Applications of machine learning methods increasingly deal with graph structured data through kernels. Most existing graph kernels compare graphs in terms of features defined on small subgraphs such as walks, paths or graphlets, adopting an inherently local perspective. However, several interesting properties such as girth or chromatic number are global properties of the graph, and are not captured in local substructures. This paper presents two graph kernels defined on unlabeled graphs which capture global properties of graphs using the celebrated Lovász number and its associated orthonormal representation. We make progress towards theoretical results aiding kernel choice, proving a result about the separation margin of our kernel for classes of graphs. We give empirical results on classification of synthesized graphs with important global properties as well as established benchmark graph datasets, showing that the accuracy of our kernels is better than or competitive to existing graph kernels.

This paper presents a novel method for entity disambiguation in anonymized graphs using local neighborhood structure. Most existing approaches leverage node information, which might not be available in several contexts due to privacy concerns, or information about the sources of the data. We consider this problem in the supervised setting where we are provided only with a base graph and a set of nodes labelled as ambiguous or unambiguous. We characterize the similarity between two nodes based on their local neighborhood structure using graph kernels; and solve the resulting classification task using SVMs. We give empirical evidence on two real-world datasets, comparing our approach to a state-of-the-art method, highlighting the advantages of our approach. We show that using less information, our method is significantly better in terms of either speed or accuracy or both. We also present extensions of two existing graphs kernels, namely, the direct product kernel and the shortest-path kernel, with significant improvements in accuracy. For the direct product kernel, our extension also provides significant computational benefits. Moreover, we design and implement the algorithms of our method to work in a distributed fashion using the GraphLab framework, ensuring high scalability.

Lovász introduced the theta function in his seminal paper [23] giving his celebrated solution to the problem of computing the Shannon capacity of the pentagon. Since then, the Lovász theta function has come to play a central role in information theory, graph theory and combinatorial optimization [11, 10], indeed Goemans [10] was led to remark: “it seems all paths lead to ϑ!”. The definition of the theta function also gives an elegant geometrical representation of the graph via an embedding in a spherical cap on the unit sphere which has many applications in graph theory and machine learning, some of them perhaps not yet fully appreciated. It is one of the goals of this paper to highlight how the Lovász embedding is a powerful and unifying tool in diverse graph theory and data mining applications.

The problem of identifying user intent has received considerable attention in recent years, particularly in the context of improving the search experience via query contextualization. Intent can be characterized by multiple dimensions, which are often not observed from query words alone. Accurate identification of Intent from query words remains a challenging problem primarily because it is extremely difficult to discover these dimensions. The problem is often significantly compounded due to lack of representative training sample. We present a generic, extensible framework for learning the multi-dimensional representation of user intent from the query words. The approach models the latent relationships between facets using tree structured distribution which leads to an efficient and convergent algorithm, FastQ, for identifying the multi-faceted intent of users based on just the query words. We also incorporated WordNet to extend the system capabilities to queries which contain words that do not appear in the training data. Empirical results show that FastQ yields accurate identification of intent when compared to a gold standard.

BACKGROUND: Temporal analysis of gene expression data has been limited to identifying genes whose expression varies with time and/or correlation between genes that have similar temporal profiles. Often, the methods do not consider the underlying network constraints that connect the genes. It is becoming increasingly evident that interactions change substantially with time. Thus far, there is no systematic method to relate the temporal changes in gene expression to the dynamics of interactions between them. Information on interaction dynamics would open up possibilities for discovering new mechanisms of regulation by providing valuable insight into identifying time-sensitive interactions as well as permit studies on the effect of a genetic perturbation. RESULTS: We present NETGEM, a tractable model rooted in Markov dynamics, for analyzing the dynamics of the interactions between proteins based on the dynamics of the expression changes of the genes that encode them. The model treats the interaction strengths as random variables which are modulated by suitable priors. This approach is necessitated by the extremely small sample size of the datasets, relative to the number of interactions. The model is amenable to a linear time algorithm for efficient inference. Using temporal gene expression data, NETGEM was successful in identifying (i) temporal interactions and determining their strength, (ii) functional categories of the actively interacting partners and (iii) dynamics of interactions in perturbed networks. CONCLUSIONS: NETGEM represents an optimal trade-off between model complexity and data requirement. It was able to deduce actively interacting genes and functional categories from temporal gene expression data. It permits inference by incorporating the information available in perturbed networks. Given that the inputs to NETGEM are only the network and the temporal variation of the nodes, this algorithm promises to have widespread applications, beyond biological systems.The source code for NETGEM is available from https://github.com/vjethava/NETGEM.