Using Graph Algorithms For Advanced Analytics - Part 4 Similarity 30 graph algorithms 4 similarity (1)

Graph Gurus 30
Using Graph Algorithms for Advanced Analytics
Part 4 - Similarity
1

© 2020 TigerGraph. All Rights Reserved
Today's Presenter
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Victor Lee
Head of Product Strategy & Developer Relations
● BS in Electrical Engineering and Computer
Science from UC Berkeley, MS in Electrical
Engineering from Stanford University
● PhD in Computer Science from Kent State
University focused on graph data mining
● 20+ years in tech industry

Some Housekeeping Items
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submit your questions at any time using the Q&A tab in the menu
● The webinar is being recorded and will uploaded to our website shortly
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you
● If you have issues with Zoom please contact the panelists via chat
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Today’s Outline
5
1
3
2
Recap of Parts 1 to 3:
Path, Centrality & Community Graph
Algorithms
Similarity Algorithms
Local vs. Global structure/properties
Same is Easy; Similarity is Tricky
What factors are important to you?
4
Demo
Running and modifying GSQL
Similarity Algorithms

Review: Analytics with Graph Algorithms
● Graph algorithms answer fundamental questions about
connected data
● Each algorithm in a library is tool in an analytics toolkit
● Building blocks for more complex business questions
6
Specialized functions Combine to make
something better

Example Questions/Analyses for Graph Algorithms
Which entity is most centrally
located?
● For delivery logistics or greatest visibility
● Closeness Centrality, Betweenness
Centrality algorithms
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How much influence does this
entity exert over the others?
● For market penetration & buyer influence
● PageRank algorithm
Which entity has similar relationships
to this entity?
● For grouping customers, products, etc.
● Cosine Similarity, SimRank, RoleSim
algorithms
What are the natural community
groupings in the graph?
● For partitioning risk groups, workgroups,
product offerings, etc.
● Community Detection, MinCut algorithms

Summary for Shortest Path Algorithms
Graph Gurus 26
8
1
4
3
Graph Algorithms - tools and building
blocks for analyzing graph data
GSQL Algorithm Library - runs
in-database, high-performance,
easy to read and modify
Shortest Path Algorithms - different
algorithms for weighted and
unweighted graphs
2 Learning To Use Algorithms - know what
problem they solve, pros and cons

Summary for Centrality Algorithms
Graph Gurus 27
9
1
4
3
Centrality Algorithms - abstract
concepts of location and travel
Customizing GSQL Library algorithms is
easy and familiar, like procedural SQL
PageRank - uses directed referral edges
to find the most influential nodes.
Personalized PageRank is localized.
2 Closeness and Betweenness use shortest
paths. Betweenness is more complex.

Summary for Community Detection Algorithms
Graph Gurus 29
10
1
3
2
Community Detection Algorithms
Use connectedness to decide
boundaries
Strict vs. Lenient Community Rules
Black&white rules are not always helpful.
Louvain uses relative density.
Communities are Clusters, not Partitions
Don't have to include everyone.
Can overlap?
4
Pre- or Post- step with other algorithms
Many algorithms assume you start
from just one connected community

Some Types of Graph Algorithms
● Search
● Path Finding & Analytics
● Centrality / Ranking
● Clustering / Community Detection
● Similarity
● Classification
11

Healthcare Best Practices: Identify Similar Individuals
12
Wellness, resources,
and cost at stake
● Track events and
interactions in the
patient's journey
● What makes this
individual and their
journey significant?
● What are key
points, when the
right intervention is
essential?

Other Use Cases
● What were the early signs that
made the opportunity stand
out?
● What steps did the investor
take?
● How did the opportunity and
market change?
13
Find Investment Opportunities
Similar to Successful Ones:
Possible signs:
● Sudden suspicious transactions
○ Size
○ Transaction type
○ Business type
○ Platform used
● Connections to parties already
considered high risk
Find Activity Similar to That of a
Known Fraudster/Swindler:

Modeling Similarity as a Graph Problem
Tables:
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Customer
Supplier
Location 2
Product
Payment
PURCHASED
RESIDES
SHIPS
TO
PURCHASED
SHIPS FROM
A
C
C
EPTED
MAKES
Location 2
N
O
TIFIES
Entity
Graph: Simple hub-and-spoke
pattern
Location 1
Entity itself is in one table, but the
factors that make the entity distinctive
require joins to other tables

"Same" is Easy; Similar is Tricky
● Conceptually easy to find exact matches
○ But exact match is rarely needed or appropriate
● Similarity is in the Eye of the Beholder
○ What Factors do you care about?
○ What are their relative importance?
● Are you outcome-driven?
○ Graph-based approach is good because it shows you all known
associations, without picking in advance which ones matter.
○ Machine learning can help pick the important factors.
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What Factors to Use
16
Q: Which is more similar
to a hippopotamus:
a whale or a pig?
A: If you look are regular
observations, it's a pig.
If you look at genes, it's
a whale.

Classical Feature-Based Similarity Functions
● Jaccard Similarity
● Cosine Similarity
● Graph-based variations
17

Jaccard Similarity
Count how many features are in common
● When you have non-numeric, categorical, yes/no features
● Jaccard value ranges from 0 to 1
18
Example:
● Basket 1 has {milk, bread, chicken, mushrooms, bananas}
● Basket 2 has {bread, cheese, ham, bananas}
● Basket 3 has {tofu, noodles, bok choy, mushrooms,}
Jacc(1,2) = |{bread,bananas}| / |{milk, bread, chicken, mushrooms, bananas, cheese, ham} = 2/7
Jacc(1,3) = |{mushrooms}| / |{milk, bread, chicken, mushrooms, bananas,tofu,noodles, bok choy} = 1/8
A B
A ∩ B
A ∪ B

Cosine Similarity
If each item is described by a list of numerical values (a vector),
then multiply the vectors together and divide by their lengths.
● If A=B, then Cos(A,B) = 1
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A= (6,2)
B= (4,4)
Cos(A,B) = (6*4 + 2*4) / [√(6*6+2*2)√(4*4 + 4*4)]
= (24+8) / [√40 √32 ] = 0.8944

Graph-Based Structural Similarity
Use a vertex's neighbors as its feature set
● Jaccard: Count each neighboring vertex
20
A
Order
W
B
X
Y
Z
2
3
1
2
1
4
A's neighbors = {W,Y,Z}
B's neighbors = {W,X,Z}
Jacc(A,B) = |{W,Z}| / |{W,X,Y,Z}|
= 2/4
W,X,Y,Z represent feature vertices, different vertex types than A,B

Graph-Based Structural Similarity
Use a vertex's neighbors as its feature set
● Cosine: Use edge weights to each neighboring vertex
21
A
Order
W
B
X
Y
Z
2
3
1
2
1
4
A's weighted neighbors = {2,0,4,1}
B's weighted neighbors = {3,1,0,2}
Cos(A,B) = 8 / [√21√14] = 0.4666
W,X,Y,Z represent feature vertices, different vertex types than A,B

SimRank
1. A vertex is perfectly similar to itself:
2. Two vertices are similar if they have similar neighbors:
, where
Ai = each (in)neighbor of U
Bj = each (in)neighbor of V
c = constant, typically 0.6 to 0.8
Can be computed iteratively, like PageRank
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SimRank Example
1st Round: sr(A,B) = c * Avg [ sr(W,W), sr(Y,W), sr(Z,W),
sr(W,X), sr(Y,X), sr(Z,X),
sr(W,Z), sr(Y,Z), sr(Z,Z)]
= c*(1+0+0+0+0+0+0+0+1)/9 = 2c/9
23
A
Order
W
B
X
Y
Z
2
3
1
2
1
4
A and B each have 3 neighbors, so there
are 9 possible pairs of neighbors.
2 of the neighbors are shared (W and Z)
To complete round 1, compute scores for every other pair of vertices.
For round 2, repeat, using the round 1 values for computing the average SimRank of neighbors.

Comments
● Cosine, Jaccard are local computations, looking only one hop deep.
● SimRank analyzes more of the graph (typically the whole graph),
looks deeper to find more meaningful similarity, thus requires more
computation.
● NOTE: Cosine, Jaccard, and SimRank work okay on homogenous
graphs (one type of vertex, but have even more meaning with
bipartite graphs, where there are Entity vertices and Feature vertices.
● Drawback: SimRank penalizes for having more neighbors in common.
24

A More Rigorous Sense of Structural Similarity
● Smith family structurally equivalent to Jones family?
● Smith family similar to Lee family?
● What about the individuals:
Who is S3 similar to? The most similar? Somewhat similar?
25

RoleSim
Two vertices are similar if they have similar neighborhoods, where both size
and type of neighborhood matters.
● Key difference from SimRank is to find not the average neighbor
pairing but the optimal neighbor pairing.
w(M) is a maximal matching of the neighbors Nu
and Nv
of vertices u
and v, respectively.
● If neighborhoods of u and v are equivalent, then RoleSim(u,v) = 1
26

RoleSim Example
1st Round: rs(A,B) = (1-b) * Max [ sr(W,W), sr(Y,W), sr(Z,W),
sr(W,X), sr(Y,X), sr(Z,X),
sr(W,Z), sr(Y,Z), sr(Z,Z)] / 3 + b
= (1-b)*(1+1+0)/3 + b = 2(1-b)/3 + b
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A
Order
W
B
X
Y
Z
2
3
1
2
1
4
A and B each have 3 neighbors, so we
seek 3 pairs of neighbors.
2 of the neighbors are shared (W and Z)
To complete round 1, compute scores for every other pair of vertices.
For round 2, repeat, using the round 1 values for computing the max. RoleSim of neighbor-pairs.

DEMO
GSQL Graph Algorithms in TigerGraph Cloud
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GSQL Graph Algorithm Library
● Written in GSQL - high-level, parallelized
● Open-source, user-extensible
● Well-documented
29
docs.tigergraph.com/graph-algorithm-library

TigerGraph GSQL Graph Algorithm Library
✓ Call each algorithm as a GSQL query
or as a RESTful endpoint
✓ Run the algorithms in-database (don't
export the data)
✓ Option to update the graph with the
algorithm results
✓ Able to modify/customize the
algorithms. Turing-complete
language.
✓ Massively parallel processing to
handle big graphs
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Summary
31
1
3
2
Similarity is in the Eye of the Beholder
What factors matter to you? How
much?
Jaccard and Cosine Similarity
Counting matches vs. measuring
numerical alignment
Graph modeling helps with Similarity
Hub-and-spoke view
4
Deeper Measures: SimRank and RoleSim
Define similarity recursively, look multiple
hops deep (globally)

Q&A
Please submit your questions via the Q&A tab in Zoom
32

More Questions?
Join our Developer Forum
https://groups.google.com/a/opengsql.org/forum/#!forum/gsql-users
Sign up for our Developer Ofﬁce Hours (every Thursday at 11 AM PST)
https://info.tigergraph.com/officehours
33

Additional Resources
Start Free at TigerGraph Cloud Today!
https://www.tigergraph.com/cloud/
Test Drive Online Demo
https://www.tigergraph.com/demo
Download the Developer Edition
https://www.tigergraph.com/download/
Guru Scripts
https://github.com/tigergraph/ecosys/tree/master/guru_scripts
34

Upcoming Graph Guru Events
Coming to London, San Francisco, Seattle and
more. View all events and request your own here:
https://www.tigergraph.com/graphguruscomestoyou/
Next webinar: Using Giraffle to Manage
Deployments at an Enterprise Scale
Wednesday, March 11, at 11am PST
https://info.tigergraph.com/webinar-giraffle
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Using Graph Algorithms For Advanced Analytics - Part 4 Similarity 30 graph algorithms 4 similarity (1)

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