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...ity is thus independent of the length of the vectors. Its value ranges from 0 (for totally orthogonal vectors) to 1 (for vectors pointing into the same direction). 4.3 FolkRank The PageRank algorithm =-=[34]-=- reflects the idea that a web page is important if there are many pages linking to it, and if those pages are important themselves. We employed the same principle for folksonomies [8]: a resource whic...

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...ty and relatedness are semantic notions, one way of defining them for a folksonomy is to map the tags to a thesaurus or lexicon like Roget’s thesaurus 3 3 http://www.gutenberg.org/etext/22or WordNet =-=[2]-=-, and to measure the relatedness there by means of well-known metrics. The other option is to define measures of relatedness directly on the network structure of the folksonomy. One important reason f...

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...of harvesting the emergent semantics of a folksonomy. In this paper we analyse five measures of tag relatedness: the co-occurrence count, three distributional measures which use the cosine similarity =-=[7]-=- in the vector spaces spanned by users, tags, and resources, respectively, and FolkRank [8], a graph-based measure that is an adaptation of PageRank [9] to folksonomies. Our analysis is based on data ...

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...nd E = {{u, t, r} | (u, t, r) ∈ Y } is the set of hyper-edges. Alternatively, the folksonomy hyper-graph can be represented as a threedimensional (binary) adjacency matrix. In Formal Concept Analysis =-=[32]-=- this structure is known as a triadic context [33]. All these equivalent notions make explicit that folksonomies are special cases of three-mode data. Since measures of similarity and relatedness are ...

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...e taxonomic path length in WordNet. Black bars (top) show the Jiang-Conrath measure of semantic distance. combines the taxonomic path length with an information-theoretic similarity measure by Resnik =-=[35]-=-. We use the implementation of those measures available in the WordNet::Similarity library [36]. It is important to remark that [1] provides a pragmatic grounding of the JiangConrath measure by means ...

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...ons of WordNet to infer corresponding semantic relations in the folksonomy. In WordNet, we measure the similarity by using both the taxonomic path length and a similarity measure by Jiang and Conrath =-=[10]-=- that has been validated through user studies and applications [1]. The use of taxonomic path lengths, in particular, allows us to inspect the edge composition of paths leading from one tag to the cor...

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...studies about folksonomies is Ref. [11], where several concepts of bottomup social annotation are introduced. Ref. [12, 13, 11] provide overviews of the strengths and weaknesses of such systems. Ref. =-=[14, 15]-=- introduce a tri-partite graph representation for folksonomies, where nodes are users, tags and resources. Ref. [16] provides a first quantitative analysis of del.icio.us. We investigated the distribu...

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... distance. combines the taxonomic path length with an information-theoretic similarity measure by Resnik [35]. We use the implementation of those measures available in the WordNet::Similarity library =-=[36]-=-. It is important to remark that [1] provides a pragmatic grounding of the JiangConrath measure by means of user studies and by its superior performance in the context of a spell-checking application....

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...on 6. We discuss our results in the context of ontology learning and related tasks in Section 7, where we also point to future work. 2 Related Work One of the first studies about folksonomies is Ref. =-=[11]-=-, where several concepts of bottomup social annotation are introduced. Ref. [12, 13, 11] provide overviews of the strengths and weaknesses of such systems. Ref. [14, 15] introduce a tri-partite graph ...

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...llows for an evaluation with well-established measures of similarity in existing lexical databases. Budanitsky and Hirst pointed out that similarity can be considered as a special case of relatedness =-=[1]-=-. As both similarity and relatedness are semantic notions, one way of defining them for a folksonomy is to map the tags to a thesaurus or lexicon like Roget’s thesaurus 3 3 http://www.gutenberg.org/et...

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... which states that words found in similar contexts tend to be semantically similar. From a linguistic point of view, these two families of measures focus on orthogonal aspects of structural semiotics =-=[5, 6]-=-. The co-occurrence measures address the so-called syntagmatic relation, where words are considered related if they occur in the same part of text. The contextual measures address the paradigmatic rel...

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...ncept of bottom-up social annotation are introduced. Ref. [15, 18] introduce a tri-partite graph representation for folk4 http://del.icio.us/sonomies, where nodes are users, tags and resources. Ref. =-=[9]-=- provides a first quantitative analysis of del.icio.us. A considerable number of investigations is motivated by the vision of “bridging the gap” between the Semantic Web and Web 2.0 by means of ontolo...

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...s of tag relatedness: the co-occurrence count, three distributional measures which use the cosine similarity [7] in the vector spaces spanned by users, tags, and resources, respectively, and FolkRank =-=[8]-=-, a graph-based measure that is an adaptation of PageRank [9] to folksonomies. Our analysis is based on data from a large-scale snapshot of the popular social bookmarking system del.icio.us. 4 To prov...

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...d in several ways. Most of these definitions use statistical information about different types of co-occurrence between tags, resources and users. Other approaches adopt the distributional hypothesis =-=[3, 4]-=-, which states that words found in similar contexts tend to be semantically similar. From a linguistic point of view, these two families of measures focus on orthogonal aspects of structural semiotics...

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...udge term similarity. In order to adapt these approaches to folksonomies, several distributional measures of tag relatedness have been introduced in theoretical studies or implemented in applications =-=[23, 24]-=-. However, the choice of a specific measure of relatedness is often made without justification and often it appears to be rather ad hoc. A task which depends heavily on quantifying tag relatedness is ...

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...in approaches that analyze the content of the tagged resources with information retrieval techniques [25, 26] and approaches that use collaborative filtering methods based on the folksonomy structure =-=[27]-=-. An example of the latter class of approaches is Ref. [28], where we used our FolkRank algorithm [8] for tag recommendation. FolkRankbased measures will be also covered in this paper. Relatedness mea...

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...ne similarity of contextually associated word pairs more appropriately [. . . ].” The distributional hypothesis is also at the basis of a number of approaches to synonym acquisition from text corpora =-=[22]-=-. As in other ontology learning scenarios, clustering techniques are often applied to group similar terms extracted from a corpus, and a core building block of such procedure is the metric used to jud...

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...ces with information retrieval techniques [25, 26] and approaches that use collaborative filtering methods based on the folksonomy structure [27]. An example of the latter class of approaches is Ref. =-=[28]-=-, where we used our FolkRank algorithm [8] for tag recommendation. FolkRankbased measures will be also covered in this paper. Relatedness measures also play a role in assisting users who browse the co...

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...ies. Scientific publications in this domain are still sparse. Existing work can be broadly divided in approaches that analyze the content of the tagged resources with information retrieval techniques =-=[25, 26]-=- and approaches that use collaborative filtering methods based on the folksonomy structure [27]. An example of the latter class of approaches is Ref. [28], where we used our FolkRank algorithm [8] for...

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...ks in Section 7, where we also point to future work. 2 Related Work One of the first studies about folksonomies is Ref. [11], where several concepts of bottomup social annotation are introduced. Ref. =-=[12, 13, 11]-=- provide overviews of the strengths and weaknesses of such systems. Ref. [14, 15] introduce a tri-partite graph representation for folksonomies, where nodes are users, tags and resources. Ref. [16] pr...

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...ies. Scientific publications in this domain are still sparse. Existing work can be broadly divided in approaches that analyze the content of the tagged resources with information retrieval techniques =-=[25, 26]-=- and approaches that use collaborative filtering methods based on the folksonomy structure [27]. An example of the latter class of approaches is Ref. [28], where we used our FolkRank algorithm [8] for...

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...nodes are users, tags and resources. Ref. [16] provides a first quantitative analysis of del.icio.us. We investigated the distribution of tag co-occurrence frequencies 4 http://del.icio.us/ 2in Ref. =-=[17]-=- and the network structure of folksonomies in Ref. [18]. Tag-based metrics for resource distance have been introduced in Ref. [19]. To the best of our knowledge, no systematic characterization of tag ...

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... a first quantitative analysis of del.icio.us. We investigated the distribution of tag co-occurrence frequencies 4 http://del.icio.us/ 2in Ref. [17] and the network structure of folksonomies in Ref. =-=[18]-=-. Tag-based metrics for resource distance have been introduced in Ref. [19]. To the best of our knowledge, no systematic characterization of tag relatedness in folksonomies is available in the literat...

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...hyper-edges. Alternatively, the folksonomy hyper-graph can be represented as a threedimensional (binary) adjacency matrix. In Formal Concept Analysis [32] this structure is known as a triadic context =-=[33]-=-. All these equivalent notions make explicit that folksonomies are special cases of three-mode data. Since measures of similarity and relatedness are not well developed for three-mode data yet, we wil...

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...two tags t1 and t2 are represented by v1, v2 ∈ R n , then their cosine similarity is defined as: FolkRank v1 · v2 cossim(t1, t2) := arccos ∡(v1, v2) = ||v1||2 · ||v2||2 The PageRank algorithm =-=[1]-=- reflects the idea that a web page is important if there are many pages linking to it, and if those pages are important themselves. The same principle was employed for folksonomies in [13]: a resource...

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...d in several ways. Most of these definitions use statistical information about different types of co-occurrence between tags, resources and users. Other approaches adopt the distributional hypothesis =-=[3, 4]-=-, which states that words found in similar contexts tend to be semantically similar. From a linguistic point of view, these two families of measures focus on orthogonal aspects of structural semiotics...

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...5] provides a model of semantic-social networks for extracting lightweight ontologies from del.icio.us. Other approaches for learning taxonomic relations from tags are provided by Ref. [23, 24]. Ref. =-=[30]-=- presents a generative model for folksonomies and also addresses the learning of taxonomic relations. Ref. [31] applies statistical methods to infer global semantics from a folksonomy. The results of ...

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...studies about folksonomies is Ref. [11], where several concepts of bottomup social annotation are introduced. Ref. [12, 13, 11] provide overviews of the strengths and weaknesses of such systems. Ref. =-=[14, 15]-=- introduce a tri-partite graph representation for folksonomies, where nodes are users, tags and resources. Ref. [16] provides a first quantitative analysis of del.icio.us. We investigated the distribu...

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...emantic similarity to the case where documents are classified in the nodes of an ontology with non-hierarchical components. The measures introduced there were validated by means of a user study. Ref. =-=[21]-=- analyses distributional measures of word relatedness and compares them with measures of semantic relatedness in thesauri like WordNet. They concluded that “even though ontological measures are likely...

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...algorithm [8] for tag recommendation. FolkRankbased measures will be also covered in this paper. Relatedness measures also play a role in assisting users who browse the contents of a folksonomy. Ref. =-=[29]-=- shows that navigation in a folksonomy can be enhanced by suggesting tag relations grounded in content-based features. A considerable number of investigations are motivated by the vision of “bridging ...

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...d metrics for resource distance have been introduced in Ref. [19]. To the best of our knowledge, no systematic characterization of tag relatedness in folksonomies is available in the literature. Ref. =-=[20]-=- generalizes standard tree-based measures of semantic similarity to the case where documents are classified in the nodes of an ontology with non-hierarchical components. The measures introduced there ...

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...ks in Section 7, where we also point to future work. 2 Related Work One of the first studies about folksonomies is Ref. [11], where several concepts of bottomup social annotation are introduced. Ref. =-=[12, 13, 11]-=- provide overviews of the strengths and weaknesses of such systems. Ref. [14, 15] introduce a tri-partite graph representation for folksonomies, where nodes are users, tags and resources. Ref. [16] pr...

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...udge term similarity. In order to adapt these approaches to folksonomies, several distributional measures of tag relatedness have been introduced in theoretical studies or implemented in applications =-=[23, 24]-=-. However, the choice of a specific measure of relatedness is often made without justification and often it appears to be rather ad hoc. A task which depends heavily on quantifying tag relatedness is ...

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...pproaches for learning taxonomic relations from tags are provided by Ref. [23, 24]. Ref. [30] presents a generative model for folksonomies and also addresses the learning of taxonomic relations. Ref. =-=[31]-=- applies statistical methods to infer global semantics from a folksonomy. The results of our paper are especially relevant to inform the design of such learning methods. 3 Folksonomy Definition and Da...

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...tion of tag co-occurrence frequencies 4 http://del.icio.us/ 2in Ref. [17] and the network structure of folksonomies in Ref. [18]. Tag-based metrics for resource distance have been introduced in Ref. =-=[19]-=-. To the best of our knowledge, no systematic characterization of tag relatedness in folksonomies is available in the literature. Ref. [20] generalizes standard tree-based measures of semantic similar...

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... of a folksonomy. In this paper, we consider the three following measures for the relatedness of tags: the co-occurrence count, the cosine similarity [23] of co-occurrence distributions, and FolkRank =-=[13]-=-, a graph-based measure that is an adaptation of PageRank [20] to folksonomies. Our analysis is based on data from a large-scale snapshot of the popular social bookmarking system del.icio.us 4 . To pr...

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... which states that words found in similar contexts tend to be semantically similar. From a linguistic point of view, these two families of measures focus on orthogonal aspects of structural semiotics =-=[5, 6]-=-. The co-occurrence measures address the so-called syntagmatic relation, where words are considered related if they occur in the same part of text. The contextual measures address the paradigmatic rel...