large-scale mining of dynamic networkspapaggel/docs/talks/... · credits farzaneh heidari...
TRANSCRIPT
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Large-scale Mining of
Dynamic Networks
Manos PapagelisYork University, Toronto, Canada
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Background
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Research
Graph
Mining
Data
Mining
Big Data & Knowledge Discovery
Today
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A. Trajectory Network Mining B. Network Representation Learning
C. Streaming & Dynamic Graphs D. Social Media Mining & Analysis
E. City Science / Urban Informatics / IoT F. Natural Language Processing
Current Research focus
![Page 5: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/5.jpg)
Today’s Overview
Trajectory Network Mining
▪ Mining of Node Importance in Trajectory Networks
▪ Group Pattern Discovery of Pedestrian Trajectories
Evolving Network Mining
▪ Evolving Network Representation Learning Based on
Random Walks
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Node Importance in Trajectory
Networks
Joint work with Tilemachos Pechlivanoglou
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Trajectories of moving objects
every moving object, forms a trajectory – in 2D it is a sequence of (x, y, t)
there are trajectories of moving cars, people, birds, …
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trajectory anomaly detectiontrajectory pattern miningtrajectory classification
...more
Trajectory data mining
trajectory similarity trajectory clustering
we care about network analysis of moving objects
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Proximity networks
θ
θ
proximity
threshold
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line of sight
Distance can represent
wifi/bluetooth signal range
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Trajectory networks
Input: logs of trajectories (x, y, t) in time period [0, T]
Output: node importance metrics
The Problem
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Node Importance
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Node importance in static networks
Degree centrality Betweenness centrality
Closeness centrality Eigenvector centrality
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Node importance in TNs
connected components over time
(connectedness)
node degree over time triangles over time
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infection spreading
Applications
security in autonomous vehicles
rich dynamic network analytics
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Evaluation of Node Importance
in Trajectory Networks
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Naive approach
For every discrete time unit t:1. obtain static snapshot of the proximity network2. run static node importance algorithms on snapshot
Aggregate results at the end
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Similar to naive, but:
﹘ no final aggregation
﹘ results calculated incrementally at every step
Still every time unit
Streaming approach
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Every discrete time unit
0 ...
time
T4123
...
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Sweep Line Over Trajectories
(SLOT)
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A computational geometry algorithm that given line segments computes line segment overlaps
Efficient one pass algorithm that only processes line segments at the beginning and ending points
Sweep line algorithm
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(algorithm sketch)
represent TN edges as time intervals
apply variation of sweep line algorithm
simultaneously compute node degree, triangle membership, connected components in one pass
SLOT: Sweep Line Over Trajectories
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Represent edges as time intervals
e1:(n1,n2)
.
.
.
en
0 T
ed
ge
s
t1 t3t2 t4 t5t6 t7 t8 t9t10 t11 t12 t13
time
L
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SLOT: Sweep Line Over Trajectories
![Page 25: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/25.jpg)
⦁ node degree− nodes u, v now connected
− increment u, v node degrees
At every edge start
⦁ triangle membership− did a triangle just form?
− look for u, v common neighbors
− increment triangle (u, v, common)
⦁ connected components− did two previously disconnected
components connect?
− compare old components of u, v
− if no overlap, merge them
e:(u, v)
0
ed
ge
s
t1 t2
time
T
u
v
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⦁ node degree− nodes u, v now disconnected
− decrement u, v degree
At every edge stop
⦁ triangle membership− did a triangle just break?
− look for u, v common neighbors
− decrement triangle (u, v, common)
⦁ connected components− did a conn. compon. separate?
− BFS to see if u, v still connected
− if not, split component to two
t3
e:(u, v)
0
ed
ge
s
t1 t2 T
time
u
v
![Page 27: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/27.jpg)
Rich Analytics− node degrees: start/end time, duration
− triangles: start/end time, duration
− connected components: start/end time, duration
Exact results (not approximations)
SLOT: At the end of the algorithm …
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Evaluation of SLOT
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Node degree
1550x
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Triangle membership / connected components
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SLOT Scalability
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SLOT algorithm
trajectory networks network importance over time
SLOT properties:
- fast
- exact
- scalable
Takeaway
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Seagull migration trajectories
data from Wikelski et al. 2015
![Page 34: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/34.jpg)
Group Pattern Discovery of
Pedestrian Trajectories
Joint work with Sawas Abdullah et al.
![Page 35: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/35.jpg)
Pedestrian trajectories
![Page 36: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/36.jpg)
what is a group?
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many definitions, many algorithms
e.g., flock, convoy, evolving-clusters, gathering-pattern, … [ACM TIST Tutorial 2015]
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Finding pedestrian groups
P1P2
P3
P4
P5
P6
P7
Local Grouping
Intuitive method
Spatial-only
θproximity threshold
key ideafind pairs of pedestrians x, y where distance(x, y) < θ
expand pairs to discover groups
![Page 39: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/39.jpg)
Local grouping
![Page 40: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/40.jpg)
expand the key idea to include the
time dimension
![Page 41: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/41.jpg)
Global groups vs. Time-window groups
global grouping
time-window grouping
![Page 42: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/42.jpg)
Trajectolizer
Demo
![Page 43: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/43.jpg)
Trajectolizer: System Overview
Pedestrian Monitoring System Video Streams
Pedestrian Annotation
Raw (Pedestrian) Trajectory Streams
Refined Trajectories
Trajectory Pattern MiningTrajectory Groups
Trajectories Visualization
![Page 44: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/44.jpg)
Trajectolizer: Interactive Demo
Live Democurrent frame with pedestrian
IDs and trajectories
timeline slider area to navigate video frames
descriptive statistics about the current frame
grouping analysis
![Page 45: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/45.jpg)
A. Trajectory Network Mining B. Network Representation Learning
C. Streaming & Dynamic Graphs D. Social Media Mining & Analysis
E. City Science / Urban Informatics / IoT F. Natural Language Processing
Current Research focus
![Page 46: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/46.jpg)
EvoNRL: Evolving Network
Representation Learning Based
on Random Walks
Joint work with Farzaneh Heidari
![Page 47: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/47.jpg)
(universal language for describing complex data)
networks
![Page 48: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/48.jpg)
Classical ML Tasks in Networks
?
?
node classification
?
?
?
link predictioncommunity detection
anomaly detection
?
graph similaritytriangle count
Limitations of Classical ML: • expensive computation (high dimension computations)
• extensive domain knowledge (task specific)
![Page 49: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/49.jpg)
Network Representation Learning (NRL)
several network structural properties can be learned/embedded
(nodes, edges, subgraphs, graphs, …)
Low-dimension spaceNetwork
Premise of NRL: • faster computations (low dimension computations)
• agnostic domain knowledge (task independent)
![Page 50: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/50.jpg)
Random Walk-based NRL
1
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61
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Feed sentences to a
Skip-gram NN model
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87 8 5 4 3 5 6 7
88 4 5 6 7 8 9
89 2 1 3 5 6 7 8
90 7 4 2 1 3 5 6
Input networkObtain a set of
random walks
Treat the set of random walks
as sentences
Learn a vector representation
for each node
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61
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StaticNRL(DeepWalk, node2vec, …)
![Page 51: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/51.jpg)
but real-world networks are constantly evolving
![Page 52: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/52.jpg)
Evolving Network
Representations Learning
![Page 53: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/53.jpg)
Naive Approach
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t = 0
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t = 1 t = 2
StaticNRL StaticNRL StaticNRL
Impractical (expensive, incomparable representations)
![Page 54: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/54.jpg)
EvoNRL Key Idea
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61
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Feed sentences to a
Skip-gram NN model
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2 1 3 5 8 7 6 5
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87 8 5 4 3 5 6 7
88 4 5 6 7 8 9
89 2 1 3 5 6 7 8
90 7 4 2 1 3 5 6
Input networkObtain a set of
random walks
Treat the set of random walks
as sentences
Learn a vector representation
for each node
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2
3
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5
61
7
8
9
dynamically maintain a valid
set of random walks for
every change in the network
![Page 55: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/55.jpg)
Example: Edge Addition
7
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4
5
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8
9
t = 0 t = 1
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7
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9
1 3 5 8 7 6 4 5
2 1 3 5 8 7 6 5
.
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.
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.
87 8 5 4 3 5 6 7
88 4 5 6 7 8 9 8
89 2 1 3 5 6 7 8
90 7 4 2 1 3 5 6
addition of edge (1, 4)
1 3 5 8 7 6 4 5
2 1 3 5 8 7 6 5
.
.
.
.
.
.
.
.
87 8 5 4 3 5 6 7
88 4 5 6 7 8 9 8
89 2 1 3 5 6 7 8
90 7 4 2 1 3 5 6
need to update the RW set
1
2
3
41 2 1 4 3 5 6 7 8
{simulate the rest of the RW
similarly for edge deletion, node addition/deletion
![Page 56: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/56.jpg)
Efficiently Maintaining a
Set of Random Walks
![Page 57: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/57.jpg)
EvoNRL Operations
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1 3 5 8 7 6 4 5
2 1 3 5 8 7 6 5
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87 8 5 4 3 5 6 7
88 4 5 6 7 8 9
89 2 1 3 5 6 7 8
90 7 4 2 1 3 5 6
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1 3 5 8 7 6 4 5
2 1 3 5 8 7 6 5
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87 8 5 4 3 5 6 7
88 4 5 6 7 8 9
89 2 1 3 5 6 7 8
90 7 4 2 1 3 5 6
+ edge(n1, n2)
2 1 4 3 5 6 7 8
Operations on RW
Search a node
Delete a RW
Insert a new RW
need for an efficient indexing data structure
![Page 58: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/58.jpg)
EvoNRL Indexing
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each node is a keyword
each RW is a document
a set of RWs is a collection of documents
1 3 5 8 7 6 4 5
2 1 3 5 8 7 6 5
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.
87 8 5 4 3 5 6 7
88 4 5 6 7 8 9
89 2 1 3 5 6 7 8
90 7 4 2 1 3 5 6
Term Frequency Postings and Positions
1 3 < 2, 1 >, < 89, 2 >, < 90, 4 >
2 2 <89, 1>, <90, 3>
3 5 <1, 1>, <2, 1>, <87, 3>, <89, 3>, <90, 5>
4 4 <1, 6>, <87, 3>, <90, 2>
5 9 <1, 2>, <1, 7>, <2, 3>, <2, 7>, <87, 5>, <88, 2>, <89, 4>, <90, 6>
6 6 <1, 5>, <2, 6>, <87, 6>, <88, 3>, <89, 3>, <90, 5>
7 5 <1, 4>, <2, 5>, <87, 7>, <88, 4>, <89, 6>, <90, 7>
8 5 <1, 3>, <2, 4>, <87, 1>, <88, 6>, <89, 7>
9 1 <88, 7>
![Page 59: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/59.jpg)
Evaluation of EvoNRL
![Page 60: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/60.jpg)
Evaluation: EvoNRL vs StaticNRL
Accuracy▪ EvoNRL ≈ StaticNRL
Running Time▪ EvoNRL << StaticNRL
![Page 61: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/61.jpg)
EvoNRL has similar accuracy to StaticNRL
Accuracy: edge addition
(similar results for edge deletion, node addition/deletion)
![Page 62: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/62.jpg)
Time Performance
EvoNRL performs orders of time faster than StaticNRL
100x𝟐𝟎𝐱
![Page 63: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/63.jpg)
Takeaway
EvoNRL
time efficient
accurate
generic method
how can we learn representations of an evolving network?
![Page 64: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/64.jpg)
Credits
Farzaneh Heidari
Tilemachos Pechlivanoglou
[IEEE Big Data 2018] Fast and Accurate Mining of Node Importance in
Trajectory Networks. Tilemachos Pechlivanoglou and Manos Papagelis.
code: https://github.com/tipech/trajectory-networks
[Complex Networks 2018] EvoNRL: Evolving Network Representation
Learning Based on Random Walks. Farzaneh Heidari and Manos Papagelis.
code: https://github.com/farzana0/EvoNRL/
Abdullah Sawas et al.
[Geoinformatica 2019] A Versatile Computational Framework for Group
Pattern Mining of Pedestrian Trajectories. A. Sawas, A. Abuolaim, M. Afifi, M.
Papagelis. GeoInformatica (Vol. X, No. X, 2019)
[IEEE MDM 2018] Tensor Methods for Group Pattern Discovery of Pedestrian
Trajectories. A. Sawas, A. Abuolaim, M. Afifi, M. Papagelis. (best paper award)
demo: https://sites.google.com/view/pedestrians-group-pattern/
![Page 65: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/65.jpg)
Thank you!
![Page 66: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/66.jpg)
Questions?
![Page 67: Large-scale Mining of Dynamic Networkspapaggel/docs/talks/... · Credits Farzaneh Heidari Tilemachos Pechlivanoglou [IEEE Big Data 2018] Fast and Accurate Mining of Node Importance](https://reader033.vdocuments.net/reader033/viewer/2022042409/5f26a72c958bfc55a2380434/html5/thumbnails/67.jpg)
Data Mining Lab @ YorkU
• Mandate
− Conduct basic research / knowledge transfer
− Equip students with theoretical knowledge & practical experience
− Research focus:
▪ data mining
▪ graph mining
▪ machine learning
▪ NLP
▪ big data analytics
• Members
− Two Faculty Members (Prof. Aijun An, Prof. Manos Papagelis)
− ~20 High Quality Personnel (HQP)
▪ ~5 Postdoc, ~6 PhDs, ~8 MSc, ~3 Undergrads, ~1 staff