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.

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

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.

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

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

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

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

In spite of the popularity of probabilistic mixture models for latent structure discovery from data, mixture models do not have a natural mechanism for handling sparsity, where each data point only has a few non-zero observations. In this paper, we introduce conditional naive-Bayes (CNB) models, which generalize naive-Bayes mixture models to naturally handle sparsity by conditioning the model on observed features. Further, we present latent Dirichlet conditional naive-Bayes (LD-CNB) models, which constitute a family of powerful hierarchical Bayesian models for latent structure discovery from sparse data. The proposed family of models are quite general and can work with arbitrary regular exponential family conditional distributions. We present a variational inference based EM algorithm for

This paper deals with overlapping clustering, a trade off between crisp and fuzzy clustering. It has been motivated by recent applications in various domains such as information retrieval or biology. We show that the problem of finding a suitable coverage of data by overlapping clusters is not a trivial task. We propose a new objective criterion and the associated algorithm OKM that generalizes the k-means algorithm. Experiments show that overlapping clustering is a good alternative and indicate that OKM outperforms other existing methods. 1.

text mining, log processing, supervised machine learning, quantification, text classification, applications, pattern recognition We discuss our experiences in analyzing customer-support issues from the unstructured free-text fields of technical-support call logs. The identification of frequent issues and their accurate quantification is essential in order to track aggregate costs broken down by issue type, to appropriately target engineering resources, and to provide the best diagnosis, support and documentation for most common issues. We present a new set of techniques for doing this efficiently on an industrial scale, without requiring manual coding of calls in the call center. Our approach involves (1) a new text clustering method to identify common and emerging issues; (2) a method to rapidly train large numbers of categorizers in a practical, interactive manner; and (3) a method to accurately quantify categories, even in the face of inaccurate classifications and training sets that necessarily cannot match the class distribution of each new month’s data. We present our methodology and a tool we developed and deployed that uses these methods for tracking ongoing support issues and discovering emerging issues at HP.