t 30pt KONG: Kernels for 反白 : ordered-neighborhood graphs l 47pt 黑体 NeurIPS PS confere renc nce (poster er #122) 28pt 反白 细黑体 www.huawei.com Authors: Moez Draief, Konstantin Kutzkov, Kevin Scaman , Milan Vojnovic Date: November 30, 2018
Background Graphs are highly complex objects Combinatorial nature of the object Many relevant features size, connectivity, density, hubs, periphery, short range patterns, large- scale structure, cliques, connected components, spectral characteristics… How to make it usable for ML problems? Additional information: ordered neighborhoods All edges may not be as important (e.g. friends on a social network) #4 #5 Networks are often dynamic objects, changing through time #3 me We may have a ranking among neighbors Time of creation, importance, objective value, distance,… #1 #2 How to account for this information? Page 2 NeurIPS conference, Montréal HUAWEI TECHNOLOGIES CO., LTD. Huawei Confidential
The KONG algorithmic framework A scalable kernel representation for graphs Iterative algorithm for node representation 1) Weisfeiler-Lehman, breadth- first search… Ordered neighborhood representation using string kernels 2) K-gram counting approach, order captured by selection process Refined k-gram counting using polynomial or cosine kernels 3) More powerful representation Sketching method for kernel approximation 4) Approximate embedding of counting vectors preserving scalar products 𝑤 3 Φ 𝑤 1 Φ 𝑤 6 𝑤 6 Φ 𝑤 3 𝑤 2 Φ 𝑤 2 𝑤 5 Φ(𝐻) 𝑤 1 Φ 𝑤 4 Φ 𝑤 5 ℝ 𝑒 𝑤 4 𝐻 Page 3 NeurIPS conference, Montréal HUAWEI TECHNOLOGIES CO., LTD. Huawei Confidential
Simple example Sketching representation in ℝ 𝑒 Graph with string representations H O Φ 𝑤 1 = Φ 𝑤 2 = Φ 𝑤 5 𝑤 3 𝑤 6 Φ 𝑤 6 Φ 𝑤 3 𝑤 2 𝑤 5 A A 𝑤 4 𝑤 1 Φ 𝑤 4 A B Page 4 NeurIPS conference, Montréal HUAWEI TECHNOLOGIES CO., LTD. Huawei Confidential
Simple example Sketching representation in ℝ 𝑒 Graph with string representations H O Φ 𝑤 1 𝑤 3 𝑤 6 Φ 𝑤 6 Φ 𝑤 5 Φ 𝑤 3 𝑤 2 𝑤 5 Φ 𝑤 2 ABH AOA 𝑤 4 𝑤 1 Φ 𝑤 4 AA BA Page 5 NeurIPS conference, Montréal HUAWEI TECHNOLOGIES CO., LTD. Huawei Confidential
Simple example Sketching representation in ℝ 𝑒 Graph with string representations H O 𝑤 3 𝑤 6 Φ 𝑤 1 Φ 𝑤 6 Φ 𝑤 3 𝑤 2 𝑤 5 Φ 𝑤 5 AOAOABH ABHBAH Φ 𝑤 2 𝑤 4 𝑤 1 AAABH BAAOA Φ 𝑤 4 Page 6 NeurIPS conference, Montréal HUAWEI TECHNOLOGIES CO., LTD. Huawei Confidential
Simple example Sketching representation in ℝ 𝑒 Graph with string representations H O Φ 𝑤 1 𝑤 3 𝑤 6 Φ 𝑤 6 Φ 𝑤 3 𝑤 2 𝑤 5 AOAOABH… ABHBAH… 𝑤 4 𝑤 1 Φ 𝑤 2 Φ 𝑤 5 AAABH… Φ 𝑤 4 BAAOA… Page 7 NeurIPS conference, Montréal HUAWEI TECHNOLOGIES CO., LTD. Huawei Confidential
Simple example Sketching representation in ℝ 𝑒 Graph with string representations H O Φ 𝑤 1 𝑤 3 𝑤 6 Φ 𝑤 6 Φ 𝑤 3 𝑤 2 𝑤 5 AOAOABH… Φ(𝐻) ABHBAH… 𝑤 4 𝑤 1 Φ 𝑤 2 Φ 𝑤 5 AAABH… Φ 𝑤 4 BAAOA… Page 8 NeurIPS conference, Montréal HUAWEI TECHNOLOGIES CO., LTD. Huawei Confidential
Conclusion The KONG framework: a new scalable algorithm for graphs kernels First method using ordered neighborhoods , Highly scalable approach that can handle graphs with millions of nodes in seconds on a laptop in a single-threaded implementation, Flexibility in the choice of the kernel function, Outputs vector representations Can be used by any ML algorithm for regression, classification, clustering, etc… Excellent results on datasets from various domains, including Anomaly detection in network flow graphs, Gender prediction in recommender systems, Affluence prediction in customer purchase graphs. Poster #122 Page 9 NeurIPS conference, Montréal HUAWEI TECHNOLOGIES CO., LTD. Huawei Confidential
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