Similarity, one of six Gestalt principles, is one of the most intuitive ways to perceive the world and categorise the objects surrounding us. The notion of similarity plays an important role in many areas, and it is important to simulate human perception of similarity in order to obtain satisfying results in various applications. We draw our inspiration from Tversky's work on similarity and define property-based similarity for ontological concepts taking into account their common and distinctive features and their values. We also discuss some possible ways to improve the property-based similarity.
It is inherent to human nature to try to categorize objects surrounding us, finding patterns and forms they have in common. One of the most intuitive ways to relate two objects is through their similarity. Similarity is one of the six Gestalt principles which guide the human perception of the world, the remaining ones being: Proximity, Closure, Good Continuation, Common Fate, and Good Form.
According to Merriam Webster “similarity” is a quality that makes one person or thing like another and “similar” means having characteristics in common. There are many ways in which objects can be perceived as similar, such as having similar color, shape, size, texture etc. But if we move away from just visual stimuli, we can apply the same principles to define the semantic similarity of two objects. This leads to a similarity based on features these two objects have in common, and consequently, the lack of distinctive features characterising each object.
The concept of semantic similarity can be encountered in various fields, from
Natural Language Processing (NLP) and Information Retrieval to Semantic Web. In this
work we deal with the semantic similarity of concepts in domain ontologies
Our inspiration comes from Tversky’s work on Features of Similarity (Tversky, 1977) and we try to apply his ideas to similarity among ontological objects. More precisely, two objects are similar if they both are defined having the same properties with the same values. In addition to this simple notion of similarity, we explore how this similarity can be improved by considering relevance for properties or relevance for values or hierarchical relationships among values, Throughout this work we use domain of recipes to provide examples and explain our approach and reflections.
The rest of the paper is organised as follows. In Section 2, we provide a brief background on ontologies for knowledge representation and on the treatment of properties in OWL. We give the details of how to calculate the property-based similarity for instances in the domain ontology in Section 3 and then we look into some possible ways to improve the property-based similarity in the ontology in Section 4. We summarise the most relevant related work which regards the semantic similarity in Section 5. Finally, we conclude in Section 6. 2
In various fields, from e-commerce and e-learning to cultural heritage, medicine, digital
libraries etc., it is possible to describe the concepts of the domain by using the properties
of these concepts and their respective values. The ones that immediately come to mind
are ontologies
In this work we deal with ontologies, powerful and expressive formalisms which make it possible to explicitly specify domain elements and their properties, as well as relationships which exist among domain elements. Also, rigorous reasoning mechanisms are associated with ontologies. One standard formalism for representing ontologies is OWL.1
Throughout this work we would use domain of recipes to provide examples and explain our approach and reflections. 2.1
In ontologies expressed in OWL properties are used to describe domain elements and express their features. There are two kinds of properties in OWL: (i) object properties describing relations among individuals and (ii) data type properties providing relations among individuals and data type values. Object properties and datatype properties are defined as instances of the built-in OWL classes owl:ObjectProperty and owl:DatatypeProperty, respectively. Both are subclasses of the RDF class rdf:Property. Here, we only consider object properties, and leave the treatment of data type properties (such as literal values) for future analysis, since it is more complex.
The property axiom is used to define the characteristics of a property. Usually, it defines its domain and range. rdfs:domain links a property to a class description, whereas rdfs:range links a property to either a class description or a data range. For example: <owl:ObjectProperty rdf:ID="has_ingredient">
<rdfs:domain rdf:resource="#Recipet"/> 1 http://www.w3.org/TR/owl-ref
<rdfs:range rdf:resource="#Food"/> </owl:ObjectProperty> defines a property has ingredient which connects the elements of Recipe class to the elements of Food class.
Equivalent properties are defined with owl:equivalentProperty.
Properties can be explicitly defined for the classes and can be used to define classes with property restrictions. Our approach to similarity is best illustrated when considering instances in the ontology, hence we will provide here a brief description of properties for instances.
An instance in the ontology are characterised by its class membership, individual identity and property values. An instance inherits its properties from the classes it is an instance of and it has a specific value associated to each property. For example: <Recipe rdf:ID="Herbed_Asparagus"> <has_ingredient rdf:resource="#Asparagus"/> <has_ingredient rdf:resource="#Parmesan"/> <has_ingredient rdf:resource="#Herbs"/> <has_origin rdf:resource="#Italy"/> <suitable_for_diet rdf:resource="#"Vegetarian"/> </Recipe> defines a recipe Herbed Asparagus which has ingredients: asparagus, parmesan and herbs, originates from Italy and is suitable for vegetarians.
First of all, let us have a look at an example which should clarify the basics of our approach. We consider the domain of recipes where properties such as has ingredient, has origin, suitable for diet are defined. These properties have one or more values assigned to them. Intuitively, the similarity among recipes depends on the propertyvalue pairs they have in common. Consider for example the following recipes: Asparagus Parmigiana and Herbed Asparagus With Parmesan Cheese. They both have ingredients: Asparagus, Butter, Parmesan, Pepper among others and are both suitable for vegetarian diet. On the other hand, Indian Style Chicken has only Butter in common with any of them and is not suitable for vegetarians. So the asparagus dishes are definitely more similar among themselves than any of them with the chicken dish.
Hence, in order to determine similarity among two objects, we want to consider both, their common features and distinctive features for each of them. To this aim we use Tversky’s feature-based model of similarity (Tversky, 1977): simT (O1; O2) =
( (O1) \ (O2)) ( (O1) n (O2)) + ( (O2) n (O1)) + ( (O1) \ (O2)) : (1) where (O) is the function describing all the relevant features of the object O, and ; ; 2 R are constants which permit di erent treatment of the various components. For = 1 common features of the two objects have maximal importance and for = non-directional similarity measure is obtained. In our approach we have = = = 1.
We will be using the following notation: – common features of O1 and O2: cf(O1; O2) = (O1) \ (O2), – distinctive features of O1: df(O1) = (O1) n (O2) and – distinctive features of O2: df(O2) = (O2) n (O1).
Using this notation and setting = = = 1 the formula (1) becomes:
Since each of the domain objects has a number of property-value pairs describing
it, for each property p we will have to calculate how much it is responsible for common
features among these objects, as well as for distinctive features of each of them. We
denote these values by cfp, df1p and df2p. We consider equal the properties defined with
owl:EquivalentProperty.
In this work we present our approach only for instances of classes, although it can be
extended to classes defined with their properties and to classes defined as property
restrictions (see
Let us assume that the objects O1 and O2 have properties p1; : : : ; pn in common. We can repeat the above process for each property pi; i = 1; : : : ; n.
Now, there are two possible ways to calculate similarity between O1 and O2. First, we can obtain all common and distinctive features of O1 and O2: cf(O1; O2) = in=1cfpi df(O1) = in=1df1pi df(O2) = in=1df2pi where n is the number of properties O1 and O2 have in common. The similarity between two instances O1 and O2 is then calculated using the formula (2): sim(O1; O2) =
cf(O1; O2) df(O1) + df(O2) + cf(O1; O2) :
This method for property-based similarity of objects in the ontology was first
introduced in
Second, we can calculate partial similarities w.r.t. each property pi; i = 1; : : : ; n: simpi =
cfpi df1pi + df2pi + cfpi sim(O1; O2) = in=1simpi : and then use these similarities to calculate the total similarity between O1 and O2 as:
The above presented base case property-based similarity provides high rates of
similarity among objects which can be used in many applications. We still did not perform
the thorough evaluation but we evaluated it in the field of user interest propagation and
obtained very satisfying results
When defining the concepts of a domain, not all the properties play an equal role. Hence, it is possible to introduce the relevance of properties and assign di erent importance to di erent properties in the domain. Actually, the relevance of a property can be considered as the capacity of the property to determine the similarity between two entities. For example, in the recipe domain, the property has ingredient is far more important than has author and the two recipes with the same ingredients would be considered more similar than the two recipes with the same author. So, the property has ingredient would have a higher relevance factor than prophas author.
There are various approaches to calculation of property relevance in a domain. It can be declared a priori and although e ective, this solution may not be very feasible for a huge domain. Also, it is possible to introduce an automatic method to determine the relevance of properties. One possibility is to compute the similarity of concepts and then to calculate the relevance factor for each property as the square of the average similarity between concepts with the same value for that property. 4.2
First of all, some aspects of the domain can be seen as properties, as well as underlying hierarchy. So the question is, which way of modelling of the domain would provide better similarity with human judgement. For example, in the recipes domain, the concepts corresponding to dish type can be easily organised into a hierarchy and we can have all the instances be instances of certain Dish Type classes. On the other hand, we can simply have a property dish type and have all the recipes be instances of Recipe. 4.3
One of the problems with the approach in which all the values for properties are treated equally is that they might not contribute to the overall similarity with the same degree, since some values might be more important in a certain context than the other. For example, if we consider recipes and the has ingredient the values beef or asparagus would be more important than salt or pepper. Hence, we come to the point where we might need to introduce relevance for values, along the lines for relevance for properties. These would have to be proposed by domain experts or calculated by an algorithm designed for this purpose. 4.4
Another possible improvement of property based similarity is to take into account the underlying hierarchy which might exist among the concepts used as values for properties. For example, if we consider recipes and the property has ingredient, one recipe can have ingredient Fusilli and the other one Spaghetti. Although these two concepts are not equal, they could be considered equal or equal to a certain degree (e.g. 80% equal), since they are both types of pasta, and are descendants of Pasta concept. So it might be possible to consider “almost equal” direct descendants of a certain concept and even less equal second degree descendants of a certain concept. 5
There are various approaches to calculating similarity among concepts, depending on the data structure used to represent the domain and on the amount and type of data available about the concepts of the domain. The principal approaches to similarity calculation are the following: (i) information content-based methods, (ii) distance-based methods and (iii) feature-based methods. Various hybrid methods combine some of the above methods.
In his seminal paper,
The origins of the distance-based approach go back to
A semantic similarity measure for OWL objects introduced by
The similarity measure introduced by Zadeh and Reformat (2013) is similar to ours in the sense that it uses Tversky’s feature-based model for calculating similarity and then calculates object’s common and distinctive features by observing all the relations the objects have in the given ontology.
In the realm of “Conceptual Spaces” proposed by
Recently, Conceptual Spaces have been integrated with ontological formalisms to
form hybrid knowledge bases by
In this work we present an approach to calculate similarity based on properties defined
in an ontology, as well as insights on which other factors can be included to improve
this similarity in di erent contexts. We limited ourselves to presenting the approach
only for the instances in the ontology, although the approach can be applied to classes
and classes defined as property restrictions as well. In addition, this approach can be
applied to linked open data
In the case presented here, the prerequisite is the ontology with explicitly defined properties for classes, rather than only a simple taxonomy of concepts. We only dealt with object type properties in this work, since data type properties, such as literals, require more complex analysis.
One of the limitations of the present approach, known for Tversky’s notion of similarity, is that in the case of concepts with few properties defined for them, is is possible that some concepts would be equally similar to the concepts which in reality have different degrees of similarity with them. This problem can be overcome by enlarging the knowledge base with as many properties as possible for each concept. Also, by assigning relevance to certain properties, the more important features would be taken into account.
The evaluation of the approach on di erent datasets is being carried out and would be published elsewhere.
Tversky, A. (1977). Features of similarity. Psychological Review, 84(4):327–352. Wu, Z. and Palmer, M. (1994). Verbs semantics and lexical selection. In 32nd Annual Meeting on Association for Computational Linguistics, pages 133–138. Association for Computational Linguistics.
Zadeh, P. D. H. and Reformat, M. (2013). Assessment of semantic similarity of concepts defined in ontology. Information Sciences, 250:21–39.