Spectral clustering refers to a flexible class of clustering procedures that can produce high-quality clusterings on small data sets but which has limited applicability to large-scale problems due to its computational complexity of O(n 3), with n the number of data points. We extend the range of spectral clustering by developing a general framework for fast approximate spectral clustering in which a distortion-minimizing local transformation is first applied to the data. This framework is based on a theoretical analysis that provides a statistical characterization of the effect of local distortion on the mis-clustering rate. We develop two concrete instances of our general framework, one based on local k-means clustering (KASP) and one based on random projection trees (RASP). Extensive experiments show that these algorithms can achieve significant speedups with little degradation in clustering accuracy. Specifically, our algorithms outperform k-means by a large margin in terms of accuracy, and run several times faster than approximate spectral clustering based on the Nyström method, with comparable accuracy and significantly smaller memory footprint. Remarkably, our algorithms make it possible for a single machine to spectral cluster data sets with a million observations within several minutes. 1

There is an increasing quantity of data with uncertainty arising from applications such as sensor network measurements, record linkage, and as output of mining algorithms. This uncertainty is typically formalized as probability density functions over tuple values. Beyond storing and processing such data in a DBMS, it is necessary to perform other data analysis tasks such as data mining. We study the core mining problem of clustering on uncertain data, and define appropriate natural generalizations of standard clustering optimization criteria. Two variations arise, depending on whether a point is automatically associated with its optimal center, or whether it must be assigned to a fixed cluster no matter where it is actually located. For uncertain versions of k-means and k-median, we show reductions to their corresponding weighted versions on data with no uncertainties. These are simple in the unassigned case, but require some care for the assigned version. Our most interesting results are for uncertain k-center, which generalizes both traditional k-center and k-median objectives. We show a variety of bicriteria approximation algorithms. One picks O(kɛ −1 log 2 n) centers and achieves a (1 + ɛ) approximation to the best uncertain k-centers. Another picks 2k centers and achieves a constant factor approximation. Collectively, these results are the first known guaranteed approximation algorithms for the problems of clustering uncertain data.

When people try to find particular objects in natural scenes they make extensive use of knowledge about how and where objects tend to appear in a scene. Although many forms of such “top-down ” knowledge have been incorporated into saliency map models of visual search, surprisingly, the role of object appearance has been infrequently investigated. Here we present an appearance based saliency model derived in a Bayesian framework. We compare our approach with both bottom-up saliency algorithms as well as the state-of-the-art Contextual Guidance model of Torralba et al. (2006) at predicting human fixations. Although both top-down approaches use very different types of information, they achieve similar performance; each substantially better than the purely bottom-up models. Our experiments reveal that a simple model of object appearance can predict human fixations quite well, even making the same mistakes as people.

Abstract—In this paper, we generalize the notions of centroids (and barycenters) to the broad class of information-theoretic distortion measures called Bregman divergences. Bregman divergences form a rich and versatile family of distances that unifies quadratic Euclidean distances with various well-known statistical entropic measures. Since besides the squared Euclidean distance, Bregman divergences are asymmetric, we consider the left-sided and right-sided centroids and the symmetrized centroids as minimizers of average Bregman distortions. We prove that all three centroids are unique and give closed-form solutions for the sided centroids that are generalized means. Furthermore, we design a provably fast and efficient arbitrary close approximation algorithm for the symmetrized centroid based on its exact geometric characterization. The geometric approximation algorithm requires only to walk on a geodesic linking the two left/right-sided centroids. We report on our implementation for computing entropic centers of image histogram clusters and entropic centers of multivariate normal distributions that are useful operations for processing multimedia information and retrieval. These experiments illustrate that our generic methods compare favorably with former limited ad hoc methods. Index Terms—Bregman divergence, Bregman information, Bregman power divergence, Burbea–Rao divergence, centroid,

Common visual codebook generation methods used in a Bag of Visual words model, e.g. k-means or Gaussian Mixture Model, use the Euclidean distance to cluster features into visual code words. However, most popular visual descriptors are histograms of image measurements. It has been shown that the Histogram Intersection Kernel (HIK) is more effective than the Euclidean distance in supervised learning tasks with histogram features. In this paper, we demonstrate that HIK can also be used in an unsupervised manner to significantly improve the generation of visual codebooks. We propose a histogram kernel k-means algorithm which is easy to implement and runs almost as fast as k-means. The HIK codebook has consistently higher recognition accuracy over k-means codebooks by 2-4%. In addition, we propose a one-class SVM formulation to create more effective visual code words which can achieve even higher accuracy. The proposed method has established new state-of-the-art performance numbers for 3 popular benchmark datasets on object and scene recognition. In addition, we show that the standard k-median clustering method can be used for visual codebook generation and can act as a compromise between HIK and k-means approaches. 1.

We study the use of viral marketing strategies on social networks to maximize revenue from the sale of a single product. We propose a model in which the decision of a buyer to buy the product is influenced by friends that own the product and the price at which the product is offered. The influence model we analyze is quite general, naturally extending both the Linear Threshold model and the Independent Cascade model, while also incorporating price information. We consider sales proceeding in a cascading manner through the network, i.e. a buyer is offered the product via recommendations from its neighbors who own the product. In this setting, the seller influences events by offering a cashback to recommenders and by setting prices (via coupons or discounts) for each buyer in the social network. Finding a seller strategy which maximizes the expected revenue in this setting turns out to be NPhard. However, we propose a seller strategy that generates revenue guaranteed to be within a constant factor of the optimal strategy in a wide variety of models. The strategy is based on an influence-andexploit idea, and it consists of finding the right trade-off at each time step between: generating revenue from the current user versus offering the product for free and using the influence generated from this sale later in the process. We also show how local search can be used to improve the performance of this technique in practice. 1

Abstract — The k-means method is one of the most widely used clustering algorithms, drawing its popularity from its speed in practice. Recently, however, it was shown to have exponential worst-case running time. In order to close the gap between practical performance and theoretical analysis, the k-means method has been studied in the model of smoothed analysis. But even the smoothed analyses so far are unsatisfactory as the bounds are still superpolynomial in the number n of data points. In this paper, we settle the smoothed running time of the k-means method. We show that the smoothed number of iterations is bounded by a polynomial in n and 1/σ, where σ is the standard deviation of the Gaussian perturbations. This means that if an arbitrary input data set is randomly perturbed, then the k-means method will run in expected polynomial time on that input set. Keywords-k-means; clustering; smoothed analysis 1.

Centroidal Voronoi tessellation (CVT) is a fundamental geometric structure that finds many applications in

We study the generalized k-median problem with respect to a Bregman divergence Dφ. Given a finite set P ⊆ Rd of size n, our goal is to find a set C of size k such that the sum of errors cost(P, C) = p∈P minc∈C Dφ(p, c) } is minimized. The Bregman k-median problem plays an important role in many applications, e.g. information theory, statistics, text classification, and speech processing. We give the first coreset construction for this problem for a large subclass of Bregman divergences, including important dissimilarity measures such as the Kullback-Leibler divergence and the Itakura-Saito divergence. Using these coresets, we give a (1 + ɛ)-approximation algorithm for( the Bregman k-median problem with running time O dkn + d2 k ( 2 ɛ)Θ(1) log k+2) n. This result improves over the previousely fastest known (1+ɛ)-approximation algorithm from [1]. Unlike the analysis of most coreset constructions our analysis does not rely on the construction of ɛ-nets. Instead, we prove our results by purely combinatorial means. 1

We perform an in-depth study of SEO attacks that spread malware by poisoning search results for popular queries. Such attacks, although recent, appear to be both widespread and effective. They compromise legitimate Web sites and generate a large number of fake pages targeting trendy keywords. We first dissect one example attack that affects over 5,000 Web domains and attracts over 81,000 user visits. Further, we develop de-SEO, a system that automatically detects these attacks. Using large datasets with hundreds of billions of URLs, deSEO successfully identifies multiple malicious SEO campaigns. In particular, applying the URL signatures derived from deSEO, we find 36 % of sampled searches to Google and Bing contain at least one malicious link in the top results at the time of our experiment. 1