1. K.L Ong, W. Li, W.K. Ng, and E.P. Lim
SCLOPE: An Algorithm for Clustering Data Streams of Categorical Attributes
K.L Ong, W. Li, W.K. Ng, and E.P. Lim
Proc. of the 6th Int. Conf. on Data Warehousing and Knowledge Discovery, Zaragoza, Spain, September 2004 (DaWak04)
2019/5/25
報告人:吳建良

2. Outline Clustering a Data Stream of Categorical Attributes
SCLOPE Algorithm
CluStream Framework
CLOPE Algorithm
FP-Tree-Like Structure
Experimental Results

3. Clustering a Data Stream of Categorical Attributes
Technically challenges
High dimensions
Sparsity problem in categorical datasets
Additional stream constraints
One pass I/O
Low CPU consumption

4. SCLOPE Algorithm Adopt two aspects of CluStream framework SCLOPE
Pyramidal time frame: store summary statistics at different time periods
Separate the process of clustering
Online micro-clustering component
Offline macro-clustering component
SCLOPE
Online:
Pyramidal time frame, FP-Tree-like structure
Offline:
CLOPE Clustering Algorithm

5. CLOPE Clustering Algorithm
Cluster quality measure
Histogram Similarity
A larger height-to width ratio  better intra-cluster similarity
H=S/W
Tid
Items 1 ab 2
abc 3
acd 4 de 5
def

6. CLOPE Clustering Algorithm (cont.)
Suppose Clustering C={C1, C2, …, Ck}
Height-to-width ratio
Gradient G(Ci)=H(Ci)/W(Ci)=S(Ci)/W(Ci)2
Criterion function
r: repulsion
Control the level of intra-cluster similarity

7. CLOPE Clustering Algorithm (cont.)
a b
C1={T1}
Initial Phase:
Tid
Items
Clus 1 ab 2
abc 3
acd 4 de 5
def
T2 is temporally added into C1
Profit=0.55
a b c
C1={T1, T2} or
Create a new cluster C2
Profit=0.41
C2={T2} C1 C1 C1 C2 C2
T3 is temporally added into C1
Profit=0.5 or
Create a new cluster C2
Profit=0.41
a c d
C2={T3}
a b c d
C1={T1, T2 , T3}
a b c d
C1={T1, T2 , T3}
d e f
C2={T4, T5}
Final Result:

8. CLOPE Clustering Algorithm (cont.)
Iteration Phase:
Repeat
moved=false
For all transaction t in the database
move t to an existing cluster or new cluster Cj that maximize profit
If Ci≠Cj then
write <t, j>
moved=true
Until not moved

9. Maintain Summary Statistics
Data streams
A set of records R1,…, Ri,… arriving at time stamps t1,…, ti,…
Each record R contains attributes A={a1, a2, …, aj}
A micro-cluster within time window (time tp ~ tq) is defined as a tuple
: a vector of record identifiers
: cluster histogram
- width:
- size:
- height: size to width ratio

10. FP-Tree-Like Structure
Drawbacks of CLOP
Multiple scans of the dataset
Multiple evaluations of the criterion function for each record
FP-tree-like structure
Require two scans of dataset
Determine the singleton frequency 
Insert each into FP-tree after arranging all attributes according to their descending singleton frequency
Share common prefixes
Without the need to compute clustering criterion

11. Construct FP-Tree-Like Structure
Tid
Items 1 ab 2
abc 3
acd 4 de 5
def
Tid
Items 1 ab 2
abc 3
adc 4 de 5
def
Scan database once
a:3, d:3, b:2, c:2, e:2, f:1
Arrange
null
a:3
b:2
c:1
d:1
d:2
e:2
f:1

12. FP-Tree-Like Structure
Each path (from the root to a leaf node) is a micro-cluster
The number of micro-clusters are depend on the available memory space
Merge strategy
Select node which has longest common prefix
Select any two paths passing through the node
Merge its corresponding

13. Online Micro-clustering Component of SCLOPE
On beginning of (window wi) do
1: if (i=0) then Q’ ←{a random order of v1,…,v∣A∣}
2: T ← new FP-tree and Q ←Q’
3: for all (incoming record ) do
4: order R according to Q and
5: if (R can be inserted completely along an existing path Pi in T) then 6:
7: else
8: Pj ← new path in T and ← new cluster histogram for Pj 9:

14. Online Micro-clustering Component of SCLOPE
On end of (window wi) do
10: L ← {<n, height(n)>: n is a node in T with > 2 children}
11: order L according to height(n)
12: while do
13: select <n, height(n)> with largest value
14: select paths Pi, Pj where
15:
16: delete
17: output micro-clusters and cluster histograms

15. Offline Macro-clustering Component of SCLOPE
Time-horizon h and repulsion r
h: span one or more windows
r: control the intra-cluster similarity
Profit function: clustering criterion
Each micro-cluster is treated as a pseudo-record
#Micro-cluster physical records
It takes less time to converge on the clustering criterion

16. Experimental Results Environment Aspects: Dataset CPU Pentium-4: 2GHz
RAM: 1GB
OS: Windows 2000
Aspects:
Performance, scalability, cluster accuracy
Dataset
Real-world, synthetic data

17. Performance and Scalability
Real-life data
FIMI repository (

19. Performance and Scalability (cont.)
Synthetic data
IBM synthetic data generator
Dataset: 50k records
(a) 50 clusters
(b) 100 clusters
(c) 500 clusters

20. #Attributes: 1000

21. Cluster Accuracy Mushroom data set Purity metric
117 distinct attributes and 8124 records
Two classes
4208 edible , and 3916 poisonous
Purity metric
the average percentage of the dominant class label in each cluster

22. Cluster Accuracy (cont.)
Online micro-clustering component of SCLOPE
SCLOPE v.s CLOPE