Bipartite Graph Partitioning Research Articles

Mining online communities to inform strategic messaging: practical methods to identify community-level insights

The ability of OSNs to propagate civil unrest has been powerfully observed through the rise of the ISIS and the ongoing conflict in Crimea. As a result, the ability to understand and in some cases mitigate the effects of user communities promoting civil unrest online has become an important area of research. Although methods to detect large online extremist communities have emerged in literature, the ability to summarize community content in meaningful ways remains an open research question. We introduce novel applications of the following methods: ideological user clustering with bipartite spectral graph partitioning, narrative mining with hash tag co-occurrence graph clustering, and identifying radicalization with directed URL sharing networks. In each case we describe how the method can be applied to social media. We subsequently apply them to online Twitter communities interested in the Syrian revolution and ongoing Crimean conflict.

Pelabelan 0-Anti Ajaib dan 2-Anti Ajaib untuk Graf Tangga L

For a connected graph and a subset of . For a vertex the distance betwen and is . For an ordered k-partition of , the representation of with respect to is The k-partition is a resolving partition if are distinct for every The minimum k for which there is a resolving partition of is the partition dimension of In this paper will shown resolving partition of connected graph order where is a bipartite graph. Then it is shown dimension partition of bipartite graph, are pd(Kst)=n-1

A novel combination of second-order statistical features and segmentation using multi-layer superpixels for salient object detection

Salient object detection is one of the outstanding capabilities of the human visual system (HVS). The researcher community aims at developing a salient object detection model that matches the detection accuracy as well as computation time taken by the humans. These models can be developed in either spatial domain or frequency domain. Spatial domain models provide good detection accuracy at the cost of high computational time while frequency domain models offer fast computational speed to meet real-time requirements at the cost of poor detection accuracy. In order to induce a trade-off between computational time and accuracy, we propose a model which provides high detection accuracy without taking much of computation time. To detect the salient object with an accurate shape, we first segment the given image by utilizing a bipartite graph partitioning approach which aggregates multi-layer superpixels in a principled and effective manner. Second, the saliency of each segmented region is computed based on a hypercomplex Fourier transform (HFT) saliency map reconstructed using amplitude spectrum, filtered at an appropriate scale chosen using statistical features extracted from grey- level co-occurrence matrix and original phase spectrum. Finally, a saliency map is generated by taking average of the HFT coefficients of each region in the segmented image and then using the average HFT intensity value of the entire image as a threshold to clearly separate salient object from the background. The performance of the proposed model is evaluated in terms of F---measure, area under curve (AUC), and computation time using six publicly available image datasets. Both qualitative and quantitative evaluations on six publicly available datasets demonstrate the robustness and efficiency of the proposed model against twenty popular state-of-the-art methods.

A Parallel Personalized Recommendation Algorithm Using Bipartite Graphs

BDM-NBI algorithm is proposed in this paper. It focuses on the analysis of a personalized recommendation algorithm that utilizes a weighted bipartite graph suitable for processing big data. To improve the performance of this recommendation algorithm through parallel processing techniques, a sparse matrix partitioning algorithm is then developed that uses the bipartite graph as input. Our algorithm adopts bipartite graph partitioning using a vertex separator method that partitions a high-dimensional sparse matrix into a pseudo-block based diagonal matrix. Then, the recommendation algorithm analyzes all weighted sub-matrices in parallel. We produce the global recommendation weighted matrix by merging all of the sub-matrices in parallel. Experiments with Hadoop show that our algorithm has good approximation for small matrices and excellent scalability.

Index partitioning through a bipartite graph model for faster similarity search in recommendation systems

Scalability of a recommendation system is an important factor for large e-commerce sites containing millions of products visited by millions of users. Similarity search is the core operation in recommendation systems. In this paper, we explain a framework to alleviate performance bottleneck of similarity search for very large-scale recommendation systems. The framework employs inverted index for real-time similarity search and handles dynamic updates. As the inverted index gets larger, retrieving recommendations become computationally expensive. There are various works devoted to solve this problem, such as clustering and preprocessing to compute recommendations offline. Our solution is based on bipartite graph partitioning for minimizing the affinity between entities in different partitions. Number of operations in similarity search is reduced by executing search within the closest partitions to the query. Parts are balanced, so that computational loads of partitions are almost the same, which is significant for reducing the computational cost. Sequential experiments with several different recommendation approaches and large datasets consisting of millions of users and items validate the scalability of the proposed recommendation framework. Accuracy drops only by a small factor due to partitioning, if any. Even slight improvements in recommendation accuracy are observed in our collaborative filtering experiments.

Spectral co-clustering ensemble

The goal of co-clustering is to simultaneously cluster the rows and columns of an input data matrix. It overcomes several limitations associated with traditional clustering methods by allowing automatic discovery of similarity based on a subset of attributes. However, different co-clustering models usually produce very distinct results since each algorithm has its own bias due to the optimization of different criteria. The idea of combining different co-clustering results emerged as an alternative approach for improving the performance of co-clustering algorithms. Similar to clustering ensembles, co-clustering ensembles provide a framework for combining multiple base co-clusterings of a dataset to generate a stable and robust consensus co-clustering result. In this paper, a novel co-clustering ensemble algorithm named spectral co-clustering ensemble (SCCE) is presented. SCCE performs ensemble tasks on base row clusters and column clusters of a dataset simultaneously, and obtains an optimization co-clustering result. Meanwhile, SCCE is a matrix decomposition based approach which can be formulated as a bipartite graph partition problem and solve it efficiently with the selected eigenvectors. To the best of our knowledge, this is the first work on using spectral algorithm for co-clustering ensemble. Extensive experiments on benchmark datasets demonstrate the effectiveness of the proposed method. Our study also shows that SCCE has some favorable merits compared with many state of the art methods.

Analyzing phonetic variation in the traditional English dialects: Simultaneously clustering dialects and phonetic features

This study explores the linguistic application of bipartite spectral graph partitioning, a graph-theoretic technique that simultaneously identifies clusters of similar localities as well as clusters of features characteristic of those localities. We compare the results using this approach with previously published results on the same dataset using cluster and principal component analysis (Shackleton 2007). Although the results of the spectral partitioning method and Shackleton's approach overlap to a broad extent, the analyses offer complementary insights into the data. The traditional cluster analysis detects some clusters that are not identified by the spectral partitioning analysis, whereas the reverse also occurs. Similarly, the principal component analysis and the spectral partitioning analysis detect many overlapping but also some different linguistic variants. The main benefit of the bipartite spectral graph partitioning method over the alternative approaches remains its ability to simultaneously identify sensible geographical clusters of localities with their corresponding linguistic features.

CBIR-MD/BGP: CBIR-MD System based on Bipartite Graph Partitioning

Content based image retrieval system for medical images is a method of retrieving medical images based on similarity of their visual contents. An efficient CBIR-MD system can help the doctors in retrieving similar medical image from the dataset to diagnose the disease efficiently. In this paper, a system is proposed in which query image is divided into equal size sub-blocks. The feature extraction of each sub-block is carried out using Haar wavelet and Fourier descriptor. A matching scheme based on Most Similar Highest Priority (MSHP) principle and the adjacency matrix of bipartite graph partitioning (BGP) formed using sub-blocks of query and target image, is provided for matching the image. The performance of proposed system is investigated in terms of precision-recall.

Robust optimization of graph partitioning involving interval uncertainty

The graph partitioning problem consists of partitioning the vertex set of a graph into several disjoint subsets so that the sum of weights of the edges between the disjoint subsets is minimized. In this paper, robust optimization models with two decomposition algorithms are introduced to solve the graph partitioning problem with interval uncertain weights of edges. The bipartite graph partitioning problem with edge uncertainty is also presented. Throughout this paper, we make no assumption regarding the probability of the uncertain weights.

Improving Information Retrieval System by Co-clustering Web Documents and Queries

World Wide Web is considered the most valuable place for Information Retrieval and Knowledge Discovery. While retrieving information through user queries, a search engine results in a large and unmanageable collection of documents. A more efficient way to organize the documents can be a combination of clustering and ranking, where clustering can group the documents and ranking can be applied for ordering the pages within each cluster. This paper proposes an approach to co-clustering web documents and queries. When user issues a query, we construct a Query-Document Bipartite Graph from click log data. Then, we co-cluster the web documents and queries simultaneous based on the bipartite spectral graph partitioning which uses the second singular vectors of an appropriately scaled query-document matrix to yield good bipartition and rank the queries and documents on the bipartite graph via an iterative process like HITS. The results of experiments show promising improvement.

Multi-way clustering and biclustering by the Ratio cut and Normalized cut in graphs

In this paper, we consider the multi-way clustering problem based on graph partitioning models by the Ratio cut and Normalized cut. We formulate the problem using new quadratic models. Spectral relaxations, new semidefinite programming relaxations and linearization techniques are used to solve these problems. It has been shown that our proposed methods can obtain improved solutions. We also adapt our proposed techniques to the bipartite graph partitioning problem for biclustering.

Bipartite spectral graph partitioning for clustering dialect varieties and detecting their linguistic features

In this study we use bipartite spectral graph partitioning to simultaneously cluster varieties and identify their most distinctive linguistic features in Dutch dialect data. While clustering geographical varieties with respect to their features, e.g. pronunciation, is not new, the simultaneous identification of the features which give rise to the geographical clustering presents novel opportunities in dialectometry. Earlier methods aggregated sound differences and clustered on the basis of aggregate differences. The determination of the significant features which co-vary with cluster membership was carried out on a post hoc basis. Bipartite spectral graph clustering simultaneously seeks groups of individual features which are strongly associated, even while seeking groups of sites which share subsets of these same features. We show that the application of this method results in clear and sensible geographical groupings and discuss and analyze the importance of the concomitant features.

Linear and quadratic programming approaches for the general graph partitioning problem

The graph partitioning problem is to partition the vertex set of a graph into a number of nonempty subsets so that the total weight of edges connecting distinct subsets is minimized. Previous research requires the input of cardinalities of subsets or the number of subsets for equipartition. In this paper, the problem is formulated as a zero-one quadratic programming problem without the input of cardinalities. We also present three equivalent zero-one linear integer programming reformulations. Because of its importance in data biclustering, the bipartite graph partitioning is also studied. Several new methods to determine the number of subsets and the cardinalities are presented for practical applications. In addition, hierarchy partitioning and partitioning of bipartite graphs without reordering one vertex set, are studied.

Bipartite isoperimetric graph partitioning for data co-clustering

Data co-clustering refers to the problem of simultaneous clustering of two data types. Typically, the data is stored in a contingency or co-occurrence matrix C where rows and columns of the matrix represent the data types to be co-clustered. An entry C ij of the matrix signifies the relation between the data type represented by row i and column j. Co-clustering is the problem of deriving sub-matrices from the larger data matrix by simultaneously clustering rows and columns of the data matrix. In this paper, we present a novel graph theoretic approach to data co-clustering. The two data types are modeled as the two sets of vertices of a weighted bipartite graph. We then propose Isoperimetric Co-clustering Algorithm (ICA)--a new method for partitioning the bipartite graph. ICA requires a simple solution to a sparse system of linear equations instead of the eigenvalue or SVD problem in the popular spectral co-clustering approach. Our theoretical analysis and extensive experiments performed on publicly available datasets demonstrate the advantages of ICA over other approaches in terms of the quality, efficiency and stability in partitioning the bipartite graph.

Optimal Partition of a Bipartite Graph with Prescribed Layout into Non-Crossing b-Matchings

Abstract In this paper we deal with the problem of partitioning the edge set of a bipartite graph G = ( L ∪ R , E ) with prescribed layout into the minimum number of non-crossing b-matchings. Some bounds and properties are discussed and an exact O ( | E | log log min { | L | , | R | } ) is presented for its solution.