Abstract. Given a collection of images of a static scene taken by many different people, we identify and segment interesting objects. To solve this problem, we use the distribution of images in the collection along with a new field-of-view cue, which leverages the observation that people tend to take photos that frame an object of interest within the field of view. Hence, image features that appear together in many images are likely to be part of the same object. We evaluate the effectiveness of this cue by comparing the segmentations computed by our method against hand-labeled ones for several different models. We also show how the results of our segmentations can be used to highlight important objects in the scene and label them using noisy user-specified textual tag data. These methods are demonstrated on photos of several popular tourist sites downloaded from the Internet. 1

We investigate measures of the clusterability of data sets. Namely, ways to define how ‘strong ’ or ‘conclusive ’ is the clustering structure of a given data set. We address this issue with generality, aiming for conclusions that apply regardless of any particular clustering algorithm or any specific data generation model. We survey several notions of clusterability that have been discussed in the literature, as well as propose a new notion of data clusterability. Our comparison of these notions reveals that, although they all attempt to evaluate the same intuitive property, they are pairwise inconsistent. Our analysis discovers an interesting phenomenon; the more clusterable a data set is, the easier it is (computationally) to find a close-to-optimal clustering of that data. It has been recently shown that such a property holds with respect to one notion of clusterability, ‘k- separability’. We show that this phenomenon holds for other notions as well. In particular, we prove that for well clusterable data, using the clusterability notions we discuss, near-optimal clustering can be efficiently computed. Finally, we investigate how hard it is to determine the clusterability value of a given data set. In most cases, it turns out that this is an NP-hard problem. 1.

Clustering is crucial for many NLP tasks and applications. However, evaluating the results of a clustering algorithm is hard. In this paper we focus on the evaluation setting in which a gold standard solution is available. We discuss two existing information theory based measures, V and VI, and show that they are both hard to use when comparing the performance of different algorithms and different datasets. The V measure favors solutions having a large number of clusters, while the range of scores given by VI depends on the size of the dataset. We present a new measure, NVI, which normalizes VI to address the latter problem. We demonstrate the superiority of NVI in a large experiment involving an important NLP application, grammar induction, using real corpus data in English, German and Chinese. 1

We present a novel fully unsupervised algorithm for POS induction from plain text, motivated by the cognitive notion of prototypes. The algorithm first identifies landmark clusters of words, serving as the cores of the induced POS categories. The rest of the words are subsequently mapped to these clusters. We utilize morphological and distributional representations computed in a fully unsupervised manner. We evaluate our algorithm on English and German, achieving the best reported results for this task. 1

In comparing clusterings, several different distances and indices are in use. We prove that the Misclassification Error distance, the Hamming distance (equivalent to the unadjusted Rand index), and the dχ2 distance between partitions are equivalent in the neighborhood of 0. In other words, if two partitions are very similar, then one distance defines upper and lower bounds on the other and viceversa. The proof is geometric and relies on the convexity of a certain set of probability measures. To my knowledge, this is the first result of its kind. The motivation for this work is in the area of data clustering. Practically, these distances are frequently used to compare two clusterings of a set of observations. Theoretically, such distances are involved in formulating and proving properties of clusterig algorithms. Besides, our results apply to any pair of finite valued random variables, and provides simple yet tight upper and lower bounds on the χ 2 measure of (in)dependence valid when the two variables are strongly dependent. 1 Motivation Clustering, or finding partitions in data, has become an increasingly popular part of data

Clustering is a central technique in NLP. Consequently, clustering evaluation is of great importance. Many clustering algorithms are evaluated by their success in tagging corpus tokens. In this paper we discuss type level evaluation, which reflects class membership only and is independent of the token statistics of a particular reference corpus. Type level evaluation casts light on the merits of algorithms, and for some applications is a more natural measure of the algorithm’s quality. We propose new type level evaluation measures that, contrary to existing measures, are applicable when items are polysemous, the common case in NLP. We demonstrate the benefits of our measures using a detailed case study, POS induction. We experiment with seven leading algorithms, obtaining useful insights and showing that token and type level measures can weakly or even negatively correlate, which underscores the fact that these two approaches reveal different aspects of clustering quality. 1

Modern unsupervised POS taggers usually apply an optimization procedure to a nonconvex function, and tend to converge to local maxima that are sensitive to starting conditions. The quality of the tagging induced by such algorithms is thus highly variable, and researchers report average results over several random initializations. Consequently, applications are not guaranteed to use an induced tagging of the quality reported for the algorithm. In this paper we address this issue using an unsupervised test for intrinsic clustering quality. We run a base tagger with different random initializations, and select the best tagging using the quality test. As a base tagger, we modify a leading unsupervised POS tagger (Clark, 2003) to constrain the distributions of word types across clusters to be Zipfian, allowing us to utilize a perplexity-based quality test. We show that the correlation between our quality test and gold standard-based tagging quality measures is high. Our results are better in most evaluation measures than all results reported in the literature for this task, and are always better than the Clark average results. 1

We summarize here the types of different clustering algorithms included in our applications and software. Existing algorithms are most often described as either statistical and algorithmic. The statistical models are primarily mixture models, including a large variety of finite mixture models (Fraley and Raftery, 2002; Banerjee et al., 2005; Quinn et al., 2006), infinite mixture models based on the Dirichlet process prior (Blei and Jordan, 2006), and mixture models (Blei, Ng and Jordan, 2003). The algorithmic approaches include methods that partition the documents directly, those that create a hierarchy of clusterings, and those which add an additional step to the clustering procedure. The methods include some which identify an exemplar document for each cluster (Kaufman and Rousseeuw, 1990; Frey and Dueck, 2007) and those which do not (Schrodt and Gerner, 1997; Shi and Malik, 2000; Ng, Jordan and Weiss, 2002; von Luxburg, 2007). The hierarchical methods can be further sub-divided into agglomerative (Hastie, Tibshirani and Friedman, 2001), divisive (Kaufman and Rousseeuw, 1990), and other hybrid methods (Gan, Ma and Wu, 2007). To use in our program, we obtain a flat partition of the documents from hierachical clustering methods. A final group includes methods which group words and documents together simulatenously (Dhillon, 2003) and those which embed the documents into lower dimensional space and then cluster (Kohonen,

Abstract—We focus on the detection of communities in multi-scale networks, namely networks made of different levels of organization and in which modules exist at different scales. It is first shown that methods based on modularity are not appropriate to uncover modules in empirical networks, mainly because modularity optimization has an intrinsic bias towards partitions having a characteristic number of modules which might not be compatible with the modular organization of the system. We argue for the use of more flexible quality functions incorporating a resolution parameter that allows us to reveal the natural scales of the system. Different types of multi-resolution quality functions are described and unified by looking at the partitioning problem from a dynamical viewpoint. Finally, significant values of the resolution parameter are selected by using complementary measures of robustness of the uncovered partitions. The methods are illustrated on a benchmark and an empirical network. Index Terms—community detection, complex networks, modularity, multi-scale. I.

Complex network analysis involves the study of the properties of various real world networks. In this broad field, research on community structures forms an important sub area. The strength of community structure is typically quantified by the modularity measure. The measure is based on summing the differences in actual and expected fraction of edges per community (across all communities in the network), whereby the latter is computed based on randomizing the edges subjected to certain constrains. In this paper, we investigate the differences between two commonly used definitions of modularity and highlight one of them as inadequate for quantifying the strength of community structures. We first show this by mathematical proving. We then investigate the empirical differences by developing and testing two variants of a community detection algorithm whereby the variants differ based on their modularity definitions. We observe varying differences in detection accuracy when applying the variants on artificially generated networks. For networks with strong community structures, we show that sensible results are still obtainable with the inadequate measure, which explains why this issue did not come to light previously.