The slide of our research "Fast RankClus Algorithm via Dynamic Score Tracking on Bi-type Information Networks"

1. Fast RankClus Algorithm via Dynamic Rank Score Tracking
on Bi-type Information Networks
iiWAS 2019
Kotaro Yamazaki✝ , Shohei Matsugu✝
Hiroaki Shiokawa✝✝, Hiroyuki Kitagawa✝✝
✝: Graduate School of SIE, University of Tsukuba
✝✝: Center for Computational Sciences, University of Tsukuba

2. Background
2

3. Background:
Ubiquitous Information Networks
• Information network:
Each node represents an entity and each link(edge) a relationship between
entities
• Homogeneous vs. Heterogeneous networks
- Homogeneous Network
Single type Object
E.g., Co-author network, Web pages, Friendship network
Most Current studies are on homogeneous network
- Heterogeneous Network
Objects belong to several types
E.g., Conference-author network, Medical networks
Most real system can be modeled as heterogeneous network
3

4. Background:
RankClus
[Sun et al.,EDBT’09]
Ranking-based Clustering algorithm for Heterogeneous Network
The Methodology
• Ranking as the features of clusters
• Clustering so that each node has the highest rank score.
• Repeat and improve the quality of clustering and ranking mutually
4
Heterogeneous Network
RankClus
Framework
with rank scores

5. Background:
Bottleneck of RankClus
Consumes much computational cost in ranking process
5
Why?
• Generate subgraphs
as many as the number of clusters
• Iteratively updates rank scores
for all nodesClustering
Initialization
Ranking
Repeat

6. •Pruning-RankClus[Yamazaki et, al. iiWAS’18]
The fast RankClus algorithm by pruning nodes
- Approach
Specify nodes that not significantly affect clustering
result and prune them
- Bottleneck
Difficult to prune while maintaining accuracy
Needs to set many user-specific parameters
6
Background:
Related Work

7. Background:
Our Goal
Reduce the computational cost of RankClus
7
Local update
Approach
Focus on the dynamic graph property of RankClus and
compute only evolving nodes and their neighbors efficiently

8. Background:
Our Contributions
1. Efficient
Our proposed method outperforms RankClus and the state-
of-the-art(Pruning-RankClus) algorithm
2. Highly Accurate
Although our proposed algorithm does not compute the
entire graph, its clustering results are more accurate than
those of the state-of-the-art algorithm
3. Easy to deploy
Our proposed method requires fewer user- specified
parameters than the state-of-the-art algorithm
8

9. Preliminary
9

10. Preliminary:
Data Model: Bi-type Information Network
• A graph consist of two kinds of nodes X and Y.
E.g.) Conference-author network
- Links can exist between
 Conference (X) and author (Y)
 Author (Y) and author (Y)
10
Target type
Target of clustering
Attribute type
Support information for clustering
X Y

11. Preliminary:
Algorithm Framework - Overview
11
Clustering
Initialization
Ranking
Step 0:
Step 1:
Step 2:
Repeat
with each rank scores
Target type
• Bi-type Information network: 𝔾
• Cluster number: K
• 𝑅𝑎𝑛𝑘𝑖𝑛𝑔 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛: 𝑓
𝐾 = 2
Ex)
𝑓
Output
Input

12. Clustering
Initialization
Ranking
Step 0:
Step 1:
Step 2:
1. Partition target-type nodes into K
clusters
2. Construct subgraphs based on
their clusters
Repeat
Preliminary:
Step 0: Partition and Construct Subgraphs
12

13. Preliminary:
Step 1: Ranking for Each Subgraph
13
Compute rank scores for each type
by a ranking function
Clustering
Initialization
Ranking
Step 0:
Step 1:
Step 2:
Repeat
Ranking for all nodes

14. Preliminary:
Step 2: Clustering for Each Target Node
14
• Considers the rank scores of attribute
type as cluster features
• Estimates the posterior probability that
target nodes belongs to a cluster.
Clustering
Initialization
Ranking
Step 0:
Step 1:
Step 2:
Repeat
Re-assign new cluster

15. 15
Preliminarily:
Key Observations
About subgraph 𝔾𝑖 in each iteration
1. Inserts new nodes and edges into 𝔾𝑖
2. Remove several nodes and edges from 𝔾𝑖
Each subgraph can be regarded as a dynamic graph
𝒕
𝒕+1
𝒕+2

16. Proposed Method
16

17. Proposed Method:
Problem Setting
• Given: 𝔾0at initial time t = 0
17
…
Problem at time t = 0:
1.Initialization
2. Ranking (Ranking function: Personalized PageRank)
3. Clustering
Problem at time 𝑡:
1. Compute approx. rank score
2. Clustering
…
…
Given at time 𝑡:
Nodes and Edges are inserted to / remove from
or

18. Proposed Method:
Overview
Adopt A Dynamic PPR computation
based on the Gauss-Southwell method [Ohsaka KDD’15]
18
Main Idea
1. Each subgraph can be regarded as a dynamic graph
2. Previous rank score is a GOOD initial rank score.
3. We need to improve the approximate rank score locally
𝑒𝑟𝑟𝑜𝑟 < 𝜖
𝑒𝑟𝑟𝑜𝑟 ≥ 𝜖
14] Naoto Ohsaka, Takanori Maehara, and Ken-ichi Kawarabayashi. 2015.
Efficient PageRank Tracking in Evolving Networks (KDD ’15). 875–884.

19. Proposed Method:
Gauss-Southwell Method [Southwell. ‘40, ‘46]
• 𝑣-th rank score 𝑟𝑃𝑃𝑅(𝑣) of 𝔾𝑖
• Corresponding residual 𝑑(𝑣) as: 𝑑(𝑣) = 1 − 𝛼 𝑏 − 𝐼 − 𝛼𝑃 𝑟𝑃𝑃𝑅(𝑣)
Goal:
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑑 𝑣 → 0
19
𝑖
・Propagate
・Update r and d
𝑒𝑟𝑟𝑜𝑟 < 𝜖
𝑒𝑟𝑟𝑜𝑟 ≥ 𝜖
𝛼
𝑑𝑖
𝑑𝑒𝑔
𝛼
𝑑𝑖
𝑑𝑒𝑔
𝑖

20. Proposed Method:
Dynamic Rank Score Tracking
20
• Iteration number : 𝑡
𝒓 𝑷𝑷𝑹
𝒕
(𝒗 = 𝟎) = 𝒓 𝑷𝑷𝑹
(𝒕−𝟏)
𝒅 𝒕 (𝒗 = 𝟎) = 𝒅 𝒕−𝟏 + 𝜶 𝑷
(𝒕)
− 𝑷
(𝒕−𝟏)
𝒓 𝑷𝑷𝑹
(𝒕−𝟏)
Compute approx. rank score by Gauss-Southwell algorithm
At the time t: cluster is updated
Added node

21. Proposed Method:
Dynamic Rank Score Tracking
21
• Iteration number : 𝑡
𝒓 𝑷𝑷𝑹
𝒕
(𝒗 = 𝟎) = 𝒓 𝑷𝑷𝑹
(𝒕−𝟏)
𝒅 𝒕 (𝒗 = 𝟎) = 𝒅 𝒕−𝟏 + 𝜶 𝑷
(𝒕)
− 𝑷
(𝒕−𝟏)
𝒓 𝑷𝑷𝑹
(𝒕−𝟏)
Compute approx. rank score by Gauss-Southwell algorithm
𝒗 = 𝟎: Compute initial solution
𝑒𝑟𝑟𝑜𝑟 < 𝜖
𝑒𝑟𝑟𝑜𝑟 ≥ 𝜖

22. Proposed Method:
Dynamic Rank Score Tracking
• Iteration number : 𝑡
𝒙 𝒌 𝒕 𝟎 = 𝒙 𝒌 𝒕 − 𝟏
𝒓 𝒌 𝒕 𝟎 = 𝒓 𝒌 𝒕 − 𝟏 + 𝜶 𝑷 𝒌 𝒕 − 𝑷 𝒌 𝒕 − 𝟏 𝒙 𝒌 𝒕 − 𝟏
Compute approx. rank score by Gauss-Southwell algorithm
22
𝑖
𝒗 = 1
・Propagate
・Update r and d
𝑒𝑟𝑟𝑜𝑟 < 𝜖
𝑒𝑟𝑟𝑜𝑟 ≥ 𝜖

23. 23
𝑖
𝒗 = 𝟐
• Iteration number : 𝑡
𝒙 𝒌 𝒕 𝟎 = 𝒙 𝒌 𝒕 − 𝟏
𝒓 𝒌 𝒕 𝟎 = 𝒓 𝒌 𝒕 − 𝟏 + 𝜶 𝑷 𝒌 𝒕 − 𝑷 𝒌 𝒕 − 𝟏 𝒙 𝒌 𝒕 − 𝟏
Compute approx. rank score by Gauss-Southwell algorithm
Proposed Method:
Dynamic Rank Score Tracking
𝑒𝑟𝑟𝑜𝑟 < 𝜖
𝑒𝑟𝑟𝑜𝑟 ≥ 𝜖

24. Evaluation Experiments
25

25. Evaluation Experiments:
Setup
• Datasets
• Algorithms
- Proposed method: reduce the cost by updating locally
- RankClus: the original algorithm
- Pruning: reduce the cost by pruning
[Yamazaki, et al. iiWAS’ 18] [Yamazaki, et al. JDI’ 19]
• Evaluation Criterion
- NMI (Normalized Mutual Information)
NMI takes a value between 0 (no mutual information) and 1
(perfect correlation)
26
Dataset name # of |X| # of |Y| # of edges
DBLP 20 5,693 95,516
Yahoo-msg 57 100,001 6,359,436

26. Evaluation Experiments:
Running Time Analysis
27
Running times of each algorithm
(𝐾 = 4, 𝜖 = 10−9
) (𝐾 = 10, 𝜖 = 10−9
)

27. Evaluation Experiments:
Parameter Analysis (1/2)
28
Running times by varying 𝜖
Yahoo-msgDBLP

28. Evaluation Experiments:
Parameter Analysis (2/2)
29
Running times by varying the number of clusters 𝐾
Yahoo-msg

29. Evaluation Experiments:
Clustering Accuracy Analysis
NMI score of Proposal by varying 𝜖
30
Comparing with the original RankClus result

30. Conclusion
31

31. Conclusion
• Main Approach
- Focus on the dynamic graph property of RankClus and
compute only evolving nodes and their neighbors
• Evaluation Result
- Confirm our proposed method can obtain clusters almost
twice as faster than competitive method while keeping
the clustering accuracy for two real-world dataset
32
Propose efficient RankClus algorithm
for large-scale bi-type information networks