Results 1 - 10
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40
R.: Towards internet-scale multiview stereo
- In: Proceedings of IEEE CVPR
, 2010
"... This paper introduces an approach for enabling existing multi-view stereo methods to operate on extremely large unstructured photo collections. The main idea is to decompose the collection into a set of overlapping sets of photos that can be processed in parallel, and to merge the resulting reconstr ..."
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Cited by 101 (6 self)
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This paper introduces an approach for enabling existing multi-view stereo methods to operate on extremely large unstructured photo collections. The main idea is to decompose the collection into a set of overlapping sets of photos that can be processed in parallel, and to merge the resulting reconstructions. This overlapping clustering problem is formulated as a constrained optimization and solved iteratively. The merging algorithm, designed to be parallel and out-of-core, incorporates robust filtering steps to eliminate low-quality reconstructions and enforce global visibility constraints. The approach has been tested on several large datasets downloaded from Flickr.com, including one with over ten thousand images, yielding a 3D reconstruction with nearly thirty million points. 1.
Multi-way clustering on relation graphs
- In Proc. of the 7th SIAM Intl. Conf. on Data Mining
, 2006
"... A number of real-world domains such as social networks and e-commerce involve heterogeneous data that describes relations between multiple classes of entities. Understanding the natural structure of this type of heterogeneous relational data is essential both for exploratory analysis and for perform ..."
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Cited by 36 (3 self)
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A number of real-world domains such as social networks and e-commerce involve heterogeneous data that describes relations between multiple classes of entities. Understanding the natural structure of this type of heterogeneous relational data is essential both for exploratory analysis and for performing various predictive modeling tasks. In this paper, we propose a principled multi-way clustering framework for relational data, wherein different types of entities are simultaneously clustered based not only on their intrinsic attribute values, but also on the multiple relations between the entities. To achieve this, we introduce a relation graph model that describes all the known relations between the different entity classes, in which each relation between a given set of entity classes is represented in the form of multi-modal tensor over an appropriate domain. Our multi-way clustering formulation is driven by the objective of capturing the maximal “information ” in the original relation graph, i.e., accurately approximating the set of tensors corresponding to the various relations. This formulation is applicable to all Bregman divergences (a broad family of loss functions that includes squared Euclidean distance, KL-divergence), and also permits analysis of mixed data types using convex combinations of appropriate Bregman loss functions. Furthermore, we present a large family of structurally different multi-way clustering schemes that preserve various linear summary statistics of the original data. We accomplish the above generalizations by extending a recently proposed key theoretical result, namely the minimum Bregman information principle [1], to the relation graph setting. We also describe an efficient multi-way clustering algorithm based on alternate minimization that generalizes a number of other recently proposed clustering methods. Empirical results on datasets obtained from real-world domains (e.g., movie recommendations, newsgroup articles) demonstrate the generality and efficacy of our framework. 1
A Game-Theoretic Approach to Hypergraph Clustering
, 2009
"... Hypergraph clustering refers to the process of extracting maximally coherent groups from a set of objects using high-order (rather than pairwise) similarities. Traditional approaches to this problem are based on the idea of partitioning the input data into a user-defined number of classes, thereby o ..."
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Cited by 26 (2 self)
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Hypergraph clustering refers to the process of extracting maximally coherent groups from a set of objects using high-order (rather than pairwise) similarities. Traditional approaches to this problem are based on the idea of partitioning the input data into a user-defined number of classes, thereby obtaining the clusters as a by-product of the partitioning process. In this paper, we provide a radically different perspective to the problem. In contrast to the classical approach, we attempt to provide a meaningful formalization of the very notion of a cluster and we show that game theory offers an attractive and unexplored perspective that serves well our purpose. Specifically, we show that the hypergraph clustering problem can be naturally cast into a non-cooperative multi-player “clustering game”, whereby the notion of a cluster is equivalent to a classical game-theoretic equilibrium concept. From the computational viewpoint, we show that the problem of finding the equilibria of our clustering game is equivalent to locally optimizing a polynomial function over the standard simplex, and we provide a discrete-time dynamics to perform this optimization. Experiments are presented which show the superiority of our approach over state-of-the-art hypergraph clustering techniques.
What is a Cluster? Perspectives from Game Theory
"... “Since no paradigm ever solves all the problems it defines and since no two paradigms leave all the same problems unsolved, paradigm debates always involve the question: Which problems is it more significant to have solved?” Thomas S. Kuhn, The Structure of Scientific Revolutions (1962) There is no ..."
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Cited by 12 (0 self)
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“Since no paradigm ever solves all the problems it defines and since no two paradigms leave all the same problems unsolved, paradigm debates always involve the question: Which problems is it more significant to have solved?” Thomas S. Kuhn, The Structure of Scientific Revolutions (1962) There is no shortage of clustering algorithms, and recently a new wave of excitement has spread across the machine learning community mainly because of the important development of spectral methods. At the same time, there is also growing interest around fundamental questions pertaining to the very nature of the clustering problem (see, e.g., [17, 1, 28]). Yet, despite the tremendous progress in the field, the clustering problem remains elusive and a satisfactory answer even to the most basic questions is still to come. Upon scrutinizing the relevant literature on the subject, it becomes apparent that the vast majority of the existing approaches deal with a very specific version of the problem, which asks for partitioning the input data into coherent classes. In fact, almost invariably, the problem of clustering is defined as a partitioning problem, and even the classical distinction between hierarchical and partitional algorithms
Multiplicative mixture models for overlapping clustering
, 2008
"... The problem of overlapping clustering, where a point is allowed to belong to multiple clusters, is becoming increasingly important in a variety of applications. In this paper, we present an overlapping clustering algorithm based on multiplicative mixture models. We analyze a general setting where ea ..."
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Cited by 12 (3 self)
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The problem of overlapping clustering, where a point is allowed to belong to multiple clusters, is becoming increasingly important in a variety of applications. In this paper, we present an overlapping clustering algorithm based on multiplicative mixture models. We analyze a general setting where each component of the multiplicative mixture is from an exponential family, and present an efficient alternating maximization algorithm to learn the model and infer overlapping clusters. We also show that when each component is assumed to be a Gaussian, we can apply the kernel trick leading to non-linear cluster separators and obtain better clustering quality. The efficacy of the proposed algorithms is demonstrated using experiments on both UCI benchmark datasets and a microarray gene expression dataset. 1
Cluster ranking with an application to mining mailbox networks
- In ICDM ’06: Proceedings of the Sixth International Conference on Data Mining
, 2006
"... We initiate the study of a new clustering framework, called cluster ranking. Rather than simply partitioning a network into clusters, a cluster ranking algorithm also orders the clusters by their strength. To this end, we introduce a novel strength measure for clusters—the integrated cohesion—which ..."
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Cited by 11 (2 self)
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We initiate the study of a new clustering framework, called cluster ranking. Rather than simply partitioning a network into clusters, a cluster ranking algorithm also orders the clusters by their strength. To this end, we introduce a novel strength measure for clusters—the integrated cohesion—which is applicable to arbitrary weighted networks. We then present C-Rank: a new cluster ranking algorithm. Given a network with arbitrary pairwise similarity weights, C-Rank creates a list of overlapping clusters and ranks them by their integrated cohesion. We provide extensive theoretical and empirical analysis of C-Rank and show that it is likely to have high precision and recall. A main component of C-Rank is a heuristic algorithm for finding sparse vertex separators. At the core of this algorithm is a new connection between the well known measure of vertex betweenness and multicommodity flow. Our experiments focus on mining mailbox networks. A mailbox network is an egocentric social network, consisting of contacts with whom an individual exchanges email. Ties among contacts are represented by the frequency of their co–occurrence on message headers. C-Rank is well suited to mine such networks, since they are abundant with overlapping communities of highly variable strengths. We demonstrate the effectiveness of C-Rank on the Enron data set, consisting of 130 mailbox networks. 1
Banded structure in binary matrices
- In KDD ’08: Proceeding of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
, 2008
"... A 0–1 matrix has a banded structure if both rows and columns can be permuted so that the non-zero entries exhibit a staircase pattern of overlapping rows. The concept of banded matrices has its origins in numerical analysis, where entries can be viewed as descriptions between the problem variables; ..."
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Cited by 10 (0 self)
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A 0–1 matrix has a banded structure if both rows and columns can be permuted so that the non-zero entries exhibit a staircase pattern of overlapping rows. The concept of banded matrices has its origins in numerical analysis, where entries can be viewed as descriptions between the problem variables; the bandedness corresponds to variables that are coupled over short distances. Banded data occurs also in other applications, for example in the physical mapping problem of the human genome, in paleontological data, in network data and in the discovery of overlapping communities without cycles. We study in this paper the banded structure of binary matrices, give a formal definition of the concept and discuss its theoretical properties. We consider the algorithmic problems of computing how far a matrix is from being banded, and of finding a good submatrix of the original data that exhibits approximate bandedness. Finally, we show by experiments on real data from ecology and other applications the usefulness of the concept. Our results reveal that bands exist in real datasets and that the final obtained ordering of rows and columns have natural interpretations.
Learnable Similarity Functions and Their Applications to Clustering and Record Linkage
, 2004
"... rship (Xing et al. 2003), and relative comparisons (Schultz & Joachims 2004). These approaches have shown improvements over traditional similarity functions for different data types such as vectors in Euclidean space, strings, and database records composed of multiple text fields. While these in ..."
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Cited by 10 (0 self)
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rship (Xing et al. 2003), and relative comparisons (Schultz & Joachims 2004). These approaches have shown improvements over traditional similarity functions for different data types such as vectors in Euclidean space, strings, and database records composed of multiple text fields. While these initial results are encouraging, there still remains a large number of similarity functions that are currently unable to adapt to a particular domain. In our research, we attempt to bridge this gap by developing both new learnable similarity functions and methods for their application to particular problems in machine learning and data mining. In preliminary work, we proposed two learnable similarity functions for strings that adapt distance computations given training pairs of equivalent and non-equivalent strings (Bilenko & Mooney 2003a). The first function is based on a probabilistic model of edit distance with affine gaps (Gus- Copyright c # 2004, American Association for Artificial Intelli
A segment-based approach to clustering multitopic documents
- in Text Mining Workshop, SIAM Datamining Conference
"... Document clustering has been recognized as a central problem in text data management, and it becomes particularly challenging when documents have multiple topics. In this paper we address the problem of multi-topic document clustering by leveraging the natural composition of documents in text segmen ..."
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Cited by 9 (2 self)
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Document clustering has been recognized as a central problem in text data management, and it becomes particularly challenging when documents have multiple topics. In this paper we address the problem of multi-topic document clustering by leveraging the natural composition of documents in text segments, which bear one or more topics on their own. We propose a segment-based document clustering framework, which is designed to induce a classification of documents starting from the identification of cohesive groups of segment-based portions of the original documents. We empirically give evidence of the significance of our approach on different, large collections of multi-topic documents. 1
Overlapping correlation clustering
- In ICDM
, 2011
"... Abstract—We introduce a new approach to the problem of overlapping clustering. The main idea is to formulate overlapping clustering as an optimization problem in which each data point is mapped to a small set of labels, representing membership to different clusters. The objective is to find a mappin ..."
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Cited by 7 (1 self)
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Abstract—We introduce a new approach to the problem of overlapping clustering. The main idea is to formulate overlapping clustering as an optimization problem in which each data point is mapped to a small set of labels, representing membership to different clusters. The objective is to find a mapping so that the distances between data points agree as much as possible with distances taken over their label sets. To define distances between label sets, we consider two measures: a set-intersection indicator function and the Jaccard coefficient. To solve the main optimization problem we propose a localsearch algorithm. The iterative step of our algorithm requires solving non-trivial optimization subproblems, which, for the measures of set-intersection and Jaccard, we solve using a greedy method and non-negative least squares, respectively. Since our frameworks uses pairwise similarities of objects as the input, it lends itself naturally to the task of clustering structured objects for which feature vectors can be difficult to obtain. As a proof of concept we show how easily our framework can be applied in two different complex application domains. Firstly, we develop overlapping clustering of animal trajectories, obtaining zoologically meaningful results. Secondly, we apply our framework for overlapping clustering of proteins based on pairwise similarities of aminoacid sequences, outperforming the of state-of-the-art method in matching a ground truth taxonomy. I.
