Sparse Learning over Infinite Subgraph Features

We present a supervised-learning algorithm from graph data (a set of graphs) for arbitrary twice-differentiable loss functions and sparse linear models over all possible subgraph features. To date, it has been shown that under all possible subgraph features, several types of sparse learning, such as Adaboost, LPBoost, LARS/LASSO, and sparse PLS regression, can be performed. Particularly emphasis is placed on simultaneous learning of relevant features from an infinite set of candidates. We first generalize techniques used in all these preceding studies to derive an unifying bounding technique for arbitrary separable functions. We then carefully use this bounding to make block coordinate gradient descent feasible over infinite subgraph features, resulting in a fast converging algorithm that can solve a wider class of sparse learning problems over graph data. We also empirically study the differences from the existing approaches in convergence property, selected subgraph features, and search-space sizes. We further discuss several unnoticed issues in sparse learning over all possible subgraph features.Comment: 42 pages, 24 figures, 4 table

Glycoinformatics: Data Mining-based Approaches

Carbohydrates or glycans are major cellular macromolecules, working for a variety of vital biological functions. Due to long-term efforts by experimentalists, the current number of structurally different, determined carbohydrates has exceeded 10,000 or more. As a result data mining-based approaches for glycans (or trees in a computer science sense) have attracted attention and have been developed over the last five years, presenting new techniques even from computer science viewpoints. This review summarizes cutting-edge techniques for glycans in each of the three categories of data mining: classification, clustering and frequent pattern mining, and shows results obtained by applying these techniques to real sets of glycan structures

A Survey on Graph Kernels

Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner's guide to kernel-based graph classification

Discourse Structure in Machine Translation Evaluation

In this article, we explore the potential of using sentence-level discourse structure for machine translation evaluation. We first design discourse-aware similarity measures, which use all-subtree kernels to compare discourse parse trees in accordance with the Rhetorical Structure Theory (RST). Then, we show that a simple linear combination with these measures can help improve various existing machine translation evaluation metrics regarding correlation with human judgments both at the segment- and at the system-level. This suggests that discourse information is complementary to the information used by many of the existing evaluation metrics, and thus it could be taken into account when developing richer evaluation metrics, such as the WMT-14 winning combined metric DiscoTKparty. We also provide a detailed analysis of the relevance of various discourse elements and relations from the RST parse trees for machine translation evaluation. In particular we show that: (i) all aspects of the RST tree are relevant, (ii) nuclearity is more useful than relation type, and (iii) the similarity of the translation RST tree to the reference tree is positively correlated with translation quality.Comment: machine translation, machine translation evaluation, discourse analysis. Computational Linguistics, 201

Efficient Frequent Subtree Mining Beyond Forests

A common paradigm in distance-based learning is to embed the instance space into some appropriately chosen feature space equipped with a metric and to define the dissimilarity between instances by the distance of their images in the feature space. If the instances are graphs, then frequent connected subgraphs are a well-suited pattern language to define such feature spaces. Identifying the set of frequent connected subgraphs and subsequently computing embeddings for graph instances, however, is computationally intractable. As a result, existing frequent subgraph mining algorithms either restrict the structural complexity of the instance graphs or require exponential delay between the output of subsequent patterns. Hence distance-based learners lack an efficient way to operate on arbitrary graph data. To resolve this problem, in this thesis we present a mining system that gives up the demand on the completeness of the pattern set to instead guarantee a polynomial delay between subsequent patterns. Complementing this, we devise efficient methods to compute the embedding of arbitrary graphs into the Hamming space spanned by our pattern set. As a result, we present a system that allows to efficiently apply distance-based learning methods to arbitrary graph databases. To overcome the computational intractability of the mining step, we consider only frequent subtrees for arbitrary graph databases. This restriction alone, however, does not suffice to make the problem tractable. We reduce the mining problem from arbitrary graphs to forests by replacing each graph by a polynomially sized forest obtained from a random sample of its spanning trees. This results in an incomplete mining algorithm. However, we prove that the probability of missing a frequent subtree pattern is low. We show empirically that this is true in practice even for very small sized forests. As a result, our algorithm is able to mine frequent subtrees in a range of graph databases where state-of-the-art exact frequent subgraph mining systems fail to produce patterns in reasonable time or even at all. Furthermore, the predictive performance of our patterns is comparable to that of exact frequent connected subgraphs, where available. The above method considers polynomially many spanning trees for the forest, while many graphs have exponentially many spanning trees. The number of patterns found by our mining algorithm can be negatively influenced by this exponential gap. We hence propose a method that can (implicitly) consider forests of exponential size, while remaining computationally tractable. This results in a higher recall for our incomplete mining algorithm. Furthermore, the methods extend the known positive results on the tractability of exact frequent subtree mining to a novel class of transaction graphs. We conjecture that the next natural extension of our results to a larger transaction graph class is at least as difficult as proving whether P = NP, or not. Regarding the graph embedding step, we apply a similar strategy as in the mining step. We represent a novel graph by a forest of its spanning trees and decide whether the frequent trees from the mining step are subgraph isomorphic to this forest. As a result, the embedding computation has one-sided error with respect to the exact subgraph isomorphism test but is computationally tractable. Furthermore, we show that we can leverage a partial order on the pattern set. This structure can be used to reduce the runtime of the embedding computation dramatically. For the special case of Jaccard-similarity between graph embeddings, a further substantial reduction of runtime can be achieved using min-hashing. The Jaccard-distance can be approximated using small sketch vectors that can be computed fast, again using the partial order on the tree patterns

Discovery of Dependency Tree Patterns for Relation Extraction

PACLIC 23 / City University of Hong Kong / 3-5 December 200

Quantifying Privacy Loss of Human Mobility Graph Topology

Human mobility is often represented as a mobility network, or graph, with nodes representing places of significance which an individual visits, such as their home, work, places of social amenity, etc., and edge weights corresponding to probability estimates of movements between these places. Previous research has shown that individuals can be identified by a small number of geolocated nodes in their mobility network, rendering mobility trace anonymization a hard task. In this paper we build on prior work and demonstrate that even when all location and timestamp information is removed from nodes, the graph topology of an individual mobility network itself is often uniquely identifying. Further, we observe that a mobility network is often unique, even when only a small number of the most popular nodes and edges are considered. We evaluate our approach using a large dataset of cell-tower location traces from 1 500 smartphone handsets with a mean duration of 430 days. We process the data to derive the top−N places visited by the device in the trace, and find that 93% of traces have a unique top−10 mobility network, and all traces are unique when considering top−15 mobility networks. Since mobility patterns, and therefore mobility networks for an individual, vary over time, we use graph kernel distance functions, to determine whether two mobility networks, taken at different points in time, represent the same individual. We then show that our distance metrics, while imperfect predictors, perform significantly better than a random strategy and therefore our approach represents a significant loss in privacy

Propagation Kernels

We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage early-stage distributions from propagation schemes such as random walks to capture structural information encoded in node labels, attributes, and edge information. This has two benefits. First, off-the-shelf propagation schemes can be used to naturally construct kernels for many graph types, including labeled, partially labeled, unlabeled, directed, and attributed graphs. Second, by leveraging existing efficient and informative propagation schemes, propagation kernels can be considerably faster than state-of-the-art approaches without sacrificing predictive performance. We will also show that if the graphs at hand have a regular structure, for instance when modeling image or video data, one can exploit this regularity to scale the kernel computation to large databases of graphs with thousands of nodes. We support our contributions by exhaustive experiments on a number of real-world graphs from a variety of application domains