1 Introduction
A synonymy dictionary, representing synonymy relations between the individual words, can be modeled as an undirected graph where nodes are words and edges are synonymy relations.^{1}^{1}1In the context of this work, we assume that synonymy is a relation of lexical semantic equivalence which is contextindependent, as opposed to ‘‘contextual synonyms’’ [32]. Such a graph, called a synonymy graph or a synonymy network, tends to have a clustered structure [7]. This property is exploited by various graphbased word sense induction (WSI) methods, such as [22]. The goal of such WSI methods is to build a word sense inventory from various networks, such as synonymy graphs, cooccurrence graphs, graphs of distributionally related words, etc. (see a survey by Navigli [19]).
The clusters are densely connected subgraphs of synonymy graph that correspond to the groups of semantically equivalent words or synsets (sets of synonyms). Synsets are building blocks for WordNet [5] and similar lexical databases used in various applications, such as information retrieval [14]. Graphbased WSI combined with graph clustering makes it possible to induce synsets in an unsupervised way [12, 30]. However, these methods are highly sensitive to the structure of the input synonymy graph [30], which motivates the development of synonymy graph expansion methods.
In this paper, we are focused on the data sparseness reduction problem in the synonymy graphs. This problem is inherent to the majority of manually constructed lexicalsemantic graphs due to the Zipf’s law of word frequencies [33]: the long tail of rare words is inherently underrepresented. In this work, given a synonymy graph and a graph clustering algorithm, we compare the performance of two methods designed to improve synset induction. The goal of each method is to improve the final synset cluster structures. Both methods are based on the assumption that synonymy is a symmetric relation. We run our experiments on the Russian language using the Watset stateoftheart unsupervised synset induction method [30].
The contribution of this paper is a study of two principally different methods for dealing with the sparsity of the input synonymy graphs. The former, relation transitivity method, is based on expansion of the synonymy graph. The latter, synset merging method, is based on the mutual similarity of synsets.
2 Related Work
Hope and Keller [12] introduced the MaxMax clustering algorithm particularly designed for the word sense induction task. In a nutshell, pairs of nodes are grouped if they have a maximal mutual affinity. The algorithm starts by converting the undirected input graph into a directed graph by keeping the maximal affinity nodes of each node. Next, all nodes are marked as root nodes. Finally, for each root node, the following procedure is repeated: all transitive children of this root form a cluster and the root are marked as nonroot nodes; a root node together with all its transitive children form a fuzzy cluster.
Van Dongen[3] presented the Markov Clustering (MCL) algorithm for graphs based on simulation of stochastic flow in graphs. MCL simulates random walks within a graph by alternation of two operators called expansion and inflation, which recompute the class labels. This approch has been successfully used for the word sense induction task [4].
Biemann [1] introduced Chinese Whispers, a clustering algorithm for weighted graphs that can be considered as a special case of MCL with a simplified class update step. At each iteration, the labels of all the nodes are updated according to the majority labels among the neighboring nodes. The author showed usefulness of the algorithm for induction of word senses based on corpusinduced graphs.
The ECO approach [8] was applied to induce a WordNet of the Portuguese language.^{2}^{2}2http://ontopt.dei.uc.pt
In its core, ECO is based on a clustering algorithm that was used to induce synsets from synonymy dictionaries. The algorithm starts by adding random noise to edge weights. Then, the approach applies Markov Clustering of this graph several times to estimate the probability of each word pair being in the same synset. Finally, candidate pairs over a certain threshold are added to output synsets.
In our experiments, we rely on the Watset synset induction method [30] based on a graph metaclustering algorithm that combines local and global hard clustering to obtain a fuzzy graph clustering. The authors shown that this approach outperforms all methods mentioned above on the synset induction task and therefore we use it as the strongest baseline to date.
Meyer and Gurevich [17] presented an approach for construction of an ontologized version of Wiktionary, by formation of ontological concepts and relationships between them from the ambiguous input dictionary, yet their approach does not involve graph clustering.
3 Two Approaches to Cope with Dictionary Sparseness
We propose two approaches for dealing with the incompleteness of the input synonymy dictionaries of a graphbased synset induction method, such as Watset or MaxMax. First, we describe a graphbased approach that preprocesses the input graph by adding new edges. This step is applied before the synset induction clustering. Second, we describe an approach that postprocesses the synsets by merging highly semantically related synsets. This step is applied after the synset induction clustering step, refining its results.
3.1 Expansion of Synonymy Graph via Relation Transitivity
Assuming that synonymy is an equivalence relation due to its reflexiveness, symmetry, and transitivity, we can insert additional edges into the synonymy graph between nodes that are transitively, synonymous, i.e. are connected by a short path of synonymy links. We assume that if an edge for a pair of synonyms is missing, the graph still contains several relatively short paths connecting the nodes corresponding to these words.
Firstly, for each vertex, we extract its neighbors and the neighbors of these neighbors. Secondly, we compute the set of candidate edges by connecting the disconnected vertices. Then, we compute the number of simple paths between the vertices in candidate edges. Finally, we add an edge into the graph if there are at least such paths which lengths are in the range .
Particularly, the algorithm works as follows:

extract a firstorder ego network and a secondorder ego network for each node;

generate the set of candidate edges that connect the disconnected nodes in , i.e., the total number of the candidates is , where is the number of all 2combinations over the element set and is the set of edges in ;

keep only those edge candidates that satisfy two conditions: 1) there are at least paths in , so no path contains the initial ego node, and 2) the length of each path belongs to the interval .
The approach has two parameters: the minimal number of paths to consider and the path length interval . It should be noted that this approach processes the input synonymy graph without taking the polysemous words into account. Such words are then handled by the Watset algorithm that induces word senses based on the expanded synonymy graph.
3.2 Synset Merging based on Synset Vector Representations
We assume that closely related synsets carry equivalent meanings and use the following procedure to merge nearduplicate synsets:

identify the closely related synsets using the algorithm [20] that considers two objects as closely related if they are mutual neighbors of each other;

merge the closely related synsets in a specific order: the smallest synsets are merged first, the largest are merged later; every synset can be merged only once in order to avoid giant merged clusters.
This approach has two parameters: the number of nearest neighbors to consider (fixed to in our experiments)^{3}^{3}3In general, the method can be parametrized by two different parameters: – the number of nearest neighbors from the word to the word and – the number of nearest neighbors from the word to the word . In our case, for simplicity, we set . and the maximal number of merged synsets , e.g., if then only the first mutual nearest neighbor is merged. It should be noted that this approach operates on synsets that which are already have been discovered by Watset. Therefore, the merged synsets are composed of disambiguated word senses.
4 Evaluation
We evaluate the performance of the proposed approaches using the Watset graph clustering method that shows stateoftheart results on synset induction [30]. Watset is a metaclustering algorithm that disambiguates a (word) graph by first performing egonetwork clustering to split nodes (words) into (word) senses. Then a global clustering is used to form (syn)sets of senses. For both clustering steps, any graph clustering algorithm can be employed; in [30], it was shown that combinations of Chinese Whispers [1] (CW) and Markov Clustering [3] (MCL) provide the best results. We also evaluated the same approaches with the MaxMax [12] method, but the results were virtually the same, so we omitted them for brevity.
4.1 Datasets
We evaluate the proposed augmentation approaches on two gold standard datasets for Russian: RuWordNet [15] and YARN [2]. Both are analogues of the original English WordNet [5].
We used the same input graph as in [30]; the graph is based on three synonymy dictionaries, the Russian Wiktionary, the Abramov’s dictionary and the UNLDC dictionary. The graph is weighted using the similarities from Russian Distributional Thesaurus (RDT) [23].^{4}^{4}4http://russe.nlpub.ru/downloads. To construct synset embeddings, we used word vectors from the RDT.
The lexicon of the input dictionary is different from the lexicon of RuWordNet
[15], which includes a lot of domainspecific synsets. At the same time, the input dataset is the same as the data sources used for boostrapping YARN [2].The summary of the datasets is shown in Table 1: the ‘‘# words’’ column specifies the number of lexical units in the dataset (nodes of the input graph), the ‘‘# synonyms’’ column indicates the number of synonymy pairs appearing in the dataset (edges of the input graph). The problem of dictionary sparsity is the fact that some edges (synonyms) are missing in the input resource. Finally, the ‘‘# synsets’’ column specifies the number of resulting synsets (if applicable).
Resource  # words  # synsets  # synonyms 
Input Synonymy Dictionary: Wiktionary  n/a  
Induced Synsets: Watset MCLMCL  
Induced Synsets: Watset CWMCL  
Gold Synsets: RuWordNet  
Gold Synsets: YARN 
4.2 Quality Measures
We report results according to standard word sense induction evaluation measures: paired precision, recall and Fscore
[16], i.e., each cluster of words yields synonymy pairs. The exact same evaluation protocol was used in the original Watset publication. We perform evaluation on the intersection of gold standard lexicon and the lexicon of the induced resource.4.3 Results
The evaluation results are shown in Figure 3. As one may observe, in the case of the RuWordNet dataset, the method based on the transitivity expansion rendered almost no improvements in terms of recall while dramatically dropping the precision. The second method, based on synset embeddings shows much better results on this dataset: It substantially improves recall, yet at the cost of a drop in precision.
In case of the YARN dataset, the results are similar with the graphbased method significantly lagging behind the vectorbased method. However, in this case, the difference in the observed performance is smaller with some configurations of the graphbased methods approaching the performance of the vectorbased method. Similarly to the first dataset, both methods trade off gains in recall for the drops in precision. Note, however, that the vectorbased method can perform a shift of the ‘‘sweet spot’’ of the clustering approach. While the Fmeasure remains at the same level, it is possible to obtain higher levels of recall, which can be useful for some applications. In the following section, we perform error analysis for each method.
5 Discussion
Perfect synonyms are very rare, which is confirmed by the precisionrecall plot in Figure 3. Both methods insert relations of other types, such as association, cohyponymy, hypernymy, etc. Recall increases with the level of inclusiveness of the configuration; this also causes significant drops in precision. The expansion methods presented in this paper could therefore be more useful for generation of other types of symmetric semantic relations, such as cohyponymy.
5.1 Error Analysis: Synonymy Transitivity
We tried the following configurations of the approach: , . However, only the variations with a small allowed length and a high number of found simple paths yielded viable results.
We explain the quick drops in precision by the fact that no word is a perfect synonym of another [10]. This results in the potential loss of the synonymy relation on each additional transitive node. While having a lot of pertinent edge insertions like ‘‘оказываться–появляться (show up – appear)’’ or ‘‘подтрунивать–стебаться (prank – make jokes)’’, this method introduces such false positives like ‘‘кий–хлыст (cue – whip)’’, ‘‘шеф–царь (boss – tsar)’’, ‘‘солидный–корректный (solid – correct)’’, etc.
One of the reasons of this outcome is that adding new edges increases the size of the communities. They capture neighboring vertices and edges belonging to other communities in the initial graph. Hence, on the one hand, we obtain communities with excess elements, while on the other hand, we observe depleted communities.
5.2 Error Analysis: Synset Merging
The different configurations of the vectorbased method in this plot correspond to the following values of the parameter (the maximum number of merged synsets): 1, 2, 3, 5, 10. Merging more than one synset at a time provides a substantial gain in the recall, yet again at the cost of the precision drop.
Table 2 presents an example of correct merging of synsets. The results of the clustering generate multiple small synsets that refer to the same meaning. Such synsets tend to be mutual nearest neighbors. Top ten most similar synsets to the synset ‘‘cynicism’’ are depicted. In this table, we also indicate whether each neighbor is the mutual nearest neighbor or not. In this example, the method of mutual nearest neighbors perfectly achieves its goal of merging synonymous synsets.
Table 3 presents an example of a wrong merging of synsets on the example of the synset ‘‘zinc, Zn’’. This sample illustrates the reasons behind the drops in precision. While different chemical elements, such as zinc and cobalt are strongly semantically related, they are cohyponyms of the common hypernym ‘‘chemical element’’, and not synonyms, i.e. terms with equivalent meanings. This result is in line with the prior results showing that the majority of the nearest neighbors delivered by the distributional semantic models, such as the skipgram model [18] used in our experiments, tend to be cohyponyms as shown in prior studies [31, 11, 25, 24]. The results presented in both Table 2 and 3 have been manually annotated by a single expert.
Similarity  Related Synset  Predicted  Gold  
1  0.866  беспринципность, цинизм (unprincipledness, cynicism)  true  true 
2  0.856  беспринципность, циничность (unprincipledness, cynicism)  true  true 
3  0.853  кинизм, беспардонность, цинизм (cynicism, shamelessness, cynicism)  true  true 
4  0.734  нахрапистость, нахальство, нахальность, циничность, бесцеремонность, нецеремонность (сheekiness, impudence, cheekiness, cynicism, brusqueness, unceremoniousness)  false  false 
5  0.677  грубость, примитивизм (rudeness, primitivism)  false  false 
6  0.677  хамство, лапидарность, хамёж, топорность, грубость, прямолинейность (rudeness, conciseness, rudeness, clumsiness, rudeness, straightness)  false  false 
7  0.674  безнравственность, беспринципность, злонравие, аморальность (wickedness, lack of principles, depravity, immorality)  false  false 
8  0.671  бесстыдство, непристойность, бессовестность, нахрап (immorality, lack of principle, malice, immorality)  false  false 
9  0.663  скепсис, скептичность (skepticism, skepticism)  true  false 
10  0.661  фанатизм, ханжество (bigotry, bigotry)  false  false 
Similarity  Related Synset  Predicted  Gold  
1  0.676  станнат кобальта, кобальт (cobalt stannate, cobalt)  true  false 
2  0.673  Mg, магний (Mg, magnesium)  true  false 
3  0.670  глиний, крылатый металл, алюминий, Al (сlay, winged metal, aluminum, Al)  false  false 
4  0.663  фосфор, P (phosphorus, P)  true  false 
5  0.646  оксид, окись (oxide, oxide)  false  false 
6  0.631  гидрооксид, гидроокись, гидроксид (hydroxide, hydroxide, hydroxide)  false  false 
7  0.630  ванадий, V (vanadium, V)  true  false 
8  0.628  рибофлавин, лактофлавин, витамин В (riboflavin, lactoflavin, vitamin B)  false  false 
9  0.624  иодат, йодид, йодат (iodate, iodide, iodate)  false  false 
10  0.618  кремний, Si (silicon, Si)  false  false 
5.3 Other Ways to Deal with Sparseness of the Input Dictionary
In this section, we discuss avenues for future work: the prominent approaches that might be useful in addressing the sparseness of the synonym dictionaries.
Lexicalsyntactic patterns for extraction of synonyms.
Hearst patterns are widely used to mine hypernymy relations from text [27]. Such patterns can be also learned automatically [29, 28]. In [21], seven patterns for extraction of synonyms were proposed, which function in the same was as the Hearst patterns for hypernymy extraction. Such synonymy extraction patterns can be also learned automatically in the same fashion as patterns for hypernymy extraction from text [29]. Finally, hypernyms, antonyms, and other relations extracted from text can be used to filter our nonsynonymous candidates.
Global clustering of synsets.
It is possible to find groups of semantically related words (cliquelike structures) and expand synonyms only within such communities with a graph clustering algorithm, such as Chinese Whispers [1]. The current graphbased transitivity expansion method does not consider the structure of the communities of the synonymy graph.
Synonymy detection as an anaphora resolution problem.
Another observation is that synonyms are often not used in the same sentence, but instead used to ensure linguistic variance of the text. In this respect, synonymy extraction task is similar to the anaphora resolution task
[13]. This line of work is related to prior work of [6] in detecting ‘‘bridging mentions’’.Crowdsourcing.
Finally, the last option is simply to improve the quality of the input dictionaries by the means of crowdsourcing [9]. Namely, involving more people to edit Wiktionary that we use as the input data will increase the coverage of the extracted synsets, but largescale crowdsourcing requires a set of elaborated quality control measures.
6 Conclusion
In this paper, we explored two alternative strategies for coping with the problem of inherent sparsity and incompleteness of the synonymy dictionaries. These sparsity issues hamper performance of the methods for automatic induction of synsets, such as MaxMax [12] and Watset [30]. One of the proposed methods performs preprocessing of the graph of synonyms, while the second one performs postprocessing of the induced synsets.
Our experiments on two large scale datasets show that (1) both methods are able to substantially improve recall, but at the cost of substantial drops of precision; (2) the postprocessing approach yields better results overall. We conclude our study with an overview of prominent alternative approaches for expansion of incomplete synonymy dictionaries.
We believe the results of our study will be useful for both enriching the available lexical semantic resources like OntoWiktionary [17] as well as for increasing the lexical coverage of the input data for the graphbased word sense induction methods.
Acknowledgements.
We acknowledge the support of the Deutsche Forschungsgemeinschaft (DFG) under the ‘‘JOINT’’ project, the DAAD, the RFBR under the projects no. 163700203 мол_а and no. 163700354 мол_а, and the RFH under the project no. 160412019. The calculations were carried out using the supercomputer ‘‘Uran’’ at the Krasovskii Institute of Mathematics and Mechanics. Finally, we also thank four anonymous reviewers for their helpful comments.
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