Graph-based synset induction methods, such as MaxMax and Watset, induce synsets by performing a global clustering of a synonymy graph. However, such methods are sensitive to the structure of the input synonymy graph: sparseness of the input dictionary can substantially reduce the quality of the extracted synsets. In this paper, we propose two different approaches designed to alleviate the incompleteness of the input dictionaries. The first one performs a pre-processing of the graph by adding missing edges, while the second one performs a post-processing by merging similar synset clusters. We evaluate these approaches on two datasets for the Russian language and discuss their impact on the performance of synset induction methods. Finally, we perform an extensive error analysis of each approach and discuss prominent alternative methods for coping with the problem of sparsity of the synonymy dictionaries.
Biemann @cite_14 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 corpus-induced graphs.
@cite_14
1987302197 2166557397 2105333851 2891781872
We introduce Chinese Whispers, a randomized graph-clustering algorithm, which is time-linear in the number of edges. After a detailed definition of the algorithm and a discussion of its strengths and weaknesses, the performance of Chinese Whispers is measured on Natural Language Processing (NLP) problems as diverse as language separation, acquisition of syntactic word classes and word sense disambiguation. At this, the fact is employed that the small-world property holds for many graphs in NLP. A cluster algorithm for graphs called the (MCL algorithm) is introduced. The algorithm provides basically an interface to an algebraic process defined on stochastic matrices, called the MCL process. The graphs may be both weighted (with nonnegative weight) and directed. Let @math be such a graph. The MCL algorithm simulates flow in @math by first identifying @math in a canonical way with a Markov graph @math . Flow is then alternatingly expanded and contracted, leading to a row of Markov Graphs @math . Flow expansion corresponds with taking the @math power of a stochastic matrix, where @math . Flow contraction corresponds with a parametrized operator @math , @math , which maps the set of (column) stochastic matrices onto itself. The image @math is obtained by raising each entry in @math to the @math power and rescaling each column to have sum @math again. The heuristic underlying this approach is the expectation that flow between dense regions which are sparsely connected will evaporate. The invariant limits of the process are easily derived and in practice the process converges very fast to such a limit, the structure of which has a generic interpretation as an overlapping clustering of the graph @math . Overlap is limited to cases where the input graph has a symmetric structure inducing it. The contraction and expansion parameters of the MCL process influence the granularity of the output. The algorithm is space and time efficient and lends itself to drastic scaling. This report describes the MCL algorithm and process, convergence towards equilibrium states, interpretation of the states as clusterings, and implementation and scalability. The algorithm is introduced by first considering several related proposals towards graph clustering, of both combinatorial and probabilistic nature. Gossiping is a distributed process whose purpose is to enable the members of a group of n>1 autonomous agents to asymptotically determine in a decentralized manner, the average of the initial values of their scalar gossip variables. This paper analyzes the accelerated gossip algorithms, first proposed in Cao, Spielman, and Yeh (2006), in which local memory is exploited by installing shift-registers at each agent. For the two-register case, the existence of the desired convergence is established under a symmetry assumption by separately studying the convergence in expectation and in mean square. In particular, the optimal rate of convergence in expectation is derived which is faster than that of the standard gossip algorithm, and a sufficient condition on the adjustable parameter for the convergence in mean square is provided. These theoretical results are validated for some classes of networks by comparison with existing empirical data. More general multi-register cases are also discussed. Following the success of deep convolutional networks in various vision and speech related tasks, researchers have started investigating generalizations of the well-known technique for graph-structured data. A recently-proposed method called Graph Convolutional Networks has been able to achieve state-of-the-art results in the task of node classification. However, since the proposed method relies on localized first-order approximations of spectral graph convolutions, it is unable to capture higher-order interactions between nodes in the graph. In this work, we propose a motif-based graph attention model, called Motif Convolutional Networks (MCNs), which generalizes past approaches by using weighted multi-hop motif adjacency matrices to capture higher-order neighborhoods. A novel attention mechanism is used to allow each individual node to select the most relevant neighborhood to apply its filter. Experiments show that our proposed method is able to achieve state-of-the-art results on the semi-supervised node classification task.