In this paper, we propose a simple and effective geometric model fitting method to fit and segment multi-structure data even in the presence of severe outliers. We cast the task of geometric model fitting as a representative mode-seeking problem on hypergraphs. Specifically, a hypergraph is first constructed, where the vertices represent model hypotheses and the hyperedges denote data points. The hypergraph involves higher-order similarities (instead of pairwise similarities used on a simple graph), and it can characterize complex relationships between model hypotheses and data points. In addition, we develop a hypergraph reduction technique to remove “insignificant” vertices while retaining as many “significant” vertices as possible in the hypergraph. Based on the simplified hypergraph, we then propose a novel mode-seeking algorithm to search for representative modes within reasonable time. Finally, the proposed mode-seeking algorithm detects modes according to two key elements, i.e., the weighting scores of vertices and the similarity analysis between vertices. Overall, the proposed fitting method is able to efficiently and effectively estimate the number and the parameters of model instances in the data simultaneously. Experimental results demonstrate that the proposed method achieves significant superiority over several state-of-the-art model fitting methods on both synthetic data and real images.
Compared with the hypergraph constructed in the previous methods (e.g., @cite_15 @cite_6 @cite_32 @cite_29 ), where a hyperedge is constrained to connect with a fixed number of vertices, the hyperedge of hypergraphs constructed in this paper can connect with a varying number of vertices (that is we construct non-uniform hypergraphs as those in @cite_0 ) . In addition, the vertices of the hypergraph constructed in the previous methods (e.g., @cite_15 @cite_6 @cite_32 @cite_29 ) represent data points, while the vertices of the hypergraph constructed in this paper denote model hypotheses. Therefore, we can directly deal with the model fitting problem in the parameter space.
@cite_29 @cite_32 @cite_6 @cite_0 @cite_15
152560764 2012184117 1997991368 346586460 2158340552
Abstract An elegant and general way to apply graph partitioning algorithms to hypergraphs would be to model hypergraphs by graphs and apply the graph algorithms to these models. Of course such models have to simulate the given hypergraphs with respect to their cut properties. An edge-weighted graph ( V , E ) is a cut-model for an edge-weighted hypergraph ( V , H ) if the weight of the edges cut by any bipartition of V in the graph is the same as the weight of the hyperedges cut by the same bipartition in the hypergraph. We show that there is no cut-model in general. Next we examine whether the addition of dummy vertices helps: An edge-weighted graph ( V ∪ D , E ) is a mincut-model for an edge-weighted hypergraph ( V, H ) if the weight of the hyperedges cut by a bipartition of the hypergraphs vertices is the same as the weight of a minimum cut separating the two parts in the graph. We construct such models using positive and negative weights. On the other hand, we show that there is no mincut-model in general if only positive weights are allowed. In this paper, we present a new hypergraph-partitioning algorithm that is based on the multilevel paradigm. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed. A bisection of the smallest hypergraph is computed and it is used to obtain a bisection of the original hypergraph by successively projecting and refining the bisection to the next level finer hypergraph. We have developed new hypergraph coarsening strategies within the multilevel framework. We evaluate their performance both in terms of the size of the hyperedge cut on the bisection, as well as on the run time for a number of very large scale integration circuits. Our experiments show that our multilevel hypergraph-partitioning algorithm produces high-quality partitioning in a relatively small amount of time. The quality of the partitionings produced by our scheme are on the average 6 -23 better than those produced by other state-of-the-art schemes. Furthermore, our partitioning algorithm is significantly faster, often requiring 4-10 times less time than that required by the other schemes. Our multilevel hypergraph-partitioning algorithm scales very well for large hypergraphs. Hypergraphs with over 100 000 vertices can be bisected in a few minutes on today's workstations. Also, on the large hypergraphs, our scheme outperforms other schemes (in hyperedge cut) quite consistently with larger margins (9 -30 ). A h-uniform hypergraph H=(V,E) is called (l,k)-orientable if there exists an assignment of each hyperedge e to exactly l of its vertices such that no vertex is assigned more than k hyperedges. Let H_ n,m,h be a hypergraph, drawn uniformly at random from the set of all h-uniform hypergraphs with n vertices and m edges. In this paper, we determine the threshold of the existence of a (l,k)-orientation of H_ n,m,h for k>=1 and h>l>=1, extending recent results motivated by applications such as cuckoo hashing or load balancing with guaranteed maximum load. Our proof combines the local weak convergence of sparse graphs and a careful analysis of a Gibbs measure on spanning subgraphs with degree constraints. It allows us to deal with a much broader class than the uniform hypergraphs. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. Hypergraph partitioning is an important problem with extensive application to many areas, including VLSI design [Alpert and Kahng, 1995], efficient storage of large databases on disks [Shekhar and Liu, 1996], and data mining [, 1996; , 1999b] . The problem is to partition the vertices of a hypergraph into k equal-size parts, such that the number of hyperedges connecting vertices in different parts is minimized. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . The minimum 3-way cut problem in an edge-weighted hypergraph is to find a partition of the vertices into 3 nonempty sets minimizing the total weight of hyperedges that have at least two endpoints in two different sets. In this paper we show that a minimum 3-way cut in hypergraphs can be found by using O(n^3) hypergraph minimum (s,t) cut computations, where n is the number of vertices in the hypergraph. Our simple algorithm is the first polynomial-time algorithm for finding minimum 3-way cuts in hypergraphs. In recent years scholars have built maps of science by connecting the academic fields that cite each other, are cited together, or that cite a similar literature. But since scholars cannot always publish in the fields they cite, or that cite them, these science maps are only rough proxies for the potential of a scholar, organization, or country, to enter a new academic field. Here we use a large dataset of scholarly publications disambiguated at the individual level to create a map of science-or research space-where links connect pairs of fields based on the probability that an individual has published in both of them. We find that the research space is a significantly more accurate predictor of the fields that individuals and organizations will enter in the future than citation based science maps. At the country level, however, the research space and citations based science maps are equally accurate. These findings show that data on career trajectories-the set of fields that individuals have previously published in-provide more accurate predictors of future research output for more focalized units-such as individuals or organizations-than citation based science maps. Citation relationship between scientific publications has been successfully used for scholarly bibliometrics, information retrieval and data mining tasks, and citation-based recommendation algorithms are well documented. While previous studies investigated citation relations from various viewpoints, most of them share the same assumption that, if paper1 cites paper2 (or author1 cites author2), they are connected, regardless of citation importance, sentiment, reason, topic, or motivation. However, this assumption is oversimplified. In this study, we employ an innovative "context-rich heterogeneous network" approach, which paves a new way for citation recommendation task. In the network, we characterize 1) the importance of citation relationships between citing and cited papers, and 2) the topical citation motivation. Unlike earlier studies, the citation information, in this paper, is characterized by citation textual contexts extracted from the full-text citing paper. We also propose algorithm to cope with the situation when large portion of full-text missing information exists in the bibliographic repository. Evaluation results show that, context-rich heterogeneous network can significantly enhance the citation recommendation performance. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] Let h>w>0 be two fixed integers. Let H be a random hypergraph whose hyperedges are all of cardinality h. To w-orient a hyperedge, we assign exactly w of its vertices positive signs with respect to the hyperedge, and the rest negative. A (w,k)-orientation of H consists of a w-orientation of all hyperedges of H, such that each vertex receives at most k positive signs from its incident hyperedges. When k is large enough, we determine the threshold of the existence of a (w,k)-orientation of a random hypergraph. The (w,k)-orientation of hypergraphs is strongly related to a general version of the off-line load balancing problem. The graph case, when h=2 and w=1, was solved recently by Cain, Sanders and Wormald and independently by Fernholz and Ramachandran, thereby settling a conjecture made by Karp and Saks. Motivated by a problem of cuckoo hashing, the special hypergraph case with w=k=1, was solved in three separate preprints dating from October 2009, by Frieze and Melsted, by Fountoulakis and Panagiotou, and by Dietzfelbinger, Goerdt, Mitzenmacher, Montanari, Pagh and Rink. Let H d (n,p) signify a random d -uniform hypergraph with n vertices in which each of the @math possible edges is present with probability p = p(n) independently, and let H d (n,m) denote a uniformly distributed d -uniform hypergraph with n vertices and m edges. We derive local limit theorems for the joint distribution of the number of vertices and the number of edges in the largest component of H d (n,p) and H d (n,m) in the regime @math , resp. d(d−1)m n >1+ϵ, where ϵ>0 is arbitrarily small but fixed as n → ∞. The proofs are based on a purely probabilistic approach. Clustering of data in a large dimension space is of a great interest in many data mining appli cations In this paper we propose a method for clustering of data in a high dimensional space based on a hypergraph model In this method the relationship present in the original data in high dimensional space are mapped into a hypergraph A hyperedge represents a relationship a n ity among subsets of data and the weight of the hyperedge re ects the strength of this a nity A hypergraph partitioning algorithm is used to nd a partitioning of the vertices such that the corresponding data items in each partition are highly related and the weight of the hyperedges cut by the partitioning is minimized We present results of experiments on two di erent data sets S P stock data for the period of and protein coding data These experiments demonstrate that our approach is applicable and e ective in high dimensional datasets Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... Denote by an @math -component a connected @math -uniform hypergraph with @math edges and @math vertices. We prove that the expected number of creations of @math -component during a random hypergraph process tends to 1 as @math and @math tend to @math with the total number of vertices @math such that @math . Under the same conditions, we also show that the expected number of vertices that ever belong to an @math -component is approximately @math . As an immediate consequence, it follows that with high probability the largest @math -component during the process is of size @math . Our results give insight about the size of giant components inside the phase transition of random hypergraphs. Abstract We would like to classify the vertices of a hypergraph in the way that ‘similar’ vertices (those having many incident edges in common) belong to the same cluster. The problem is formulated as follows: given a connected hypergraph on n vertices and fixing the integer k (1 k ⩽ n ), we are looking for k -partition of the set of vertices such that the edges of the corresponding cut-set be as few as possible. We introduce some combinatorial measures characterizing this structural property and give upper and lower bounds for them by means of the k smallest eigenvalues of the hypergraph. For this purpose the notion of spectra of hypergraphs — which is the generalization of C -spectra of graphs — is also introduced together with k-dimensional Euclidean representations . We shall that the existence of k 'small' eigenvalues is a necessary but not sufficient condition for the existence of a good clustering. In addition the representatives of the vertices in an optimal k -dimensional Euclidean representation of the hypergraph should be well separated by means of their Euclidean distances. In this case the k -partition giving the optimal clustering is also obtained by this classification method. The Interconnection Graph Problem (IGP) is to compute for a given hypergraph H= (V, R) a graph G= (V, E) with the minimum number of edges |E| such that for all hyperedges N? Rthe subgraph of Ginduced by Nis connected. Computing feasible interconnection graphs is basically motivated by the design of reconfigurable interconnection networks. This paper proves that IGP is NP-complete and hard to approximate even when all hyperedges of Hhave at most three vertices. Afterwards it presents a search tree based parameterized algorithm showing that the problem is fixed-parameter tractable when the hyperedge size of His bounded. Moreover, the paper gives a reduction based greedy algorithm and closes with its experimental justification. A new form of document coupling called co-citation is defined as the frequency with which two documents are cited together. The co-citation frequency of two scientific papers can be determined by comparing lists of citing documents in the Science Citation Index and counting identical entries. Networks of co-cited papers can be generated for specific scientific specialties, and an example is drawn from the literature of particle physics. Co-citation patterns are found to differ significantly from bibliographic coupling patterns, but to agree generally with patterns of direct citation. Clusters of co-cited papers provide a new way to study the specialty structure of science. They may provide a new approach to indexing and to the creation of SDI profiles. Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different partitions of a hyperedge incur the same cost. However, this assumption fails to leverage the fact that different subsets of vertices within the same hyperedge may have different structural importance. We hence propose a new hypergraph clustering technique, termed inhomogeneous hypergraph partitioning, which assigns different costs to different hyperedge cuts. We prove that inhomogeneous partitioning produces a quadratic approximation to the optimal solution if the inhomogeneous costs satisfy submodularity constraints. Moreover, we demonstrate that inhomogenous partitioning offers significant performance improvements in applications such as structure learning of rankings, subspace segmentation and motif clustering.