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Existing research on finding social groups mostly focuses on dense subgraphs in social networks. However, finding socially tenuous groups also has many important applications. In this article, we introduce the notion of $k$ k -triangles to measure the tenuity of a group. We then formulate a new research problem, Minimum $k$ k -Triangle Disconnected Group with No-Pair Constraint (MkTG), to find a socially tenuous group from the online social network. We prove that MkTG is NP-hard and inapproximable within any ratio. Two algorithms, namely TERA and TERA-ADV, are designed for solving MkTG effectively and efficiently. Further, we examine the MkTG problem on tree-based social networks, due to their structural resemblance with corporate social networks built upon the supervision relation. Accordingly, we devise an efficient algorithm, namely Tenuity Maximization for Trees (TMT), to obtain the optimal solution in polynomial time. In addition, we study a more general version of MkTG, named Generalized Minimum $k$ k -Triangle Disconnected Group without No-Pair Constraint (MkTG-G). We formulate MkTG-G, analyze its inapproximability, and propose a randomized approximation algorithm, named Randomized Ranking with Limited Neighborhood Participation (RLNP). Experimental results on real datasets manifest that the proposed algorithms outperform the baselines in terms of both efficiency and solution quality. [ABSTRACT FROM AUTHOR]

Static and dynamic clustering algorithms are a fundamental tool in any machine learning library. Most of the efforts in developing dynamic machine learning and data mining algorithms have been focusing on the sliding window model or more simplistic models. However, in many real-world applications one might need to deal with arbitrary deletions and insertions. For example, one might need to remove data items that are not necessarily the oldest ones, because they have been flagged as containing inappropriate content or due to privacy concerns. Clustering trajectory data might also require to deal with more general update operations. We develop a $(2+\epsilon)$ (2 + ε) -approximation algorithm for the $k$ k -center clustering problem with “small” amortized cost under the fully dynamic adversarial model. In such a model, points can be added or removed arbitrarily, provided that the adversary does not have access to the random choices of our algorithm. The amortized cost of our algorithm is poly-logarithmic when the ratio between the maximum and minimum distance between any two points in input is bounded by a polynomial, while $k$ k and $\epsilon$ ε are constant. Furthermore, we significantly improve the memory requirement of our fully dynamic algorithm, although at the cost of a worse approximation ratio of $4 +\epsilon$ 4 + ε . Our theoretical results are complemented with an extensive experimental evaluation on dynamic data from Twitter, Flickr, as well as trajectory data, demonstrating the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

We present new algorithms for $k$ k -means clustering on a data stream with a focus on providing fast responses to clustering queries. Compared to the state-of-the-art, our algorithms provide substantial improvements in the query time for cluster-center queries while retaining the desirable properties of provably small approximation error and low space usage. Our proposed clustering algorithms systematically reuse the “coresets” (summaries of data) computed for recent queries in answering the current clustering query, a novel technique which we refer to as coreset caching. We also present an algorithm called OnlineCC that integrates the coreset caching idea with a simple sequential streaming $k$ k -means algorithm. In practice, OnlineCC algorithm can provide constant query time. We present both theoretical analysis and detailed experiments demonstrating the correctness, accuracy, and efficiency of all our proposed clustering algorithms. [ABSTRACT FROM AUTHOR]

Shortest path query in road network is pervasive in various location-based services nowadays. As the business expands, the scalability issue becomes severer and more servers are deployed to cope with it. Moreover, as the traffic condition keeps changing over time, the existing index-based approaches can hardly adapt to the real-life dynamic environment. Therefore, batch shortest path algorithms have been proposed recently to answer a set of queries together using shareable computation. Besides, they can also work in a highly dynamic environment as no index is needed. However, the existing batch algorithms either assume the batch queries are finely decomposed or just process them without differentiation, resulting in poor query efficiency. In this work, we assume the traffic condition is stable over a short period and treat the issued queries within that period as a stream of query sets. Specifically, we first propose three query set decomposition methods to cluster one query set into multiple query subsets: Zigzag that considers the 1-N shared computation; Co-Clustering that considers the source and target's spatial locality; and Search-Space-Aware that further incorporates search space estimation. After that, we propose two batch algorithms that take advantage of the previously decomposed query sets for efficient query answering: R2R that finds a set of approximate shortest paths from one region to another with bounded error; and Local Cache that improves the existing Global Cache with higher cache hit ratio. Finally, we design three efficient stream processing methods for intra-batch shared computation. The experiments on a large real-world query sets verify the effectiveness and efficiency of our decomposition methods compared with the state-of-the-art batch algorithms. [ABSTRACT FROM AUTHOR]

Density Peak Clustering (DPC), a popular density-based clustering approach, has received considerable attention from the research community primarily due to its simplicity and fewer-parameter requirement. However, the resultant clusters obtained using DPC are influenced by the sensitive parameter $d_c$ d c , which depends on data distribution and requirements of different users. Besides, the original DPC algorithm requires visiting a large number of objects, making it slow. To this end, this paper investigates index-based solutions for DPC. Specifically, we propose two list-based index methods viz. (i) a simple List Index, and (ii) an advanced Cumulative Histogram Index. Efficient query algorithms are proposed for these indices which significantly avoids irrelevant comparisons at the cost of space. For memory-constrained systems, we further introduce an approximate solution to the above indices which allows substantial reduction in the space cost, provided that slight inaccuracies are admissible. Furthermore, owing to considerably lower memory requirements of existing tree-based index structures, we also present effective pruning techniques and efficient query algorithms to support DPC using the popular Quadtree Index and R-tree Index. Finally, we practically evaluate all the above indices and present the findings and results, obtained from a set of extensive experiments on six synthetic and real datasets. The experimental insights obtained can help to guide in selecting a befitting index. [ABSTRACT FROM AUTHOR]

The $K$ K -means algorithm is one of the most popular clustering methods. However, it is a well-known fact that its performance, in terms of quality of the obtained solution and computational load, highly depends upon its initialization phase. For this reason, different initialization techniques have been developed throughout the years to enable its fast convergence to competitive solutions. In this sense, it is common practice to re-start the $K$ K -means algorithm several times via one of these techniques and keep the solution with the lowest error. Unfortunately, such a choice is still likely to be a poor approximation of the optimal set of centroids. In this article, we introduce a cheap Split-Merge step that can be used to re-start the $K$ K -means algorithm after reaching a fixed point. Under some settings, one can show that this approach reduces the error of the given fixed point without requiring any further iteration of the $K$ K -means algorithm. Moreover, experimental results show that this strategy is able to generate approximations with an associated error that is hard to reach for different multi-start methods, such as multi-start Forgy $K$ K -means, $K$ K -means++ and Hartigan $K$ K -means, while also computing a lower amount of distances than the previous algorithms. [ABSTRACT FROM AUTHOR]

Besides the traditional cartographic data sources, spatial information can also be derived from location-based sources. However, even though different location-based sources refer to the same physical world, each one has only partial coverage of the spatial entities, describe them with different attributes, and sometimes provide contradicting information. Hence, we introduce the spatial entity linkage problem, which finds which pairs of spatial entities belong to the same physical spatial entity. Our proposed solution (QuadSky) starts with a time-efficient spatial blocking technique (QuadFlex), compares pairwise the spatial entities in the same block, ranks the pairs using Pareto optimality with the SkyRank algorithm, and finally, classifies the pairs with our novel SkyEx-* family of algorithms that yield 0.85 precision and 0.85 recall for a manually labeled dataset of 1,500 pairs and 0.87 precision and 0.6 recall for a semi-manually labeled dataset of 777,452 pairs. Moreover, we provide a theoretical guarantee and formalize the SkyEx-FES algorithm that explores only 27 percent of the skylines without any loss in F-measure. Furthermore, our fully unsupervised algorithm SkyEx-D approximates the optimal result with an F-measure loss of just 0.01. Finally, QuadSky provides the best trade-off between precision and recall, and the best F-measure compared to the existing baselines and clustering techniques, and approximates the results of supervised learning solutions. [ABSTRACT FROM AUTHOR]

The social presence theory in social psychology suggests that computer-mediated online interactions are inferior to face-to-face, in-person interactions. Thus, it's important to organize social activities for online social network users to meet in person. In this paper, we consider the scenarios of organizing in person friend-making social activities via online social networks (OSNs) and formulate a new research problem, namely, Hop-bounded Maximum Group Friending (HMGF), that takes into consideration both existing friendships and the likelihood of new friend making in organization of the targeted in person friend-making social activities. To find a set of attendees for such social activities, HMGF is unique and challenging due to the interplay of the group size, the constraint on existing friendships, and the objective of maximizing the likelihood of friend making. We prove that HMGF is NP-Hard, and there exists no approximation algorithm for it unless $P=NP$ P = N P . We also provide an Integer Linear Programming (ILP) formulation for the HMGF problem. The ILP formulation, which can be solved efficiently by a commercial solver to obtain the optimal solution for small HMGF instances, acts as a baseline approach for comparison in the evaluation of the proposed algorithm. We further propose an error-bounded approximation algorithm, MaxGF, to efficiently obtain the solutions very close to the optimal solutions. To boost the performance, we devise two graph-theoretical pruning strategies, namely Neighbor Pruning and Core Pruning, which can effectively avoid redundant graph explorations to improve the performance of HMGF. We also study HMGF on a class of special graphs, threshold graphs, which have properties very similar to many online social networks. We prove that MaxGF can obtain the optimal solution to HMGF on threshold graphs in polynomial time. We conduct a user study to validate our problem formulation and perform extensive experiments on real datasets to demonstrate the efficiency and effectiveness of our proposed algorithm. The experimental results manifest that our proposed algorithms outperform the baselines, including the ILP formulation. [ABSTRACT FROM AUTHOR]

Clustering analysis has been widely used in statistics, machine learning, pattern recognition, image processing, and so on. It is a great challenge for most existing clustering algorithms to discover clusters with arbitrary shapes. Clustering algorithms based on Minimum spanning tree (MST) are able to discover clusters with arbitrary shapes, but they are time consuming and susceptible to noise points. In this paper, we employ local density peaks (LDP) to represent the whole data set and define a shared neighbors-based distance between local density peaks to better measure the dissimilarity between objects on manifold data. On the basis of local density peaks and the new distance, we propose a novel MST-based clustering algorithm called LDP-MST. It first uses local density peaks to construct MST and then repeatedly cuts the longest edge until a given number of clusters are found. The experimental results on synthetic data sets and real data sets show that our algorithm is competent with state-of-the-art methods when discovering clusters with complex structures. [ABSTRACT FROM AUTHOR]

Computer sciences and related disciplines evolve around developing, evaluating, and applying algorithms. Typically, an algorithm is not developed from scratch, but uses and builds upon existing ones, which often are proposed and published in scholarly articles. The ability to capture this evolution relationship among these algorithms in scientific literature would not only allow us to understand how a particular algorithm is composed, but also shed light on large-scale analysis of algorithmic evolution through different temporal spans and thematic scales. We propose to capture such evolution relationship between two algorithms by investigating the knowledge represented in citation contexts, where authors explain how cited algorithms are used in their works. A set of heterogeneous ensemble machine-learning methods is proposed, where the combination of two base classifiers trained with heterogeneous feature types is used to automatically identify the algorithm usage relationship. The proposed heterogeneous ensemble methods achieve the best average F1 of 0.749 and 0.905 for fine-grained and binary algorithm citation function classification, respectively. The success of this study will allow us to generate a large-scale algorithm citation network from a collection of scholarly documents representing multiple time spans, venues, and fields of study. Such a network will be used as an instrument not only to answer critical questions in algorithm search, such as identifying the most influential and generalizable algorithms, but also to study the evolution of algorithmic development and trends over time. [ABSTRACT FROM AUTHOR]

This paper focuses on scalability and robustness of spectral clustering for extremely large-scale datasets with limited resources. Two novel algorithms are proposed, namely, ultra-scalable spectral clustering (U-SPEC) and ultra-scalable ensemble clustering (U-SENC). In U-SPEC, a hybrid representative selection strategy and a fast approximation method for $K$ K -nearest representatives are proposed for the construction of a sparse affinity sub-matrix. By interpreting the sparse sub-matrix as a bipartite graph, the transfer cut is then utilized to efficiently partition the graph and obtain the clustering result. In U-SENC, multiple U-SPEC clusterers are further integrated into an ensemble clustering framework to enhance the robustness of U-SPEC while maintaining high efficiency. Based on the ensemble generation via multiple U-SEPC's, a new bipartite graph is constructed between objects and base clusters and then efficiently partitioned to achieve the consensus clustering result. It is noteworthy that both U-SPEC and U-SENC have nearly linear time and space complexity, and are capable of robustly and efficiently partitioning 10-million-level nonlinearly-separable datasets on a PC with 64 GB memory. Experiments on various large-scale datasets have demonstrated the scalability and robustness of our algorithms. The MATLAB code and experimental data are available at https://www.researchgate.net/publication/330760669. [ABSTRACT FROM AUTHOR]

The structural graph clustering algorithm SCAN is a fundamental technique for managing and analyzing graph data. However, its high runtime remains a computational bottleneck, which limits its applicability. In this paper, we propose a novel interactive approach for tackling this problem on multicore CPUs. Our algorithm, called anySCAN, iteratively processes vertices in blocks. The acquired results are merged into an underlying cluster structure consisting of the so-called super-nodes for building clusters. During its runtime, anySCAN can be suspended for examining intermediate results and resumed for finding better results at arbitrary time points, making it an anytime algorithm which is capable of handling very large graphs in an interactive way and under arbitrary time constraints. Moreover, its block processing scheme allows the design of a scalable parallel algorithm on shared memory architectures such as multicore CPUs for speeding up the algorithm further at each iteration. Consequently, anySCAN uniquely is a both interactive and work-efficient parallel algorithm. We further introduce danySCAN an efficient bulk update scheme for anySCAN on dynamic graphs in which the clusters are updated in bulks and in a parallel interactive scheme. Experiments are conducted on very large real graph datasets for demonstrating the performance of anySCAN. They show its ability to acquire very good approximate results early, leading to orders of magnitude speedup compared to SCAN and its variants. Moreover, it scales very well with the number of threads when dealing with both static and dynamic graphs. [ABSTRACT FROM AUTHOR]

The issue of missing values (MVs) has appeared widely in real-world datasets and hindered the use of many statistical or machine learning algorithms for data analytics due to their incompetence in handling incomplete datasets. To address this issue, several MV imputation algorithms have been developed. However, these approaches do not perform well when most of the incomplete tuples are clustered with each other, coined here as theClustered Missing Values Phenomenon, which attributes to the lack of sufficient complete tuples near an MV for imputation. In this paper, we propose theOrder-Sensitive Imputation for Clustered Missing values(OSICM) framework, in which missing values are imputed sequentially such that the values filled earlier in the process are also used for later imputation of other MVs. Obviously, the order of imputations is critical to the effectiveness and efficiency of OSICM framework. We formulate the searching of the optimal imputation order as an optimization problem, and show its NP-hardness. Furthermore, we devise an algorithm to find the exact optimal solution and propose two approximate/heuristic algorithms to trade off effectiveness for efficiency. Finally, we conduct extensive experiments on real and synthetic datasets to demonstrate the superiority of our OSICM framework. [ABSTRACT FROM AUTHOR]

The massive collection of data via emerging technologies like the Internet of Things (IoT) requires finding optimal ways to reduce the observations in the time series analysis domain. The IoT time series require aggregation methods that can preserve and represent the key characteristics of the data. In this paper, we propose a segmentation algorithm that adapts to unannounced mutations of the data (i.e., data drifts). The algorithm splits the data streams into blocks and groups them in square matrices, computes the Discrete Cosine Transform (DCT), and quantizes them. The key information is contained in the upper-left part of the resulting matrix. We extract this sub-matrix, compute the modulus of its eigenvalues, and remove duplicates. The algorithm, called BEATS, is designed to tackle dynamic IoT streams, whose distribution changes over time. We implement experiments with six datasets combining real, synthetic, real-world data, and data with drifts. Compared to other segmentation methods like Symbolic Aggregate approXimation (SAX), BEATS shows significant improvements. Trying it with classification and clustering algorithms it provides efficient results. BEATS is an effective mechanism to work with dynamic and multi-variate data, making it suitable for IoT data sources. The datasets, code of the algorithm and the analysis results can be accessed publicly at: https://github.com/auroragonzalez/BEATS. [ABSTRACT FROM AUTHOR]

Community discovery plays an essential role in the analysis of the structural features of complex networks. Since online networks grow increasingly large and complex over time, the methods traditionally used for community discovery cannot efficiently handle large-scale network data. This introduces the important problem of how to effectively and efficiently discover large communities from complex networks. In this study, we propose a fast parallel community discovery model called picaso (a parallel community discovery a lgorithm based on approximate optimization), which integrates two new techniques: (1) Mountain model, which works by utilizing graph theory to approximate the selection of nodes needed for merging, and (2) Landslide algorithm, which is used to update the modularity increment based on the approximated optimization. In addition, the GraphX distribution computing framework is employed in order to achieve parallel community detection over complex networks. In the proposed model, clustering on modularity is used to initialize the Mountain model as well as to compute the weight of each edge in the networks. The relationships among the communities are then simplified by applying the Landslide algorithm, which allows us to obtain the community structures of the complex networks. Extensive experiments were conducted on real and synthetic complex network datasets, and the results demonstrate that the proposed algorithm can outperform the state of the art methods, in effectiveness and efficiency, when working to solve the problem of community detection. Moreover, we demonstratively prove that overall time performance approximates to four times faster than similar approaches. Effectively our results suggest a new paradigm for large-scale community discovery of complex networks. [ABSTRACT FROM AUTHOR]

A new density-based clustering algorithm, RNN-DBSCAN, is presented which uses reverse nearest neighbor counts as an estimate of observation density. Clustering is performed using a DBSCAN-like approach based on $k$ nearest neighbor graph traversals through dense observations. RNN-DBSCAN is preferable to the popular density-based clustering algorithm DBSCAN in two aspects. First, problem complexity is reduced to the use of a single parameter (choice of $k$ nearest neighbors), and second, an improved ability for handling large variations in cluster density (heterogeneous density). The superiority of RNN-DBSCAN is demonstrated on several artificial and real-world datasets with respect to prior work on reverse nearest neighbor based clustering approaches (RECORD, IS-DBSCAN, and ISB-DBSCAN) along with DBSCAN and OPTICS. Each of these clustering approaches is described by a common graph-based interpretation wherein clusters of dense observations are defined as connected components, along with a discussion on their computational complexity. Heuristics for RNN-DBSCAN parameter selection are presented, and the effects of $k$ on RNN-DBSCAN clusterings discussed. Additionally, with respect to scalability, an approximate version of RNN-DBSCAN is presented leveraging an existing approximate $k$ nearest neighbor technique. [ABSTRACT FROM PUBLISHER]

Density Peaks (DP) is a recently proposed clustering algorithm that has distinctive advantages over existing clustering algorithms. It has already been used in a wide range of applications. However, DP requires computing the distance between every pair of input points, therefore incurring quadratic computation overhead, which is prohibitive for large data sets. In this paper, we study efficient distributed algorithms for DP. We first show that a naïve MapReduce solution (Basic-DDP) has high communication and computation overhead. Then, we propose LSH-DDP, an approximate algorithm that exploits Locality Sensitive Hashing for partitioning data, performs local computation, and aggregates local results to approximate the final results. We address several challenges in employing LSH for DP. We leverage the characteristics of DP to deal with the fact that some of the result values cannot be directly approximated in local partitions. We present formal analysis of LSH-DDP, and show that the approximation quality and the runtime can be controlled by tuning the parameters of LSH-DDP. Experimental results on both a local cluster and EC2 show that LSH-DDP achieves a factor of 1.7–70x speedup over the naïve Basic-DDP and 2x speedup over the state-of-the-art EDDPC approach, while returning comparable cluster results. Compared to the popular K-means clustering, LSH-DDP also has comparable or better performance. Furthermore, LSH-DDP could achieve even higher efficiency with a lower accuracy requirement. [ABSTRACT FROM PUBLISHER]

This work presents a feature selection method based on proximity relations learning. Each single feature is treated as a binary classifier that predicts for any three objects X, A, and B whether X is close to A or B. The performance of the classifier is a direct measure of feature quality. Any linear combination of feature-based binary classifiers naturally corresponds to feature selection. Thus, the feature selection problem is transformed into an ensemble learning problem of combining many weak classifiers into an optimized strong classifier. We provide a theoretical analysis of the generalization error of our proposed method which validates the effectiveness of our proposed method. Various experiments are conducted on synthetic data, four UCI data sets and 12 microarray data sets, and demonstrate the success of our approach applying to feature selection. A weakness of our algorithm is high time complexity. [ABSTRACT FROM PUBLISHER]

The k-nearest neighbor approach (k-NN) has been extensively used as a powerful non-parametric technique in many scientific and engineering applications. However, this approach incurs a large computational cost. Hence, this issue has become an active research field. In this work, a novel k-NN approach based on various-widths clustering, named kNNVWC, to efficiently find k-NNs for a query object from a given data set, is presented. kNNVWC does clustering using various widths, where a data set is clustered with a global width first and each produced cluster that meets the predefined criteria is recursively clustered with its own local width that suits its distribution. This reduces the clustering time, in addition to balancing the number of produced clusters and their respective sizes. Maximum efficiency is achieved by using triangle inequality to prune unlikely clusters. Experimental results demonstrate that kNNVWC performs well in finding k-NNs for query objects compared to a number of k-NN search algorithms, especially for a data set with high dimensions, various distributions and large size. [ABSTRACT FROM PUBLISHER]

Visually analyzing citation networks poses challenges to many fields of the data mining research. How can we summarize a large citation graph according to the user’s interest? In particular, how can we illustrate the impact of a highly influential paper through the summarization? Can we maintain the sensory node-link graph structure while revealing the flow-based influence patterns and preserving a fine readability? The state-of-the-art influence maximization algorithms can detect the most influential node in a citation network, but fail to summarize a graph structure to account for its influence. On the other hand, existing graph summarization methods fold large graphs into clustered views, but can not reveal the hidden influence patterns underneath the citation network. In this paper, we first formally define the Influence Graph Summarization problem on citation networks. Second, we propose a matrix decomposition based algorithm pipeline to solve the IGS problem. Our method can not only highlight the flow-based influence patterns, but also easily extend to support the rich attribute information. A prototype system called VEGAS implementing this pipeline is also developed. Third, we present a theoretical analysis on our main algorithm, which is equivalent to the kernel k-mean clustering. It can be proved that the matrix decomposition based algorithm can approximate the objective of the proposed IGS problem. Last, we conduct comprehensive experiments with real-world citation networks to compare the proposed algorithm with classical graph summarization methods. Evaluation results demonstrate that our method significantly outperforms the previous ones in optimizing both the quantitative IGS objective and the quality of the visual summarizations. [ABSTRACT FROM PUBLISHER]

Co-clustering has emerged to be a powerful data mining tool for two-dimensional co-occurrence and dyadic data. However, co-clustering algorithms often require significant computational resources and have been dismissed as impractical for large data sets. Existing studies have provided strong empirical evidence that expectation-maximization (EM) algorithms (e.g., k-means algorithm) with sequential updates can significantly reduce the computational cost without degrading the resulting solution. Motivated by this observation, we introduce sequential updates for alternate minimization co-clustering (AMCC) algorithms which are variants of EM algorithms, and also show that AMCC algorithms with sequential updates converge. We then propose two approaches to parallelize AMCC algorithms with sequential updates in a distributed environment. Both approaches are proved to maintain the convergence properties of AMCC algorithms. Based on these two approaches, we present a new distributed framework, Co-ClusterD, which supports efficient implementations of AMCC algorithms with sequential updates. We design and implement Co-ClusterD, and show its efficiency through two AMCC algorithms: fast nonnegative matrix tri-factorization (FNMTF) and information theoretic co-clustering (ITCC). We evaluate our framework on both a local cluster of machines and the Amazon EC2 cloud. Empirical results show that AMCC algorithms implemented in Co-ClusterD can achieve a much faster convergence and often obtain better results than their traditional concurrent counterparts. [ABSTRACT FROM PUBLISHER]

In many popular applications like peer-to-peer systems, large amounts of data are distributed among multiple sources. Analysis of this data and identifying clusters is challenging due to processing, storage, and transmission costs. In this paper, we propose GDCluster, a general fully decentralized clustering method, which is capable of clustering dynamic and distributed data sets. Nodes continuously cooperate through decentralized gossip-based communication to maintain summarized views of the data set. We customize GDCluster for execution of the partition-based and density-based clustering methods on the summarized views, and also offer enhancements to the basic algorithm. Coping with dynamic data is made possible by gradually adapting the clustering model. Our experimental evaluations show that GDCluster can discover the clusters efficiently with scalable transmission cost, and also expose its supremacy in comparison to the popular method LSP2P. [ABSTRACT FROM PUBLISHER]

Users are often faced with the problem of finding complementary items that together achieve a single common goal (e.g., a starter kit for a novice astronomer, a collection of question/answers related to low-carb nutrition, a set of places to visit on holidays). In this paper, we argue that for some application scenarios returning item bundles is more appropriate than ranked lists. Thus we define composite retrieval as the problem of finding k bundles of complementary items. Beyond complementarity of items, the bundles must be valid w.r.t. a given budget, and the answer set of k bundles must exhibit diversity. We formally define the problem and show that in its general form is \bf NP-hard  and that also the special cases in which each bundle is formed by only one item, or only one bundle is sought, are hard. Our characterization however suggests how to adopt a two-phase approach (Produce-and-Choose, or PAC) in which we first produce many valid bundles, and then we choose k among them. For the first phase we devise two ad-hoc clustering algorithms, while for the second phase we adapt heuristics with approximation guarantees for a related problem. We also devise another approach which is based on first finding a k-clustering and then selecting a valid bundle from each of the produced clusters (Cluster-and-Pick, or CAP). We compare experimentally the proposed methods on two real-world data sets: the first data set is given by a sample of touristic attractions in 10 large European cities, while the second is a large database of user-generated restaurant reviews from Yahoo! Local. Our experiments show that when diversity is highly important, CAP is the best option, while when diversity is less important, a PAC approach constructing bundles around randomly chosen pivots, is better. [ABSTRACT FROM AUTHOR]

High-dimensional data arise naturally in many domains, and have regularly presented a great challenge for traditional data mining techniques, both in terms of effectiveness and efficiency. Clustering becomes difficult due to the increasing sparsity of such data, as well as the increasing difficulty in distinguishing distances between data points. In this paper, we take a novel perspective on the problem of clustering high-dimensional data. Instead of attempting to avoid the curse of dimensionality by observing a lower dimensional feature subspace, we embrace dimensionality by taking advantage of inherently high-dimensional phenomena. More specifically, we show that hubness, i.e., the tendency of high-dimensional data to contain points (hubs) that frequently occur in $(k)$-nearest-neighbor lists of other points, can be successfully exploited in clustering. We validate our hypothesis by demonstrating that hubness is a good measure of point centrality within a high-dimensional data cluster, and by proposing several hubness-based clustering algorithms, showing that major hubs can be used effectively as cluster prototypes or as guides during the search for centroid-based cluster configurations. Experimental results demonstrate good performance of our algorithms in multiple settings, particularly in the presence of large quantities of noise. The proposed methods are tailored mostly for detecting approximately hyperspherical clusters and need to be extended to properly handle clusters of arbitrary shapes. [ABSTRACT FROM PUBLISHER]

GPS-enabled devices are pervasive nowadays. Finding movement patterns in trajectory data stream is gaining in importance. We propose a group discovery framework that aims to efficiently support the online discovery of moving objects that travel together. The framework adopts a sampling-independent approach that makes no assumptions about when positions are sampled, gives no special importance to sampling points, and naturally supports the use of approximate trajectories. The framework's algorithms exploit state-of-the-art, density-based clustering (DBScan) to identify groups. The groups are scored based on their cardinality and duration, and the top-$(k)$ groups are returned. To avoid returning similar subgroups in a result, notions of domination and similarity are introduced that enable the pruning of low-interest groups. Empirical studies on real and synthetic data sets offer insight into the effectiveness and efficiency of the proposed framework. [ABSTRACT FROM PUBLISHER]

The exemplar-based data clustering problem can be formulated as minimizing an energy function defined on a Markov random field (MRF). However, most algorithms for optimizing the MRF energy function cannot be directly applied to the task of clustering, as the problem has a high-order energy function. In this paper, we first show that the high-order energy function for the clustering problem can be simplified as a pairwise energy function with the metric property, and consequently it can be optimized by the $(\alpha)$-expansion move algorithm based on graph cut. Then, the original expansion move algorithm is improved in the following two aspects: 1) Instead of solving a minimal s-t graph cut problem, we show that there is an explicit and interpretable solution for minimizing the energy function in the clustering problem. Based on this interpretation, a fast $(\alpha)$-expansion move algorithm is proposed, which is much more efficient than the graph-cut-based algorithm. 2) The fast $(\alpha)$-expansion move algorithm is further improved by extending its move space so that a larger energy value reduction can be achieved in each iteration. Experiments on benchmark data sets show that the enhanced expansion move algorithm has a better performance, compared to other state-of-the-art exemplar-based clustering algorithms. [ABSTRACT FROM AUTHOR]

Finding the appropriate number of clusters to which documents should be partitioned is crucial in document clustering. In this paper, we propose a novel approach, namely DPMFP, to discover the latent cluster structure based on the DPM model without requiring the number of clusters as input. Document features are automatically partitioned into two groups, in particular, discriminative words and nondiscriminative words, and contribute differently to document clustering. A variational inference algorithm is investigated to infer the document collection structure as well as the partition of document words at the same time. Our experiments indicate that our proposed approach performs well on the synthetic data set as well as real data sets. The comparison between our approach and state-of-the-art document clustering approaches shows that our approach is robust and effective for document clustering. [ABSTRACT FROM AUTHOR]

Entity resolution (ER) is the problem of identifying which records in a database refer to the same entity. In practice, many applications need to resolve large data sets efficiently, but do not require the ER result to be exact. For example, people data from the web may simply be too large to completely resolve with a reasonable amount of work. As another example, real-time applications may not be able to tolerate any ER processing that takes longer than a certain amount of time. This paper investigates how we can maximize the progress of ER with a limited amount of work using “hints,” which give information on records that are likely to refer to the same real-world entity. A hint can be represented in various formats (e.g., a grouping of records based on their likelihood of matching), and ER can use this information as a guideline for which records to compare first. We introduce a family of techniques for constructing hints efficiently and techniques for using the hints to maximize the number of matching records identified using a limited amount of work. Using real data sets, we illustrate the potential gains of our pay-as-you-go approach compared to running ER without using hints. [ABSTRACT FROM AUTHOR]

We study the problem of clustering probabilistic graphs. Similar to the problem of clustering standard graphs, probabilistic graph clustering has numerous applications, such as finding complexes in probabilistic protein-protein interaction (PPI) networks and discovering groups of users in affiliation networks. We extend the edit-distance-based definition of graph clustering to probabilistic graphs. We establish a connection between our objective function and correlation clustering to propose practical approximation algorithms for our problem. A benefit of our approach is that our objective function is parameter-free. Therefore, the number of clusters is part of the output. We also develop methods for testing the statistical significance of the output clustering and study the case of noisy clusterings. Using a real protein-protein interaction network and ground-truth data, we show that our methods discover the correct number of clusters and identify established protein relationships. Finally, we show the practicality of our techniques using a large social network of Yahoo! users consisting of one billion edges. [ABSTRACT FROM AUTHOR]

Reducing the computational complexity of inference in Bayesian Networks (BNs) is a key challenge. Current algorithms for inference convert a BN to a junction tree structure made up of clusters of the BN nodes and the resulting complexity is time exponential in the size of a cluster. The need to reduce the complexity is especially acute where the BN contains continuous nodes. We propose a new method for optimizing the calculation of Conditional Probability Tables (CPTs) involving continuous nodes, approximated in Hybrid Bayesian Networks (HBNs), using an approximation algorithm called dynamic discretization. We present an optimized solution to this problem involving binary factorization of the arithmetical expressions declared to generate the CPTs for continuous nodes for deterministic functions and statistical distributions. The proposed algorithm is implemented and tested in a commercial Hybrid Bayesian Network software package and the results of the empirical evaluation show significant performance improvement over unfactorized models. [ABSTRACT FROM PUBLISHER]

Traditional clustering techniques are inapplicable to problems where the relationships between data points evolve over time. Not only is it important for the clustering algorithm to adapt to the recent changes in the evolving data, but it also needs to take the historical relationship between the data points into consideration. In this paper, we propose ECKF, a general framework for evolutionary clustering large-scale data based on low-rank kernel matrix factorization. To the best of our knowledge, this is the first work that clusters large evolutionary data sets by the amalgamation of low-rank matrix approximation methods and matrix factorization-based clustering. Since the low-rank approximation provides a compact representation of the original matrix, and especially, the near-optimal low-rank approximation can preserve the sparsity of the original data, ECKF gains computational efficiency and hence is applicable to large evolutionary data sets. Moreover, matrix factorization-based methods have been shown to effectively cluster high-dimensional data in text mining and multimedia data analysis. From a theoretical standpoint, we mathematically prove the convergence and correctness of ECKF, and provide detailed analysis of its computational efficiency (both time and space). Through extensive experiments performed on synthetic and real data sets, we show that ECKF outperforms the existing methods in evolutionary clustering. [ABSTRACT FROM PUBLISHER]