Amin Mantrach

A family of dissimilarity measures between nodes generalizing both the shortest-path and the commute-time distances

This work introduces a new family of link-based dissimilarity measures between nodes of a weighted directed graph. This measure, called the randomized shortest-path (RSP) dissimilarity, depends on a parameter θ and has the interesting property of reducing, on one end, to the standard shortest-path distance when θ is large and, on the other end, to the commute-time (or resistance) distance when θ is small (near zero). Intuitively, it corresponds to the expected cost incurred by a random walker in order to reach a destination node from a starting node while maintaining a constant entropy (related to θ) spread in the graph. The parameter θ is therefore biasing gradually the simple random walk on the graph towards the shortest-path policy. By adopting a statistical physics approach and computing a sum over all the possible paths (discrete path integral), it is shown that the RSP dissimilarity from every node to a particular node of interest can be computed efficiently by solving two linear systems of n equations, where n is the number of nodes. On the other hand, the dissimilarity between every couple of nodes is obtained by inverting an n x n matrix. The proposed measure can be used for various graph mining tasks such as computing betweenness centrality, finding dense communities, etc, as shown in the experimental section.

A time-based collective factorization for topic discovery and monitoring in news

Discovering and tracking topic shifts in news constitutes a new challenge for applications nowadays. Topics evolve,emerge and fade, making it more difficult for the journalist -or the press consumer- to decrypt the news. For instance, the current Syrian chemical crisis has been the starting point of the UN Russian initiative and also the revival of the US France alliance. A topical mapping representing how the topics evolve in time would be helpful to contextualize information. As far as we know, few topic tracking systems can provide such temporal topic connections. In this paper, we introduce a novel framework inspired from Collective Factorization for online topic discovery able to connect topics between different time-slots. The framework learns jointly the topics evolution and their time dependencies. It offers the user the ability to control, through one unique hyper-parameter, the tradeoff between the past accumulated knowledge and the current observed data. We show, on semi-synthetic datasets and on Yahoo News articles, that our method is competitive with state-of-the-art techniques while providing a simple way to monitor topics evolution (including emerging and disappearing topics).

The Sum-over-Paths Covariance Kernel: A Novel Covariance Measure between Nodes of a Directed Graph

This work introduces a link-based covariance measure between the nodes of a weighted directed graph, where a cost is associated with each arc. To this end, a probability distribution on the (usually infinite) countable set of paths through the graph is defined by minimizing the total expected cost between all pairs of nodes while fixing the total relative entropy spread in the graph. This results in a Boltzmann distribution on the set of paths such that long (high-cost) paths occur with a low probability while short (low-cost) paths occur with a high probability. The sum-over-paths (SoP) covariance measure between nodes is then defined according to this probability distribution: two nodes are considered as highly correlated if they often co-occur together on the same - preferably short - paths. The resulting covariance matrix between nodes (say n nodes in total) is a Gram matrix and therefore defines a valid kernel on the graph. It is obtained by inverting an n\times n matrix depending on the costs assigned to the arcs. In the same spirit, a betweenness score is also defined, measuring the expected number of times a node occurs on a path. The proposed measures could be used for various graph mining tasks such as computing betweenness centrality, semi-supervised classification of nodes, visualization, etc., as shown in Section 7.

Semi-supervised classification and betweenness computation on large, sparse, directed graphs

This work addresses graph-based semi-supervised classification and betweenness computation in large, sparse, networks (several millions of nodes). The objective of semi-supervised classification is to assign a label to unlabeled nodes using the whole topology of the graph and the labeling at our disposal. Two approaches are developed to avoid explicit computation of pairwise proximity between the nodes of the graph, which would be impractical for graphs containing millions of nodes. The first approach directly computes, for each class, the sum of the similarities between the nodes to classify and the labeled nodes of the class, as suggested initially in [1,2]. Along this approach, two algorithms exploiting different state-of-the-art kernels on a graph are developed. The same strategy can also be used in order to compute a betweenness measure. The second approach works on a trellis structure built from biased random walks on the graph, extending an idea introduced in [3]. These random walks allow to define a biased bounded betweenness for the nodes of interest, defined separately for each class. All the proposed algorithms have a linear computing time in the number of edges while providing good results, and hence are applicable to large sparse networks. They are empirically validated on medium-size standard data sets and are shown to be competitive with state-of-the-art techniques. Finally, we processed a novel data set, which is made available for benchmarking, for multi-class classification in a large network: the U.S. patents citation network containing 3M nodes (of six different classes) and 38M edges. The three proposed algorithms achieve competitive results (around 85% classification rate) on this large network-they classify the unlabeled nodes within a few minutes on a standard workstation.

Dynamic Matrix Factorization with Priors on Unknown Values

Advanced and effective collaborative filtering methods based on explicit feedback assume that unknown ratings do not follow the same model as the observed ones not missing at random). In this work, we build on this assumption, and introduce a novel dynamic matrix factorization framework that allows to set an explicit prior on unknown values. When new ratings, users, or items enter the system, we can update the factorization in time independent of the size of data (number of users, items and ratings). Hence, we can quickly recommend items even to very recent users. We test our methods on three large datasets, including two very sparse ones, in static and dynamic conditions. In each case, we outrank state-of-the-art matrix factorization methods that do not use a prior on unknown ratings.

Evolution of Conversations in the Age of Email Overload

Email is a ubiquitous communications tool in the workplace and plays an important role in social interactions. Previous studies of email were largely based on surveys and limited to relatively small populations of email users within organizations. In this paper, we report results of a large-scale study of more than 2 million users exchanging 16 billion emails over several months. We quantitatively characterize the replying behavior in conversations within pairs of users. In particular, we study the time it takes the user to reply to a received message and the length of the reply sent. We consider a variety of factors that affect the reply time and length, such as the stage of the conversation, user demographics, and use of portable devices. In addition, we study how increasing load affects emailing behavior. We find that as users receive more email messages in a day, they reply to a smaller fraction of them, using shorter replies. However, their responsiveness remains intact, and they may even reply to emails faster. Finally, we predict the time to reply, length of reply, and whether the reply ends a conversation. We demonstrate considerable improvement over the baseline in all three prediction tasks, showing the significant role that the factors that we uncover play, in determining replying behavior. We rank these factors based on their predictive power. Our findings have important implications for understanding human behavior and designing better email management applications for tasks like ranking unread emails.

Leveraging Social Context for Modeling Topic Evolution

Topic discovery and evolution (TDE) has been a problem which has gained long standing interest in the research community. The goal in topic discovery is to identify groups of keywords from large corpora so that the information in those corpora are summarized succinctly. The nature of text corpora has changed dramatically in the past few years with the advent of social media. Social media services allow users to constantly share, follow and comment on posts from other users. Hence, such services have given a new dimension to the traditional text corpus. The new dimension being that todays corpora have a social context embedded in them in terms of the community of users interested in a particular post, their profiles etc. We wish to harness this social context that comes along with the textual content for TDE. In particular, our goal is to both qualitatively and quantitatively analyze when social context actually helps with TDE. Methodologically, we approach the problem of TDE by a proposing non-negative matrix factorization (NMF) based model that incorporates both the textual information and social context information. We perform experiments on large scale real world dataset of news articles, and use Twitter as the platform providing information about the social context of these news articles. We compare with and outperform several state-of-the-art baselines. Our conclusion is that using the social context information is most useful when faced with topics that are particularly difficult to detect.

A bag-of-paths framework for network data analysis

This work develops a generic framework, called the bag-of-paths (BoP), for link and network data analysis. The central idea is to assign a probability distribution on the set of all paths in a network. More precisely, a Gibbs-Boltzmann distribution is defined over a bag of paths in a network, that is, on a representation that considers all paths independently. We show that, under this distribution, the probability of drawing a path connecting two nodes can easily be computed in closed form by simple matrix inversion. This probability captures a notion of relatedness, or more precisely accessibility, between nodes of the graph: two nodes are considered as highly related when they are connected by many, preferably low-cost, paths. As an application, two families of distances between nodes are derived from the BoP probabilities. Interestingly, the second distance family interpolates between the shortest-path distance and the commute-cost distance. In addition, it extends the Bellman-Ford formula for computing the shortest-path distance in order to integrate sub-optimal paths (exploration) by simply replacing the minimum operator by the soft minimum operator. Experimental results on semi-supervised classification tasks show that both of the new distance families are competitive with other state-of-the-art approaches. In addition to the distance measures studied in this paper, the bag-of-paths framework enables straightforward computation of many other relevant network measures.

HEADS: Headline Generation as Sequence Prediction Using an Abstract Feature-Rich Space

Automatic headline generation is a sub-task of document summarization with many reported applications. In this study we present a sequence-prediction technique for learning how editors title their news stories. The introduced technique models the problem as a discrete optimization task in a feature-rich space. In this space the global optimum can be found in polynomial time by means of dynamic programming. We train and test our model on an extensive corpus of financial news, and compare it against a number of baselines by using standard metrics from the document summarization domain, as well as some new ones proposed in this work. We also assess the readability and informativeness of the generated titles through human evaluation. The obtained results are very appealing and substantiate the soundness of the approach.

Random walks based modularity: application to semi-supervised learning

Although criticized for some of its limitations, modularity remains a standard measure for analyzing social networks. Quantifying the statistical surprise in the arrangement of the edges of the network has led to simple and powerful algorithms. However, relying solely on the distribution of edges instead of more complex structures such as paths limits the extent of modularity. Indeed, recent studies have shown restrictions of optimizing modularity, for instance its resolution limit. We introduce here a novel, formal and well-defined modularity measure based on random walks. We show how this modularity can be computed from paths induced by the graph instead of the traditionally used edges. We argue that by computing modularity on paths instead of edges, more informative features can be extracted from the network. We verify this hypothesis on a semi-supervised classification procedure of the nodes in the network, where we show that, under the same settings, the features of the random walk modularity help to classify better than the features of the usual modularity. Additionally, the proposed approach outperforms the classical label propagation procedure on two data sets of labeled social networks.