The relationship between Graphs and Machine Learning is quite tightly coupled and this talk walks through how they evolve together.

1. Abstract
Graphs are the most native format to represent the data, it has built-in structure to store the contextual information and enable
data analysts to get better answers for their queries, data engineers to easily extend their eco-system, and data scientists to build
enhanced models. We can make informed decisions. In this presentation, you will learn about the evolution of the Graphs with a
review on knowledge graphs, path finding, clustering, and recommendation algorithms, how they are built and their use cases.
Also, we will review the challenges we face as processing more data comes with a cost, and how they are solved in different faces
of the machine learning lifecycle.

2. Evolution of Graph
Algorithms – Benefits
and Challenges
By Ebru Cucen
@ebrucucen
2/12/2021

3. Throughout this talk, I will show graphs in two representations with
- Left Hand Side : the data
- Right Hand Side : the schema

7. Goal
Graphs are
the most
native data
format
Graphs are
useful for all
roles in the
data habitat
Graphs
opened a
new era in
ML

9. Historical Timeline
Euler’s
Koninsberg
bridge
“Graph”
introduced
PageRank
Google’s
Knowledge
Graph
Semantic Web
Facebook’s
Entities
Graph
Yahoo’s
Knowledge
Graph
Gori, GNN
McCulloch-Pitts
Neural Nets
DeepMind
Kipf,GCN
1878
1735 1998 1999 2013
2012
2005 2016
2010
1943

10. Interest in Research
*Title and Abstract search at Dimensions.ai
“Graph” and “Neural” and “Network” *
“Graph” and “Network” *

13. Roles
Data Analysts
Data/ML Engineers
Data Scientists

14. # Knowledge Graphs

17. Let’s ask

20. https://cacm.acm.org/magazines/2019/8/238342-industry-scale-knowledge-graphs/fulltext
Users
- Ebay
- Product recommendation: node and link similarity
- Microsoft
- Bing Knowledge Graph: Q&A
- Academic Graph
- LinkedIn Graph
- IBM
- Watson Discovery
- Extend core Knowledge Graph
- Facebook
- Social Network Analysis

21. World Avatar
https://www.sciencedirect.com/science/article/abs/pii/S0098135419301589

22. http://dx.doi.org/10.1016/j.compchemeng.2019.106586

23. # Graph Algorithms

24. Basic Cypher Queries
MATCH p=(t:Talk)-[r:IS_GIVEN_BY]->(s:Speaker)
WHERE s.name= “Geoffrey” AND s.surname= “Hinton” RETURN p

25. Basic Cypher Queries
MATCH p=(g:Guest)-[r:ATTENDS]->(t:Talk)
WHERE s.name= “A” AND s.surname= “Hinton” RETURN p

26. Basic Cypher Queries
MATCH p=(s:Speaker)<-[:IS_GIVEN_BY]-(t:Talk)<-[:ATTENDS]-(g:Guest)
WHERE s.name="Geoffrey" and s.surname="Hinton"
RETURN p

27. Demo
Hume visualisation

28. E2E Process

30. What is the shortest path from Victoria to Liverpool Street Station?

32. Inherently Graph
Use cases
● Telephone network
● Internet packet routing
● Manufacturing

33. https://www.sciencedirect.com/science/article/abs/pii/S1570826818300672

34. Inherently Graph
Use cases
● Telephone network
● Internet packet routing
● Manufacturing
● Human Brain
● Neural nets are networks

35. # Graph Neural Networks

36. ML - 101
X
Input
=Layer 0
Output
1ST
Layer=Z[1]
Z ŷ
y = mx + b

37. ML - 101 - Forward Propagation
x1
x2
Input
=Layer 0
Output
1ST
Layer=Z[1]
Z1
ŷ
Z2
y = w1
x1
+ w2
x2
+ b

38. ML - 101 Backward Propagation
x1
x2
Input
=Layer 0
Output
1ST
Layer=Z[1]
Z1
ŷ
Z2
y = w1
x1
+ w2
x2
+ b

39. ML - 101 Model & Prediction
x1
x2
Input
=Layer 0
Output
1ST
Layer=Z[1]
Z1
Z2
ŷ
X =
x1 # of Beds
x2 PostCode
y = House sales price

40. Neural Networks - 101
x1
x2
Input
=Layer 0
Output
1ST
Layer=Z[1]
X =
z1
1
z1
2
z1
3
a1
1
a1
2
a1
3
a2
z2
ŷ
a3
z3
a2
z2
z1
4
2ND
Layer=Z[2]
3RD
Layer=Z[3]
X1
X2
a1
4

41. Neural Networks - 101
x1
x2
Input
=Layer 0
Output
1ST
Layer=Z[1]
X =
z1
1
z1
2
z1
3
a1
1
a1
2
a1
3
a2
z2
ŷ
a3
z3
a2
z2
a
2
z2
2ND
Layer=Z[2]
3RD
Layer=Z[3]
X1
X2
z= ∑Wi
xi
+ b
z= ∑Wx1
+ ∑Wx2
+ b
X =
a= σ(Z)
Z[1]
=
z11
z12
z21
z22
z31
z32
z41
z42
X1
X2

42. Layer 0 Output
1 Layer=Z[1]
a2
ŷ
Challenge

44. Karate Club

45. Karate Club
- Adjacency List
- Adjacency Matrix
N1 N2 N3
N1
N2
N3

46. Representing Graphs
https://distill.pub/2021/gnn-intro/
https://github.com/distillpub/post--gnn-intro

47. Clustering
Original Graph
https://arxiv.org/pdf/1609.02907.pdf
Greedy Clustering
https://doi.ieeecomputersociety.org/10.1109/TKDE.2007.190689

48. GCN
GCN
- Kipf(2007)*
https://arxiv.org/abs/1609.02907

49. GCN
GCN
- Kipf(2007)*
https://pytorch-geometric.readthedocs.io/en/latest/modules/nn.html
https://arxiv.org/abs/1609.02907

50. Torch.Geometric GCNConv
Karate club with GCN

51. Final Output
Karate club with GCN
Put original graph

52. Calculating Loss Function
Node/Edge/Graph classification
Zi
=f(hi
) Zij
=f(hi
,hj
,eij
) ZG
=f(∑i
hi)

53. Calculating Loss Function
Node/Edge/Graph classification
Zi
=f(hi
) Zij
=f(hi
,hj
,eij
) ZG
=f(∑i
hi)

54. Random Walks
- Drunk person walking
- Equal probability of paths to adjacent nodes
- Max uncertainty (local entropy)
- Measure structure of graph
- Sampling

55. # Summary

56. Conclusion
• Graph is the most native data format with built-in
semantic
• Graph opened a new era in machine learning none
of us can ignore
• Graph is very useful for all roles for E2E process

57. # Questions