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

apk2vec: Semi-supervised multi-view representation learning for profiling Android applications

Building behavior profiles of Android applications (apps) with holistic, rich and multi-view information (e.g., incorporating several semantic views of an app such as API sequences, system calls, etc.) would help catering downstream analytics tasks such as app categorization, recommendation and malware analysis significantly better. Towards this goal, we design a semi-supervised Representation Learning (RL) framework named apk2vec to automatically generate a compact representation (aka profile/embedding) for a given app. More specifically, apk2vec has the three following unique characteristics which make it an excellent choice for largescale app profiling: (1) it encompasses information from multiple semantic views such as API sequences, permissions, etc., (2) being a semi-supervised embedding technique, it can make use of labels associated with apps (e.g., malware family or app category labels) to build high quality app profiles, and (3) it combines RL and feature hashing which allows it to efficiently build profiles of apps that stream over time (i.e., online learning). The resulting semi-supervised multi-view hash embeddings of apps could then be used for a wide variety of downstream tasks such as the ones mentioned above. Our extensive evaluations with more than 42,000 apps demonstrate that apk2vec's app profiles could significantly outperform state-of-the-art techniques in four app analytics tasks namely, malware detection, familial clustering, app clone detection and app recommendation.Comment: International Conference on Data Mining, 201

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Neural function approximation on graphs: shape modelling, graph discrimination & compression

Graphs serve as a versatile mathematical abstraction of real-world phenomena in numerous scientific disciplines. This thesis is part of the Geometric Deep Learning subject area, a family of learning paradigms, that capitalise on the increasing volume of non-Euclidean data so as to solve real-world tasks in a data-driven manner. In particular, we focus on the topic of graph function approximation using neural networks, which lies at the heart of many relevant methods. In the first part of the thesis, we contribute to the understanding and design of Graph Neural Networks (GNNs). Initially, we investigate the problem of learning on signals supported on a fixed graph. We show that treating graph signals as general graph spaces is restrictive and conventional GNNs have limited expressivity. Instead, we expose a more enlightening perspective by drawing parallels between graph signals and signals on Euclidean grids, such as images and audio. Accordingly, we propose a permutation-sensitive GNN based on an operator analogous to shifts in grids and instantiate it on 3D meshes for shape modelling (Spiral Convolutions). Following, we focus on learning on general graph spaces and in particular on functions that are invariant to graph isomorphism. We identify a fundamental trade-off between invariance, expressivity and computational complexity, which we address with a symmetry-breaking mechanism based on substructure encodings (Graph Substructure Networks). Substructures are shown to be a powerful tool that provably improves expressivity while controlling computational complexity, and a useful inductive bias in network science and chemistry. In the second part of the thesis, we discuss the problem of graph compression, where we analyse the information-theoretic principles and the connections with graph generative models. We show that another inevitable trade-off surfaces, now between computational complexity and compression quality, due to graph isomorphism. We propose a substructure-based dictionary coder - Partition and Code (PnC) - with theoretical guarantees that can be adapted to different graph distributions by estimating its parameters from observations. Additionally, contrary to the majority of neural compressors, PnC is parameter and sample efficient and is therefore of wide practical relevance. Finally, within this framework, substructures are further illustrated as a decisive archetype for learning problems on graph spaces.Open Acces

Engineering a Preprocessor for Symmetry Detection

State-of-the-art solvers for symmetry detection in combinatorial objects are becoming increasingly sophisticated software libraries. Most of the solvers were initially designed with inputs from combinatorics in mind (nauty, bliss, Traces, dejavu). They excel at dealing with a complicated core of the input. Others focus on practical instances that exhibit sparsity. They excel at dealing with comparatively easy but extremely large substructures of the input (saucy). In practice, these differences manifest in significantly diverging performances on different types of graph classes. We engineer a preprocessor for symmetry detection. The result is a tool designed to shrink sparse, large substructures of the input graph. On most of the practical instances, the preprocessor improves the overall running time significantly for many of the state-of-the-art solvers. At the same time, our benchmarks show that the additional overhead is negligible. Overall we obtain single algorithms with competitive performance across all benchmark graphs. As such, the preprocessor bridges the disparity between solvers that focus on combinatorial graphs and large practical graphs. In fact, on most of the practical instances the combined setup significantly outperforms previous state-of-the-art