Generating Practical Random Hyperbolic Graphs in Near-Linear Time and with Sub-Linear Memory

Random graph models, originally conceived to study the structure of networks and the emergence of their properties, have become an indispensable tool for experimental algorithmics. Amongst them, hyperbolic random graphs form a well-accepted family, yielding realistic complex networks while being both mathematically and algorithmically tractable. We introduce two generators MemGen and HyperGen for the G_{alpha,C}(n) model, which distributes n random points within a hyperbolic plane and produces m=n*d/2 undirected edges for all point pairs close by; the expected average degree d and exponent 2*alpha+1 of the power-law degree distribution are controlled by alpha>1/2 and C. Both algorithms emit a stream of edges which they do not have to store. MemGen keeps O(n) items in internal memory and has a time complexity of O(n*log(log n) + m), which is optimal for networks with an average degree of d=Omega(log(log n)). For realistic values of d=o(n / log^{1/alpha}(n)), HyperGen reduces the memory footprint to O([n^{1-alpha}*d^alpha + log(n)]*log(n)). In an experimental evaluation, we compare HyperGen with four generators among which it is consistently the fastest. For small d=10 we measure a speed-up of 4.0 compared to the fastest publicly available generator increasing to 29.6 for d=1000. On commodity hardware, HyperGen produces 3.7e8 edges per second for graphs with 1e6 < m < 1e12 and alpha=1, utilising less than 600MB of RAM. We demonstrate nearly linear scalability on an Intel Xeon Phi

Loom: Query-aware Partitioning of Online Graphs

As with general graph processing systems, partitioning data over a cluster of machines improves the scalability of graph database management systems. However, these systems will incur additional network cost during the execution of a query workload, due to inter-partition traversals. Workload-agnostic partitioning algorithms typically minimise the likelihood of any edge crossing partition boundaries. However, these partitioners are sub-optimal with respect to many workloads, especially queries, which may require more frequent traversal of specific subsets of inter-partition edges. Furthermore, they largely unsuited to operating incrementally on dynamic, growing graphs. We present a new graph partitioning algorithm, Loom, that operates on a stream of graph updates and continuously allocates the new vertices and edges to partitions, taking into account a query workload of graph pattern expressions along with their relative frequencies. First we capture the most common patterns of edge traversals which occur when executing queries. We then compare sub-graphs, which present themselves incrementally in the graph update stream, against these common patterns. Finally we attempt to allocate each match to single partitions, reducing the number of inter-partition edges within frequently traversed sub-graphs and improving average query performance. Loom is extensively evaluated over several large test graphs with realistic query workloads and various orderings of the graph updates. We demonstrate that, given a workload, our prototype produces partitionings of significantly better quality than existing streaming graph partitioning algorithms Fennel and LDG

Generation of realistic human behaviour

As the use of computers and robots in our everyday lives increases so does the need for better interaction with these devices. Human-computer interaction relies on the ability to understand and generate human behavioural signals such as speech, facial expressions and motion. This thesis deals with the synthesis and evaluation of such signals, focusing not only on their intelligibility but also on their realism. Since these signals are often correlated, it is common for methods to drive the generation of one signal using another. The thesis begins by tackling the problem of speech-driven facial animation and proposing models capable of producing realistic animations from a single image and an audio clip. The goal of these models is to produce a video of a target person, whose lips move in accordance with the driving audio. Particular focus is also placed on a) generating spontaneous expression such as blinks, b) achieving audio-visual synchrony and c) transferring or producing natural head motion. The second problem addressed in this thesis is that of video-driven speech reconstruction, which aims at converting a silent video into waveforms containing speech. The method proposed for solving this problem is capable of generating intelligible and accurate speech for both seen and unseen speakers. The spoken content is correctly captured thanks to a perceptual loss, which uses features from pre-trained speech-driven animation models. The ability of the video-to-speech model to run in real-time allows its use in hearing assistive devices and telecommunications. The final work proposed in this thesis is a generic domain translation system, that can be used for any translation problem including those mapping across different modalities. The framework is made up of two networks performing translations in opposite directions and can be successfully applied to solve diverse sets of translation problems, including speech-driven animation and video-driven speech reconstruction.Open Acces

SocialInteractionGAN: Multi-person Interaction Sequence Generation

Prediction of human actions in social interactions has important applications in the design of social robots or artificial avatars. In this paper, we model human interaction generation as a discrete multi-sequence generation problem and present SocialInteractionGAN, a novel adversarial architecture for conditional interaction generation. Our model builds on a recurrent encoder-decoder generator network and a dual-stream discriminator. This architecture allows the discriminator to jointly assess the realism of interactions and that of individual action sequences. Within each stream a recurrent network operating on short subsequences endows the output signal with local assessments, better guiding the forthcoming generation. Crucially, contextual information on interacting participants is shared among agents and reinjected in both the generation and the discriminator evaluation processes. We show that the proposed SocialInteractionGAN succeeds in producing high realism action sequences of interacting people, comparing favorably to a diversity of recurrent and convolutional discriminator baselines. Evaluations are conducted using modified Inception Score and Fr{\'e}chet Inception Distance metrics, that we specifically design for discrete sequential generated data. The distribution of generated sequences is shown to approach closely that of real data. In particular our model properly learns the dynamics of interaction sequences, while exploiting the full range of actions