Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks

Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that exponentially grows with number of GCN layers, or a large space requirement for keeping the entire graph and the embedding of each node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm that is suitable for SGD-based training by exploiting the graph clustering structure. Cluster-GCN works as the following: at each step, it samples a block of nodes that associate with a dense subgraph identified by a graph clustering algorithm, and restricts the neighborhood search within this subgraph. This simple but effective strategy leads to significantly improved memory and computational efficiency while being able to achieve comparable test accuracy with previous algorithms. To test the scalability of our algorithm, we create a new Amazon2M data with 2 million nodes and 61 million edges which is more than 5 times larger than the previous largest publicly available dataset (Reddit). For training a 3-layer GCN on this data, Cluster-GCN is faster than the previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this data, our algorithm can finish in around 36 minutes while all the existing GCN training algorithms fail to train due to the out-of-memory issue. Furthermore, Cluster-GCN allows us to train much deeper GCN without much time and memory overhead, which leads to improved prediction accuracy---using a 5-layer Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI dataset, while the previous best result was 98.71 by [16]. Our codes are publicly available at https://github.com/google-research/google-research/tree/master/cluster_gcn.Comment: In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (KDD'19

Virtual cluster scheduling through the scheduling graph

This paper presents an instruction scheduling and cluster assignment approach for clustered processors. The proposed technique makes use of a novel representation named the scheduling graph which describes all possible schedules. A powerful deduction process is applied to this graph, reducing at each step the set of possible schedules. In contrast to traditional list scheduling techniques, the proposed scheme tries to establish relations among instructions rather than assigning each instruction to a particular cycle. The main advantage is that wrong or poor schedules can be anticipated and discarded earlier. In addition, cluster assignment of instructions is performed using another novel concept called virtual clusters, which define sets of instructions that must execute in the same cluster. These clusters are managed during the deduction process to identify incompatibilities among instructions. The mapping of virtual to physical clusters is postponed until the scheduling of the instructions has finalized. The advantages this novel approach features include: (1) accurate scheduling information when assigning, and, (2) accurate information of the cluster assignment constraints imposed by scheduling decisions. We have implemented and evaluated the proposed scheme with superblocks extracted from Speclnt95 and MediaBench. The results show that this approach produces better schedules than the previous state-of-the-art. Speed-ups are up to 15%, with average speed-ups ranging from 2.5% (2-Clusters) to 9.5% (4-Clusters).Peer ReviewedPostprint (published version

k-Nearest Neighbour Classifiers: 2nd Edition (with Python examples)

Perhaps the most straightforward classifier in the arsenal or machine learning techniques is the Nearest Neighbour Classifier -- classification is achieved by identifying the nearest neighbours to a query example and using those neighbours to determine the class of the query. This approach to classification is of particular importance because issues of poor run-time performance is not such a problem these days with the computational power that is available. This paper presents an overview of techniques for Nearest Neighbour classification focusing on; mechanisms for assessing similarity (distance), computational issues in identifying nearest neighbours and mechanisms for reducing the dimension of the data. This paper is the second edition of a paper previously published as a technical report. Sections on similarity measures for time-series, retrieval speed-up and intrinsic dimensionality have been added. An Appendix is included providing access to Python code for the key methods.Comment: 22 pages, 15 figures: An updated edition of an older tutorial on kN

Enhancing Energy Production with Exascale HPC Methods

High Performance Computing (HPC) resources have become the key actor for achieving more ambitious challenges in many disciplines. In this step beyond, an explosion on the available parallelism and the use of special purpose processors are crucial. With such a goal, the HPC4E project applies new exascale HPC techniques to energy industry simulations, customizing them if necessary, and going beyond the state-of-the-art in the required HPC exascale simulations for different energy sources. In this paper, a general overview of these methods is presented as well as some specific preliminary results.The research leading to these results has received funding from the European Union's Horizon 2020 Programme (2014-2020) under the HPC4E Project (www.hpc4e.eu), grant agreement n° 689772, the Spanish Ministry of Economy and Competitiveness under the CODEC2 project (TIN2015-63562-R), and from the Brazilian Ministry of Science, Technology and Innovation through Rede Nacional de Pesquisa (RNP). Computer time on Endeavour cluster is provided by the Intel Corporation, which enabled us to obtain the presented experimental results in uncertainty quantification in seismic imagingPostprint (author's final draft

An evaluation of intrusive instrumental intelligibility metrics

Instrumental intelligibility metrics are commonly used as an alternative to listening tests. This paper evaluates 12 monaural intrusive intelligibility metrics: SII, HEGP, CSII, HASPI, NCM, QSTI, STOI, ESTOI, MIKNN, SIMI, SIIB, and $\text{sEPSM}^\text{corr}$. In addition, this paper investigates the ability of intelligibility metrics to generalize to new types of distortions and analyzes why the top performing metrics have high performance. The intelligibility data were obtained from 11 listening tests described in the literature. The stimuli included Dutch, Danish, and English speech that was distorted by additive noise, reverberation, competing talkers, pre-processing enhancement, and post-processing enhancement. SIIB and HASPI had the highest performance achieving a correlation with listening test scores on average of $\rho=0.92$ and $\rho=0.89$, respectively. The high performance of SIIB may, in part, be the result of SIIBs developers having access to all the intelligibility data considered in the evaluation. The results show that intelligibility metrics tend to perform poorly on data sets that were not used during their development. By modifying the original implementations of SIIB and STOI, the advantage of reducing statistical dependencies between input features is demonstrated. Additionally, the paper presents a new version of SIIB called $\text{SIIB}^\text{Gauss}$, which has similar performance to SIIB and HASPI, but takes less time to compute by two orders of magnitude.Comment: Published in IEEE/ACM Transactions on Audio, Speech, and Language Processing, 201