of a particular domain, (ii) typing entities which bridge a schema level and an instance level, and (iii) determining valid types of sources and destinations for relations in a knowledge graph. Thus, the embeddings of the concepts are expected to truly reflect characteristics of ontological concepts in the embedding space. For example, the hierarchical structure of concepts is required to be represented in an embedding space. With this respect, an existing deficiency is the lack of an evaluation framework for comprehensive and fair judgment on the quality of the embeddings of concepts. This paper is particularly concerned with evaluating the quality of embeddings for concepts. It extends the state of the art by providing several intrinsic metrics for evaluating the quality of the embedding of concepts on three aspects: (i) the categorization aspect, (ii) the hierarchical aspect, and (iii) the relational aspect. Furthermore, we randomly sampled entities from DBpedia and ran a comparison study on the quality of generated embeddings from Wikipedia versus DBpedia using recent embedding models.
This paper is organized as follows: Section 2 reviews the state-of-the-art research about evaluating the quality of embeddings. Section 3 presents the preliminaries and problem statement. Then, Section 4 shortly represents popular embedding models. Section 5 proposes three evaluation tasks for measuring the quality of embeddings for ontological concepts. Each task is equipped with several intrinsic metrics which qualitatively and quantitatively assess quality. Moreover, each task exhibits an experimental study on various embedding models. We discuss the general observations concluded from the experimental study in Section 6. Last, we close with the conclusion and future work.
2 Related Work
Recent movement in the research community is more weighted towards learning high quality embeddings or employing embeddings in various applications, and the area of evaluating or benchmarking quality of embeddings in a systematic manner is less studied. However, there are a few papers about studying evaluation methods for the unsupervised learning of embeddings, but they are limited to unstructured corpora [2, 3, 18]. Thus, there is a tangible research gap regarding evaluation methods for embeddings learned from a knowledge graph. To the best of our knowledge, this is the first paper which explores and discusses intrinsic metrics for measuring quality from various dimensions over the embeddings learned out of a knowledge graph. Baroni’s work , extending his previous research , is pioneering state-of-the-art literature which provides a systematic comparison by extensive evaluation on a wide range of lexical semantics tasks and the application of diverse parameter settings. The evaluation metrics which it utilizes are the following. Semantic relatedness: Asking human subjects to measure the semantic relatedness of two given words on a numerical scale. The query inventory contained both taxonomic relations (e.g. cohyponymy relation king/queen) and broader relationships (e.g. syntagmatic relations amily/planning). Synonym detection: In this task, multiple choices are displayed for a given target word and the most similar word is detected by comparing the cosine similarity of the target word and all the choices. Concept categorization: In this task, a set of concepts are given, then the task is to group them into a taxonomic order (e.g., helicopters and motorcycles belong to the vehicle class while dogs and elephants belong to the mammal class). Selectional preference: Provides a list of noun-verb pairs, then it evaluates the relevance of a noun as a subject or as the object of the verb (e.g., for the given pair people/eat, people receives a high relevance score as the subject of eat and a low score as object). Another relevant work  published in 2015 extends Baroni’s research by employing new metrics: (i) analogy: This task aims at finding a term for a given term so that best resembles a sample relationship (e.g. king:queen, man:woman), (ii) coherence: This task expands the relatedness task to a group evaluation. It assesses the mutual relatedness of a groups of words in a small neighborhood.
3 Problem and Preliminaries
In this section, we present crucial notions utilized throughout the paper and discuss the main challenge of concern in this paper.
An unstructured corpus (i.e. textual data) encompasses a set of words. This set of words is denoted by and a given word contained in this set is denoted as . An embedding model on unstructured data generates a continuous vector representation of dimensions for each word in set , formally , where is the length of the latent vector space. Thus, the word in the space is represented by the vector .
A knowledge graph
3.2 Problem Statement
Figure 1 schematically shows the vectorization process of a knowledge graph to a low dimensional space . A knowledge graph is divided into two levels, (i) an ontology level and (ii) an instance level. All the resources from either level (i.e. classes, properties, and entities) are assigned a vector representation in the embedding space. The embedding models vary in the quality of the generated embeddings. The quality of embeddings is attributed to the true reflection of semantics and structural patterns of the knowledge graph in an embedding space. For example, entities having the same background concept (i.e. common rdf:type) are expected to be clustered close to each other in the embedding space. More importantly, their embedding is expected to be proximate to the embedding of the background concepts (represented in Figure 1). For example, the embeddings of the entities dbr:Berlin, dbr:Paris, dbr:London are expected to be close to the respective concept dbo:City and far from entities such as dbr:Barack_Obama, dbr:Bill_Clinton with the respective concept dbo:President.
This paper is particularly concerned with evaluating the quality of embeddings for concepts (i.e. ontological classes) . Generating high quality embeddings for concepts is extremely important since concepts hold the semantics of knowledge graphs. It is expected that these semantics are properly reflected in the embedding space. For example, the hierarchical semantics (i.e. taxonomic) of concepts is required to be represented in an embedding space. With this respect, an existing deficiency is the lack of an evaluation framework for comprehensive and fair judgment on the quality of the embeddings of concepts. While there has recently been a trend for either generating embeddings or employing existing embeddings in various applications, there is not yet a clear framework for intrinsically measuring the quality of embeddings. This paper contributes in providing several metrics for evaluating the quality of the embedding of concepts from three perspectives: (i) how the embedding of concepts behaves for categorizing their instantiated entities; (ii) how the embedding of concepts behaves with respect to hierarchical semantics described in the underlying ontology; and (iii) how the embedding of concepts behaves with respect to relations (i.e. object properties).
4 State-of-the-art Embedding Models
Matrix factorization methods [9, 15] and neural networks [13, 14] are two common approaches for learning dense embeddings for words. Using neural networks is a recently popularized approach. A neural network model starts the learning process with a random embedding for each word, then it iteratively enhances the quality of the embeddings with the criteria that words sharing a common context are more similar and vice versa. Thus, adjacent words acquire similar embeddings. This approach was popularized after the introduction of word2vec methods by Mikolov [13, 14], where it was shown that the semantic patterns and regularities are well captured by the generated embeddings. The word2vec methods feature two models for generating embeddings: (i) a skip-gram model and (ii) a continuous bag of words (CBOW) model. Shortly after, an outperformed model called GloVe  was introduced. However, all of these models learn embeddings out of the unstructured data. RDF2Vec  is a recent state-of-the-art embedding model which learns embeddings out of the knowledge graph. In the following, we briefly describe each model.
The skip-gram model [13, 14] learns two separate embeddings for each target word , (i) the word embedding and (ii) the context embedding. These embeddings are used to compute the probability of the word (i.e. context word) appearing in the neighborhood of word (i.e. target word), . The skip-gram algorithm (with negative sampling) starts traversing the corpus for any given target word . For any occurrence of the target word, it collects the neighboring words as positive samples and chooses noise samples as negative sampling (i.e., non-neighbor words). Eventually, the objective of the shallow neural network of the skip-gram model is to learn a word embedding maximizing its dot product with context words and minimizing its dot products with non-context words.
Continuous Bag of Words (CBOW) Model
The CBOW model is roughly similar to the skip-gram model as it is also a predictive model and learns two embeddings for each word (a word embedding and a context embedding). The difference is that CBOW predicts the target word from the context words as . Thus, the input of the neural network is composed by the context words (e.g. for the context with length 1); then, the algorithm learns the probability of appearing in the given context. Although the difference between these two algorithms is slight, they showed different performance in various tasks. State-of-the-art evaluations suggest that these algorithms are individually suited to particular tasks.
The GloVe model  is a global log-bilinear regression model for the unsupervised learning of word embeddings. It captures global statistics of words in a corpus and benefits the advantages of the other two models: (i) global matrix factorization and (ii) local context window methods. Differently from the skip-gram model, GloVe utilizes the statistics of the corpus, as it relies on global co-occurrence counts. The GloVe model outperforms the models above for word similarity, word analogy, and named entity recognition tasks.
RDF2Vec  is an approach for learning embeddings of entities in RDF graphs. It initially converts the RDF graphs into a set of sequences using two strategies: (i) Weisfeiler-Lehman Subtree RDF Graph Kernels, and (ii) graph random walks. Then, word2vec is employed for learning embeddings over these produced sequences. This approach is evaluated against multiple machine-learning tasks such as instance classification.
TransE, TransH, TransR
The TransE  and TransH  models assume that the embeddings of both the entities and relations of a knowledge graph come from the same semantic space whereas the TransR  considers two separate embedding spaces for entities and relations. The experimental study shows the superiority of the TransR approach.
5 Evaluation Scenarios
In this section, we introduce three tasks which individually measure the quality of the concept embeddings from three distinct dimensions: (i) the categorization aspect, (ii) the hierarchical aspect, and (iii) the relational aspect. Furthermore, each task is equipped with multiple metrics for evaluating a given quality dimension from various angles (i.e. quantitatively, qualitatively, subjectively, and objectively).
5.1 Task 1: Evaluating the Categorization Aspect of Concepts in Embeddings
Ontological concepts categorize entities by typing them, mainly using rdf:type
In the context of unstructured data, this metric aligns a clustering of words into different categories . We redefine this metric in the context of structured data as how well the embedding of a concept performs as the background concept of the entities typed by it (). To quantify this metric, we compute the averaged vector of the embeddings of all the entities having type (represented in Equation 1) and then compute the cosine similarity of this averaged vector and the embedding of the concept (formulated in Equation 2). Please note that throughout the paper represents the cosine similarity between the two vectors and , which is computed as .
From the DBpedia ontology, we selected 12 concepts, which are positioned in various levels of the hierarchy.
Furthermore, for each concept, we retrieved 10,000 entities typed by it (in case of unavailability, all existing entities were retrieved).
For each concept class, we retrieved 10,000 instances and their respective labels; in case of unavailability, all existing instances were retrieved.
Then, the embeddings of these concepts as well as their associated instances were computed from the embedding models: (i) skip-gram, and (ii) CBOW on both Wikipedia and DBpedia (using the RDF2Vec package
For each given concept, we measure its categorization score by computing the cosine similarity of its embedding with the averaged embeddings of its instances. Tables 1 and 2 present the results achieved for categorization scores on our collected data set. Overall, the skip-gram model outperforms the CBOW model (except in two cases). Furthermore, the embeddings learned from Wikipedia outperform the embeddings from DBpedia (again except in two cases).
|Data Set||Embedding Model||Place||Person||Organization||Country||City||President|
|Data Set||Embedding Model||Book||Film||Actor||Company||University||Writer|
This metric which was introduced in  measures whether or not a group of words adjacent in the embedding space are mutually related. Commonly, this relatedness task has been evaluated in a subjective manner (i.e. using a human judge). While in the context of structured data we define the concept of relatedness as the related entities which share a background concept, a background concept is the concept from which a given entity is typed (i.e. inherited). For example, the entities dbr:Berlin and dbr:Tehran are related because both are typed by the concept dbo:City. We utilize qualitative as well as quantitative approaches to evaluate the coherence metric. In the following, we elaborate on each approach.
Quantitative evaluation of coherence score: Suppose we have a pool of entities with various background concepts and we cluster this pool using the similarity of the embedding of entities. The expectation is that entities with a common background concept are clustered together and, more importantly, the embedding of the background concepts should be the centroid of each cluster. We follow this scenario in a reverse order. For the given concept and the given radius , we find the -top similar entities from the pool (having the highest cosine similarity with ). Then, the coherence metric for the given concept with the radius is computed as the number of entities having the same background concept as the given concept; formally expressed as:
Qualitative evaluation of coherence score: Commonly, the coherence metric has been evaluated by a qualitative approach. For example,  uses a two-dimensional visualization of word embeddings for measurement by human judges in the relatedness task. Apart from visualization, another way of qualitative evaluation is providing samples of grouped entities and a concept to a human subject to judge their relatedness.
In this experiment, we quantitatively measure the coherence score. To do that, we initially have to prepare a proper data set. Hence, for each concept, we sampled a batch containing 20 entities from the data set collected in the previous task. Then, all of these batches are mixed up as a single data set. This data set is utilized in the whole of this experiment. To measure the coherence score for every given concept, we found the top-10 entities (i.e. the radius equals to 10) which are the closest entities to the given concept (using cosine similarity over the associated embeddings). The coherence score is computed by counting the number of entities out of the top-10 entities which are typed by the given concept. For example, for the given concept dbo:Actor, if three entities out of the top-10 closest entities are not of the type dbo:Actor (e.g. dbr:Berlin), then the coherence score of dbo:Actor is 0.7. Tables 3 and 4, 5, 6 show the results achieved for the coherence scores for the 12 chosen concepts in the compiled data set. The radius set in the experiments showed in Tables 3 and 4 is 10 and in Tables 5 and 6 is 20. Within the longer radius (i.e. ), the coherence scores are increased (except for a few cases) especially for the super concepts (e.g. Person, Place and Organisation). Moreover, in most cases the skip-gram model performs better. Last, the embeddings learned from Wikipedia have the higher coherence scores than the embeddings learned from DBpedia.
|Data Set||Embedding Model||Place||Person||Organization||Country||City||President|
|Data Set||Embedding Model||Book||Film||Actor||Company||University||Writer|
|Data Set||Embedding Model||Place||Person||Organization||Country||City||President|
|Data Set||Embedding Model||Book||Film||Actor||Company||University||Writer|
5.2 Task 2: Evaluating Hierarchical Aspect of Concepts in Embeddings
There is a relatively longstanding research for measuring the similarity of two given concepts either across ontologies or inside a common ontology [12, 19, 4]. Typically, the similarity of concepts is calculated at the lexical level and at the conceptual level. However, our assumption here is that our underlying knowledge graph has a well-defined ontology as the background semantics. The concepts of the given ontology are positioned in a hierarchical order and share various levels of semantics. We present three metrics which can be employed for evaluating the embeddings of concepts with respect to the hierarchical structure and the semantics.
Absolute semantic error
We introduce the metric absolute semantic error which quantitatively measures the quality of embeddings for concepts against their semantic similarity. The semantic similarity between the two given concepts and is denoted by and can be measured by an state-of-the-art methodology [6, 7, 12, 19]. Ideally, this similarity score should be approximate to the similarity score of embeddings corresponding to those concepts denoted by (please note that this score is calculated by cosine similarity). Therefore, this expected correlation can be formally represented as . For example, the semantic similarity between the two concepts dbo:President and dbo:City is almost zero; so it is expected that their vectors reflect the similar pattern as . An intuitive methodology for measuring semantic similarity between two concepts is to utilize the distance between them in the hierarchical structure . Because, intuitively, the concepts which are placed closer in the hierarchy are more similar. In contrast, concepts placed further from each other are more dissimilar. Thus, by increasing the length of the path between two concepts in the hierarchy, their dissimilarity is increased. However, independent of the kind of methodology employed for computing the semantic similarity score, the absolute semantic distance is computed as the difference between the semantic similarity score and the similarity score of embeddings , which is formally represented in Equation 4. The higher the value of , the lower the quality of the embeddings and vice versa.
Semantic Relatedness metric
We tune this metric from [2, 18] for knowledge graphs by exchanging words for concepts. Typically, this metric represents the relatedness score of two given words. In the context of a knowledge graph, we give a pair of concepts to human judges (usually domain experts) to rate the relatedness score on a predefined scale, then, the correlation of the cosine similarity of the embeddings for concepts is measured with human judge scores using Spearman or Pearson.
The embeddings of all concepts of the knowledge graph can be represented in a two-dimensional visualization. This approach is an appropriate means for qualitative evaluation of the hierarchical aspect of concepts. The visualizations are given to a human who judges them to recognize patterns revealing the hierarchical structure and the semantics.
We chose three high level concepts from the DBpedia ontology
5.3 Task 3: Evaluating Relational Aspect of Concepts in Embeddings
There are various applications in information extraction, natural language understanding, and question answering involved in extracting either implicit or explicit relationships between entities [16, 8, 1]. A major part of evaluating the state-of-the-art approaches for relation extraction is the validation task as whether or not the inferred relation is compatible with the type of entities engaged. For example, the relation capital is valid if it is recognized between entities with the types country and city. This validation process in a knowledge graph is eased by considering the axioms rdfs:domain and rdfs:range of the schema properties and rdf:type of entities. The expectation from embeddings generated for relations is to truly reflect compatibility with the embeddings of the concepts asserted in the domain and range. With this respect, we present two metrics for evaluating the quality of the embeddings for concepts and relations.
This metric presented in [2, 3] assesses the relevance of a given noun as a subject or object of a given verb (e.g. people-eat or city-talk). We tune this metric for knowledge graphs as pairs of concept-relation which are represented to a human judge for the approval or disapproval of their compatibility.
Semantic transition distance
The inspiration for this metric comes from [14, 13], where Mikolov demonstrated that capital cities and their corresponding countries follow the same distance. We introduce this metric relying on an objective assessment. This metric considers the relational axioms (i.e. rdfs:domain and rdfs:range) in a knowledge graph. Assume that the concept is asserted as the domain of the property and the concept is asserted as its range. It is expected that the sum of the embeddings of the and conducts to the embeddings of the concept . In other words, the transition distance denoted by measures the similarity (e.g. cosine similarity) of the destination embedding and the conducted point (via ), formally expressed as:
For this task, we selected 12 object properties from the DBpedia ontology along with their corresponding domain and range concepts. Then, we measured the transition distances which are reported in Table 7. The comparative results show that the skip-gram model particularly on Wikipedia outperforms the others. Interestingly, the transition distance is very high for the properties which have the shared concepts in the domain and range positions.
|largestCountry||Populated P.||Populated P.||0.702||0.766||0.878||0.865|
As it has been observed through various evaluation tasks, there is no single embedding model which shows superior performance in every scenario. For example, while the skip-gram model performs better in the categorization task, the CBOW model performs better for the hierarchical task. Thus, one conclusion is that each of these models is suited for a specific scenario. Then, depending on the extrinsic task which consumes these embeddings, the most appropriate model should be selected. The other conclusion is that it seems that each embedding model captures specific features of the ontological concepts, so integrating or aligning these embeddings can be a solution for fully capturing all of these features. Although our initial expectation was that the embeddings learned from the knowledge graph (i.e. DBpedia) should have higher quality in comparison to the embeddings learned from unstructured data (i.e. Wikipedia), in practice we did not observe that as a constant behaviour. We attribute this issue to two matters: (i) the weaknesses of the RDF2Vec approach for generating embeddings of a knowledge graph, and (ii) the fact that Wikipedia is larger than DBpedia. The RDF2Vec approach provides a serialization on the structure of the graph (i.e. the local neighborhood of a given node is serialized) and then it runs word2vec to generate embeddings. Here, in fact there is no any discrimination between the concepts, properties, and instances, whereas the ontological resources (i.e. concepts and properties) may be required to be reinforced in the embedding model, or their embeddings have to be learned separately from the instance level. Additionally, Wikipedia is larger than DBpedia, therefore it naturally provides richer context for the embedding models, i.e. the richer context, the higher the quality of embeddings. Generally, we concluded that the current quality of the embeddings for ontological concepts is not in a satisfactory state. The evaluation results are not surprising, thus providing high quality embeddings for ontological resources is an open area for future work.
7 Conclusion and Future Work
Since ontological concepts play a crucial role in knowledge graphs, providing high quality embeddings for them is highly important. In this paper, we introduced a framework containing three distinct tasks concerned with the individual aspects of ontological concepts, (i) the categorization aspect, (ii) the hierarchical aspect, and (iii) the relational aspect. Then, for each task a number of intrinsic metrics were proposed for evaluating the quality of the embeddings. Furthermore, we prepared a suitable data set and ran a series of comparison studies on the popular embedding models for ontological concepts. We encourage the research community to utilize this framework in their future evaluation scenarios on embedding models. This will reduce misjudgment and provide greater insight in quality comparisons of embeddings of ontological concepts. We plan to extend this work in two directions. So we only relied on the intrinsic metrics for quality assurance purposes. In the next step, we plan to define multiple extrinsic tasks (e.g. natural language processing tasks or data mining tasks) exclusively tailored to measuring the quality of the embeddings of ontological concepts. We also plan to standardize our benchmarking data set and release it for reuse by the research community.
We acknowledge partial support from the National Science Foundation (NSF) awards: (1) EAR 1520870: Hazards SEES: Social and Physical Sensing Enabled Decision Support for Disaster Management and Response. (2) CNS 1513721: Context-Aware Harassment Detection on Social Media. Any opinions, findings, and conclusions/recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF.
- Currently, there are more than 149 billion triples collected from 9,960 data sets of diverse domains, observed on 14 August 2017 at http://stats.lod2.eu/
- In this work, we reference an RDF knowledge graph.
- Full URI: http://www.w3.org/1999/02/22-rdf-syntax-ns#type
- dbo: is the prefix for http://dbpedia.org/ontology/.
- Source code available at http://data.dws.informatik.uni-mannheim.de/rdf2vec/.
- Available at https://dumps.wikimedia.org/enwiki/.
- Available at http://downloads.dbpedia.org/2015-10/core-i18n/en/.
- The benchmarking datasets are available at: https://github.com/alshargi/Concept2vec
- Please note that the scale of all the diagrams is unified.
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