Answering Top-k Queries Over a Mixture of Attractive and Repulsive Dimensions

In this paper, we formulate a top-k query that compares objects in a database to a user-provided query object on a novel scoring function. The proposed scoring function combines the idea of attractive and repulsive dimensions into a general framework to overcome the weakness of traditional distance or similarity measures. We study the properties of the proposed class of scoring functions and develop efficient and scalable index structures that index the isolines of the function. We demonstrate various scenarios where the query finds application. Empirical evaluation demonstrates a performance gain of one to two orders of magnitude on querying time over existing state-of-the-art top-k techniques. Further, a qualitative analysis is performed on a real dataset to highlight the potential of the proposed query in discovering hidden data characteristics.Comment: VLDB201

GRAFENNE: Learning on Graphs with Heterogeneous and Dynamic Feature Sets

Graph neural networks (GNNs), in general, are built on the assumption of a static set of features characterizing each node in a graph. This assumption is often violated in practice. Existing methods partly address this issue through feature imputation. However, these techniques (i) assume uniformity of feature set across nodes, (ii) are transductive by nature, and (iii) fail to work when features are added or removed over time. In this work, we address these limitations through a novel GNN framework called GRAFENNE. GRAFENNE performs a novel allotropic transformation on the original graph, wherein the nodes and features are decoupled through a bipartite encoding. Through a carefully chosen message passing framework on the allotropic transformation, we make the model parameter size independent of the number of features and thereby inductive to both unseen nodes and features. We prove that GRAFENNE is at least as expressive as any of the existing message-passing GNNs in terms of Weisfeiler-Leman tests, and therefore, the additional inductivity to unseen features does not come at the cost of expressivity. In addition, as demonstrated over four real-world graphs, GRAFENNE empowers the underlying GNN with high empirical efficacy and the ability to learn in continual fashion over streaming feature sets.Comment: 17 pages, 4 figures and 9 tables. Accepted in ICML 2023, DOI will be updated once it is availabl

GSHOT: Few-shot Generative Modeling of Labeled Graphs

Deep graph generative modeling has gained enormous attraction in recent years due to its impressive ability to directly learn the underlying hidden graph distribution. Despite their initial success, these techniques, like much of the existing deep generative methods, require a large number of training samples to learn a good model. Unfortunately, large number of training samples may not always be available in scenarios such as drug discovery for rare diseases. At the same time, recent advances in few-shot learning have opened door to applications where available training data is limited. In this work, we introduce the hitherto unexplored paradigm of few-shot graph generative modeling. Towards this, we develop GSHOT, a meta-learning based framework for few-shot labeled graph generative modeling. GSHOT learns to transfer meta-knowledge from similar auxiliary graph datasets. Utilizing these prior experiences, GSHOT quickly adapts to an unseen graph dataset through self-paced fine-tuning. Through extensive experiments on datasets from diverse domains having limited training samples, we establish that GSHOT generates graphs of superior fidelity compared to existing baselines

Trajectory Aware Macro-cell Planning for Mobile Users

We design and evaluate algorithms for efficient user-mobility driven macro-cell planning in cellular networks. As cellular networks embrace heterogeneous technologies (including long range 3G/4G and short range WiFi, Femto-cells, etc.), most traffic generated by static users gets absorbed by the short-range technologies, thereby increasingly leaving mobile user traffic to macro-cells. To this end, we consider a novel approach that factors in the trajectories of mobile users as well as the impact of city geographies and their associated road networks for macro-cell planning. Given a budget k of base-stations that can be upgraded, our approach selects a deployment that impacts the most number of user trajectories. The generic formulation incorporates the notion of quality of service of a user trajectory as a parameter to allow different application-specific requirements, and operator choices.We show that the proposed trajectory utility maximization problem is NP-hard, and design multiple heuristics. We evaluate our algorithms with real and synthetic data sets emulating different city geographies to demonstrate their efficacy. For instance, with an upgrade budget k of 20%, our algorithms perform 3-8 times better in improving the user quality of service on trajectories in different city geographies when compared to greedy location-based base-station upgrades.Comment: Published in INFOCOM 201

NeuroCUT: A Neural Approach for Robust Graph Partitioning

Graph partitioning aims to divide a graph into $k$ disjoint subsets while optimizing a specific partitioning objective. The majority of formulations related to graph partitioning exhibit NP-hardness due to their combinatorial nature. As a result, conventional approximation algorithms rely on heuristic methods, sometimes with approximation guarantees and sometimes without. Unfortunately, traditional approaches are tailored for specific partitioning objectives and do not generalize well across other known partitioning objectives from the literature. To overcome this limitation, and learn heuristics from the data directly, neural approaches have emerged, demonstrating promising outcomes. In this study, we extend this line of work through a novel framework, NeuroCut. NeuroCut introduces two key innovations over prevailing methodologies. First, it is inductive to both graph topology and the partition count, which is provided at query time. Second, by leveraging a reinforcement learning based framework over node representations derived from a graph neural network, NeuroCut can accommodate any optimization objective, even those encompassing non-differentiable functions. Through empirical evaluation, we demonstrate that NeuroCut excels in identifying high-quality partitions, showcases strong generalization across a wide spectrum of partitioning objectives, and exhibits resilience to topological modifications

Discovering Symbolic Laws Directly from Trajectories with Hamiltonian Graph Neural Networks

The time evolution of physical systems is described by differential equations, which depend on abstract quantities like energy and force. Traditionally, these quantities are derived as functionals based on observables such as positions and velocities. Discovering these governing symbolic laws is the key to comprehending the interactions in nature. Here, we present a Hamiltonian graph neural network (HGNN), a physics-enforced GNN that learns the dynamics of systems directly from their trajectory. We demonstrate the performance of HGNN on n-springs, n-pendulums, gravitational systems, and binary Lennard Jones systems; HGNN learns the dynamics in excellent agreement with the ground truth from small amounts of data. We also evaluate the ability of HGNN to generalize to larger system sizes, and to hybrid spring-pendulum system that is a combination of two original systems (spring and pendulum) on which the models are trained independently. Finally, employing symbolic regression on the learned HGNN, we infer the underlying equations relating the energy functionals, even for complex systems such as the binary Lennard-Jones liquid. Our framework facilitates the interpretable discovery of interaction laws directly from physical system trajectories. Furthermore, this approach can be extended to other systems with topology-dependent dynamics, such as cells, polydisperse gels, or deformable bodies