This paper presents a new graph-based approach that induces synsets using synonymy dictionaries and word embeddings. First, we build a weighted graph of synonyms extracted from commonly available resources, such as Wiktionary. Second, we apply word sense induction to deal with ambiguous words. Finally, we cluster the disambiguated version of the ambiguous input graph into synsets. Our meta-clustering approach lets us use an efficient hard clustering algorithm to perform a fuzzy clustering of the graph. Despite its simplicity, our approach shows excellent results, outperforming five competitive state-of-the-art methods in terms of F-score on three gold standard datasets for English and Russian derived from large-scale manually constructed lexical resources.
@cite_28 is a 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 non-root nodes; a root node together with all its transitive children form a fuzzy cluster.
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The traditional approach to representing tree structures is as a rooted, directed graph with the root node at the top of the page and children nodes below the parent node with lines connecting them (Figure 1). Knuth (1968, p. 305-313) has a long discussion about this standard representation, especially why the root is at the top and he offers several alternatives including brief mention of a space-filling approach. However, the remainder of his presentation and most other discussions of trees focus on various node and edge representations. By contrast, this paper deals with a two-dimensional (2-d) space-filling approach in which each node is a rectangle whose area is proportional to some attribute such as node size. A subset T@?V of terminals is k-connected to a root s in a directed undirected graph J if J has k internally-disjoint vs-paths for every v@?T; T is k-connected in J if for every s@?T the set T@? s is k-connected to s in J. We consider the Subsetk-ConnectivityAugmentation problem: given a graph G=(V,E) with edge node-costs, a node subset T@?V, and a subgraph J=(V,E"J) of G such that T is (k-1)-connected in J, find a minimum-cost augmenting edge-set F@?E@?E"J such that T is k-connected in J@?F. The problem admits trivial ratio O(|T|^2). We consider the case |T|>k and prove that for directed undirected graphs and edge node-costs, a @r-approximation algorithm for Rooted Subsetk-Connectivity Augmentation implies the following approximation ratios for Subsetk-Connectivity Augmentation:(i)b(@r+k)+(|T||T|-k)^2O(log|T||T|-k), where b=1 for undirected graphs and b=2 for directed graphs. (ii)@r@?O(|T||T|-klogk). The best known values of @r on undirected graphs are min |T|,O(k) for edge-costs and min |T|,O(klog|T|) for node-costs; for directed graphs @r=|T| for both versions. Our results imply that unless k=|T|-o(|T|), Subsetk-Connectivity Augmentation admits the same ratios as the best known ones for the rooted version. This improves the ratios in Nutov (2009) [19] and Laekhanukit (2011) [15]. This work presents a novel procedure for computing (1) distances between nodes of a weighted, undirected, graph, called the Euclidean Commute Time Distance (ECTD), and (2) a subspace projection of the nodes of the graph that preserves as much variance as possible, in terms of the ECTD – a principal components analysis of the graph. It is based on a Markov-chain model of random walk through the graph. The model assigns transition probabilities to the links between nodes, so that a random walker can jump from node to node. A quantity, called the average commute time, computes the average time taken by a random walker for reaching node j for the first time when starting from node i, and coming back to node i. The square root of this quantity, the ECTD, is a distance measure between any two nodes, and has the nice property of decreasing when the number of paths connecting two nodes increases and when the "length" of any path decreases. The ECTD can be computed from the pseudoinverse of the Laplacian matrix of the graph, which is a kernel. We finally define the Principal Components Analysis (PCA) of a graph as the subspace projection that preserves as much variance as possible, in terms of the ECTD. This graph PCA has some interesting links with spectral graph theory, in particular spectral clustering. We propose an approach for data clustering based on optimum-path forest. The samples are taken as nodes of a graph, whose arcs are defined by an adjacency relation. The nodes are weighted by their probability density values (pdf) and a connectivity function is maximized, such that each maximum of the pdf becomes root of an optimum-path tree (cluster), composed by samples “more strongly connected” to that maximum than to any other root. We discuss the advantages over other pdf-based approaches and present extensions to large datasets with results for interactive image segmentation and for fast, accurate, and automatic brain tissue classification in magnetic resonance (MR) images. We also include experimental comparisons with other clustering approaches. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 50–68, 2009.