approximate graph embeddings in the cloud
play

Approximate Graph Embeddings in the Cloud 2 5 3 AC B 2 2 2 2 - PowerPoint PPT Presentation

Aug 25, 2023 •99 likes •329 views

Approximate Graph Embeddings in the Cloud 2 5 3 AC B 2 2 2 2 D 0 3 1 Highlights of Algorithms 2018 Matthias Rost Technische Universitt Berlin, Internet Network Architectures Stefan Schmid Universitt Wien, Communication

  1. Approximate Graph Embeddings in the Cloud 2 5 3 AC B 2 2 2 2 D 0 3 1 Highlights of Algorithms 2018 Matthias Rost Technische Universität Berlin, Internet Network Architectures Stefan Schmid Universität Wien, Communication Technologies

  2. Cloud Providers Offer Data Center Resources Customers Cloud Data Center (Amazon, Google, . . . ) Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 2

  3. Cloud Providers Offer Data Center Resources Customers Cloud Data Center (Amazon, Google, . . . ) ‘Classic’ Cloud Computing 1 4 ◮ Customer specifies A B number and ‘size’ of Virtual Machines ◮ Communication between D C VMs not modeled 3 1 Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 3

  4. Cloud Providers Offer Data Center Resources Customers Cloud Data Center (Amazon, Google, . . . ) ‘Classic’ Cloud Computing Goal: Virtual Networks (since ≈ 2006) ◮ Customer specifies 1 4 1 4 1 A B A B number and ‘size’ of ◮ Additionally: 6 Virtual Machines communication 1 1 ◮ Communication between requirements given D C D C 1 VMs not modeled 3 1 3 1 Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 4

  5. ‘Classic’ Cloud Computing Goal: Virtual Networks (since ≈ 2006) ◮ Customer specifies 1 4 1 4 1 A B A B number and ‘size’ of ◮ Additionally: 6 Virtual Machines communication 1 1 ◮ Communication between requirements given D C D C 1 VMs not modeled 3 1 3 1 The Virtual Network Embedding Problem (VNEP) Virtual Network Substrate (Physical Network) ◮ Map virtual nodes to substrate nodes 1 4 2 5 3 1 A B 3 ◮ Map virtual edges to paths in the substrate 6 1 1 2 2 ◮ Respecting capacities & mapping restrictions 2 2 D C 1 3 1 0 3 1 Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 5

  6. ‘Classic’ Cloud Computing Goal: Virtual Networks (since ≈ 2006) ◮ Customer specifies 1 4 1 4 1 A B A B number and ‘size’ of ◮ Additionally: 6 Virtual Machines communication 1 1 ◮ Communication between requirements given D C D C 1 VMs not modeled 3 1 3 1 The Virtual Network Embedding Problem (VNEP) Virtual Network Substrate (Physical Network) 2 / 2 4 / 5 1 4 3 ◮ Map virtual nodes to substrate nodes 1 A B AC B 3 ◮ Map virtual edges to paths in the substrate 6 1 1 2 2 ◮ Respecting capacities & mapping restrictions 2 2 D C D 1 3 / 3 3 1 0 / 0 1 / 1 Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 6

  7. ‘Classic’ Cloud Computing Goal: Virtual Networks (since ≈ 2006) 1 4 ◮ Customer specifies 1 4 1 A B A B number and ‘size’ of ◮ Additionally: Virtual Machines 6 communication 1 1 ◮ Communication between requirements given D C D C 1 VMs not modeled 3 1 3 1 The Virtual Network Embedding Problem (VNEP) Virtual Network Substrate (Physical Network) ◮ Map virtual nodes to substrate nodes 1 4 2 / 2 4 / 5 2 / 3 1 A B AC B 1 / 3 ◮ Map virtual edges to paths in the substrate 6 1 1 1 / 2 1 / 2 ◮ Respecting capacities & mapping restrictions 1 / 2 1 / 2 D C D 1 0 / 0 3 / 3 1 / 1 3 1 Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 7

  8. ‘Classic’ Cloud Computing Goal: Virtual Networks (since ≈ 2006) 1 4 ◮ Customer specifies 1 4 1 A B A B number and ‘size’ of ◮ Additionally: Virtual Machines 6 communication 1 1 ◮ Communication between requirements given D C D C 1 VMs not modeled 3 1 3 1 The Virtual Network Embedding Problem (VNEP) Virtual Network Substrate (Physical Network) ◮ Map virtual nodes to substrate nodes 1 4 2 / 2 4 / 5 2 / 3 1 A B AC B 1 / 3 ◮ Map virtual edges to paths in the substrate Embedding 6 1 1 1 / 2 1 / 2 ◮ Respecting capacities & mapping restrictions 1 / 2 1 / 2 D C D 1 0 / 0 3 / 3 1 / 1 3 1 Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 8

  9. The Virtual Network Embedding Problem (VNEP) Virtual Network Substrate (Physical Network) ◮ Map virtual nodes to substrate nodes 2 / 2 4 / 5 1 4 2 / 3 1 A B AC B 1 / 3 ◮ Map virtual edges to paths in the substrate Embedding 6 1 1 1 / 2 1 / 2 ◮ Respecting capacities & mapping restrictions 1 / 2 1 / 2 D C D 1 3 / 3 3 1 0 / 0 1 / 1 Related Work ◮ VNEP (and related problems) studied intensively in the networking community: > 100 papers. ◮ VNEP is related to classical problems as, e.g., subgraph isomorphism, but different . . . ◮ No approximations known for arbitrary virtual networks graphs. Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 9

  10. The Virtual Network Embedding Problem (VNEP) Virtual Network Substrate (Physical Network) ◮ Map virtual nodes to substrate nodes 2 / 2 4 / 5 1 4 2 / 3 1 A B AC B 1 / 3 ◮ Map virtual edges to paths in the substrate Embedding 6 1 1 1 / 2 1 / 2 ◮ Respecting capacities & mapping restrictions 1 / 2 1 / 2 D C D 1 3 / 3 3 1 0 / 0 1 / 1 Related Work ◮ VNEP (and related problems) studied intensively in the networking community: > 100 papers. ◮ VNEP is related to classical problems as, e.g., subgraph isomorphism, but different . . . ◮ No approximations known for arbitrary virtual networks graphs. Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 10

  11. The Virtual Network Embedding Problem (VNEP) Virtual Network Substrate (Physical Network) ◮ Map virtual nodes to substrate nodes 2 / 2 4 / 5 1 4 2 / 3 1 A B AC B 1 / 3 ◮ Map virtual edges to paths in the substrate Embedding 6 1 1 1 / 2 1 / 2 ◮ Respecting capacities & mapping restrictions 1 / 2 1 / 2 D C D 1 3 / 3 3 1 0 / 0 1 / 1 Related Work ◮ VNEP (and related problems) studied intensively in the networking community: > 100 papers. ◮ VNEP is related to classical problems as, e.g., subgraph isomorphism, but different . . . ◮ No approximations known for arbitrary virtual networks graphs. Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 11

  12. Related Work ◮ VNEP (and related problems) studied intensively in the networking community: > 100 papers. ◮ VNEP is related to classical problems as, e.g., subgraph isomorphism, but different . . . ◮ No approximations known for arbitrary virtual networks graphs. Focus: Offline Variant Setting Multiple Virtual Network requests are given Objectives Maximize profit (admission control) or minimize ‘cost’ s.t. capacity constraints . Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 12

  13. Related Work ◮ VNEP (and related problems) studied intensively in the networking community: > 100 papers. ◮ VNEP is related to classical problems as, e.g., subgraph isomorphism, but different . . . ◮ No approximations known for arbitrary virtual networks graphs. Focus: Offline Variant Setting Multiple Virtual Network requests are given Objectives Maximize profit (admission control) or minimize ‘cost’ s.t. capacity constraints . Approach: Randomized Rounding à la Raghavan & Thompson f k m k ◮ Compute opt. ‘convex combinations’ of mappings: D r = { ( ) } k for request r , r r ���� ���� weight ≥ 0 mapping ◮ Probabilistically select mapping m k r according to weight f k r for each request r ◮ Yields: approximate solutions of bounded resource augmentations with high probability Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 13

  14. Approach: Randomized Rounding à la Raghavan & Thompson f k m k ◮ Compute opt. ‘convex combinations’ of mappings: D r = { ( ) } k for request r , r r ���� ���� mapping weight ≥ 0 ◮ Probabilistically select mapping m k r according to weight f k r for each request r ◮ Yields: approximate solutions of bounded resource augmentations with high probability Main Challenge: Computing (Convex Combinations) of Valid Mappings ◮ Classic LP Formulation yields no meaningful solutions ( → unbounded integrality gap) 1 2 i i 1 1 2 k 2 j k j 1 1 1 2 j 2 j 2 k 1 2 i Substrate Request Classic LP Solution ◮ Observation: Need to fix confluence targets (here: node k ) a priori. Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 14

  15. Approach: Randomized Rounding à la Raghavan & Thompson f k m k ◮ Compute opt. ‘convex combinations’ of mappings: D r = { ( ) } k for request r , r r ���� ���� mapping weight ≥ 0 ◮ Probabilistically select mapping m k r according to weight f k r for each request r ◮ Yields: approximate solutions of bounded resource augmentations with high probability Main Challenge: Computing (Convex Combinations) of Valid Mappings ◮ Classic LP Formulation yields no meaningful solutions ( → unbounded integrality gap) 1 2 i i i 1 1 2 k 2 j k j k j 1 1 1 2 j 2 j 2 k 1 2 i Substrate Request Classic LP Solution Extraction Order ◮ Observation: Need to fix confluence targets (here: node k ) a priori. Matthias Rost (TU Berlin) Approximate Graph Embeddings in the Cloud Highlights of Algorithms 2018 15

Recommend

Exploiting Graph Embeddings for Graph Analysis Tasks Fatemeh Salehi Rizi Graph Embedding Day

Exploiting Graph Embeddings for Graph Analysis Tasks Fatemeh Salehi Rizi Graph Embedding Day

Exploiting Graph Embeddings for Graph Analysis Tasks Fatemeh Salehi Rizi Graph Embedding Day University of Lyon September 7, 2018 Outline Circle Prediction Social labels in an ego-network Semantic Content of Vector Embeddings Network

810 views • 46 slides
Graph Embeddings Alicia Frame, PhD October 10, 2019 Overview Whats an embedding? How do

Graph Embeddings Alicia Frame, PhD October 10, 2019 Overview Whats an embedding? How do

Graph Embeddings Alicia Frame, PhD October 10, 2019 Overview Whats an embedding? How do these work? Motivating Example - Word2Vec - Motivating Example - DeepWalk - Graph embeddings overview Graph embedding techniques Graph embeddings

952 views • 40 slides
of Graph Embeddings Aleksandar Bojchevski Technical University of Munich, Germany Graph

of Graph Embeddings Aleksandar Bojchevski Technical University of Munich, Germany Graph

Uncertainty and Robustness of Graph Embeddings Aleksandar Bojchevski Technical University of Munich, Germany Graph Embedding Day 2018 - Lyon Neglected aspects of graph embeddings Capturing uncertainty Robustness to noise Robustness to

885 views • 67 slides
Approximate Graph Operations on Parallel Platforms Approximate Graph Operations on Parallel

Approximate Graph Operations on Parallel Platforms Approximate Graph Operations on Parallel

Approximate Graph Operations on Parallel Platforms Approximate Graph Operations on Parallel Platforms Overview Computing similarity of nodes in two graphs Essentially ranking pairs of nodes Network similarity decomposition NSD Algorithm

496 views • 27 slides
planar graph embeddings and stat mech Richard Kenyon (Brown University) Wednesday, May 11, 16

planar graph embeddings and stat mech Richard Kenyon (Brown University) Wednesday, May 11, 16

planar graph embeddings and stat mech Richard Kenyon (Brown University) Wednesday, May 11, 16 In 2D stat mech models, appropriate graph embeddings are important e.g. Bond percolation on Z 2 . p c = 1 2 What about unequal probabilities? q q

499 views • 39 slides
Adversarial Attacks on Node Embeddings via Graph Poisoning Aleksandar Bojchevski, Stephan

Adversarial Attacks on Node Embeddings via Graph Poisoning Aleksandar Bojchevski, Stephan

Adversarial Attacks on Node Embeddings via Graph Poisoning Aleksandar Bojchevski, Stephan Gnnemann Technical University of Munich ICML 2019 Node embeddings are used to Classify scientific papers Recommend items Classify proteins

336 views • 21 slides
Graph Embeddings in Practice: A Telco Churn Prediction Use Case PhD Researcher: Sandra Mitrovi

Graph Embeddings in Practice: A Telco Churn Prediction Use Case PhD Researcher: Sandra Mitrovi

Graph Embeddings in Practice: A Telco Churn Prediction Use Case PhD Researcher: Sandra Mitrovi Supervisor: Prof. Dr. Jochen De Weerdt Department of Decision Sciences and Information Management, KU Leuven Graph Embedding Day, Lyon 07 Sept

577 views • 31 slides
Graph-Based Word Embeddings Learning Presenter: Zheng ZHANG Supervisors: Pierre

Graph-Based Word Embeddings Learning Presenter: Zheng ZHANG Supervisors: Pierre

(Post-) Doctoral Seminar of Group ILES, LIMSI 10/04/2018 Graph-Based Word Embeddings Learning Presenter: Zheng ZHANG Supervisors: Pierre ZWEIGENBAUM & Yue MA 1 Date One year ago Our plan: Using graph-of-words for

376 views • 11 slides
Learning with Approximate Kernel Embeddings Dino Sejdinovic Department of Statistics University

Learning with Approximate Kernel Embeddings Dino Sejdinovic Department of Statistics University

Learning with Approximate Kernel Embeddings Dino Sejdinovic Department of Statistics University of Oxford RegML Workshop, Simula, Oslo, 06/05/2017 D.Sejdinovic (University of Oxford) Learning with Kernel Embeddings Oslo, 06/05/2017 1 / 18

286 views • 24 slides
Fairness Constraints for Graph Embeddings* William L. Hamilton Assistant Professor at McGill

Fairness Constraints for Graph Embeddings* William L. Hamilton Assistant Professor at McGill

Fairness Constraints for Graph Embeddings* William L. Hamilton Assistant Professor at McGill University and Mila Canada CIFAR Chair in AI Visiting Researcher at Facebook AI Research *Joint work with my PhD student Joey Bose, to appear in

744 views • 38 slides
Scalable Learning of Entity and Predicate Embeddings for Knowledge Graph Completion Pasquale

Scalable Learning of Entity and Predicate Embeddings for Knowledge Graph Completion Pasquale

Scalable Learning of Entity and Predicate Embeddings for Knowledge Graph Completion Pasquale Minervini, Nicola Fanizzi, Claudia dAmato, Floriana Esposito Department of Computer Science - Universit` a degli Studi di Bari Aldo Moro, Italy {

295 views • 6 slides
Z 2 -embeddings and Tournaments Radoslav Fulek , Jan Kyn cl Z 2 -embeddings and Tournaments

Z 2 -embeddings and Tournaments Radoslav Fulek , Jan Kyn cl Z 2 -embeddings and Tournaments

Z 2 -embeddings and Tournaments Radoslav Fulek , Jan Kyn cl Z 2 -embeddings and Tournaments Radoslav Fulek , Jan Kyn cl June 12, 2018 Drawings of Graphs Drawings of Graphs G = ( V, E ) is a simple graph . The set of vertices V is finite

596 views • 56 slides
CS 4803 / 7643: Deep Learning Guest Lecture: Embeddings and world2vec Feb. 18 th 2020 Ledell Wu

CS 4803 / 7643: Deep Learning Guest Lecture: Embeddings and world2vec Feb. 18 th 2020 Ledell Wu

CS 4803 / 7643: Deep Learning Guest Lecture: Embeddings and world2vec Feb. 18 th 2020 Ledell Wu Research Engineer, Facebook AI ledell@fb.com 1 Outline Word Embeddings word2vec Graph Embeddings Applications world2vec

769 views • 41 slides
Affinity Dependent Negative Sampling for Knowledge Graph Embeddings M M Alam, H Jabeen , M Ali, K

Affinity Dependent Negative Sampling for Knowledge Graph Embeddings M M Alam, H Jabeen , M Ali, K

Affinity Dependent Negative Sampling for Knowledge Graph Embeddings M M Alam, H Jabeen , M Ali, K Mohiuddin, and J Lehmann Smart Data Analytics, University of Bonn CEPLAS, University of Cologne hajira.jabeen@uni-koeln.de HOME INTRODUCTION

323 views • 17 slides
Domain Adaptation with Adversarial Training and Graph Embeddings Firoj Alam Shafiq Joty

Domain Adaptation with Adversarial Training and Graph Embeddings Firoj Alam Shafiq Joty

Domain Adaptation with Adversarial Training and Graph Embeddings Firoj Alam Shafiq Joty Muhammad Imran @firojalam04 @mimran15 Qatar Computing Research Institute (QCRI), HBKU, Qatar School of Computer Science and Engineering Nanyang

986 views • 33 slides
Approximate Matchings in Dynamic Graph Streams Sanjeev Khanna University of Pennsylvania Joint

Approximate Matchings in Dynamic Graph Streams Sanjeev Khanna University of Pennsylvania Joint

Approximate Matchings in Dynamic Graph Streams Sanjeev Khanna University of Pennsylvania Joint work with Sepehr Assadi (Penn), Yang Li (Penn), and Grigory Yaroslavtsev (Penn). Matchings in Graphs Matching: A set of edges in a graph such that

364 views • 34 slides
Trinity A Distributed Graph Engine on a Memory Cloud 1 Motivation Polarized view on previous

Trinity A Distributed Graph Engine on a Memory Cloud 1 Motivation Polarized view on previous

Trinity A Distributed Graph Engine on a Memory Cloud 1 Motivation Polarized view on previous approaches: Graph Query Graph Scalability Database Processing Analytics Neo4J Yes Yes No No HyperGraph Yes Yes No No DB MapReduce

755 views • 11 slides
Word Embeddings Natural Language Processing VU (706.230) - Andi Rexha 02/04/2020 Word Embeddings

Word Embeddings Natural Language Processing VU (706.230) - Andi Rexha 02/04/2020 Word Embeddings

Word Embeddings Natural Language Processing VU (706.230) - Andi Rexha 02/04/2020 Word Embeddings Agenda Traditional NLP Word Embeddings-1 Word Embeddings-2 Text preprocessing Topic Modeling ELMo Bag-of-words model Neural

900 views • 64 slides
TO ANSWER EACH QUESTION . 1. Approximate the y-coordinate of the point on the line with the given

TO ANSWER EACH QUESTION . 1. Approximate the y-coordinate of the point on the line with the given

D AY 76 R EVIEW OF I NVERSE F UNCTIONS W ORK WITH PARTNER . U SE THE GRAPH TO ANSWER EACH QUESTION . 1. Approximate the y-coordinate of the point on the line with the given - coordinate. a. 0 b. 10 c. 2 2. Approximate the x-coordinate of

609 views • 23 slides
Graph Database-as-a-Service Managing Data and Its Relationships in a Cloud Alexander Pozdneev,

Graph Database-as-a-Service Managing Data and Its Relationships in a Cloud Alexander Pozdneev,

IBM Graph Graph Database-as-a-Service Managing Data and Its Relationships in a Cloud Alexander Pozdneev, @Alex_Pozdneev IBM Science and Technology Center March 2, 2017 GraphHPC-2017 From the Moscow thaw: 1953- 1968 exhibition at

633 views • 29 slides
Word Embeddings CS 6956: Deep Learning for NLP Overview Representing meaning Word

Word Embeddings CS 6956: Deep Learning for NLP Overview Representing meaning Word

Word Embeddings CS 6956: Deep Learning for NLP Overview Representing meaning Word embeddings: Early work Word embeddings via language models Word2vec and Glove Evaluating embeddings Design choices and open questions 1

422 views • 17 slides
Word Embeddings CS 6956: Deep Learning for NLP Overview Representing meaning Word

Word Embeddings CS 6956: Deep Learning for NLP Overview Representing meaning Word

Word Embeddings CS 6956: Deep Learning for NLP Overview Representing meaning Word embeddings: Early work Word embeddings via language models Word2vec and Glove Evaluating embeddings Design choices and open questions 1

1.25k views • 75 slides
Word Embeddings CS 6956: Deep Learning for NLP Overview Representing meaning Word

Word Embeddings CS 6956: Deep Learning for NLP Overview Representing meaning Word

Word Embeddings CS 6956: Deep Learning for NLP Overview Representing meaning Word embeddings: Early work Word embeddings via language models Word2vec and Glove Evaluating embeddings Design choices and open questions 1

2k views • 24 slides
Word Embeddings CS 6956: Deep Learning for NLP Overview Representing meaning Word

Word Embeddings CS 6956: Deep Learning for NLP Overview Representing meaning Word

Word Embeddings CS 6956: Deep Learning for NLP Overview Representing meaning Word embeddings: Early work Word embeddings via language models Word2vec and Glove Evaluating embeddings Design choices and open questions 1

828 views • 15 slides

More recommend