1. Mining Unusual Patterns in Data Streams in Multi-Dimensional Space
11/21/2018
Mining Unusual Patterns in Data Streams in Multi-Dimensional Space
Jiawei Han
Department of Computer Science
University of Illinois at Urbana-Champaign

2. Mining Unusual Patterns in Data Streams
Outline
Characteristics of data streams
Mining unusual patterns in data streams
Multi-dimensional regression analysis of data streams
Stream cubing and stream OLAP methods
Mining other kinds of patterns in data streams
Research problems
November 21, 2018
Mining Unusual Patterns in Data Streams

3. Mining Unusual Patterns in Data Streams
Data streams—continuous, ordered, changing, fast, huge amount
Traditional DBMS—data stored in finite, persistent data sets
Characteristics
Huge volumes of continuous data, possibly infinite
Fast changing and requires fast, real-time response
Data stream captures nicely our data processing needs of today
Random access is expensive—single linear scan algorithm (can only have one look)
Store only the summary of the data seen thus far
Most stream data are at pretty low-level or multi-dimensional in nature, needs multi-level and multi-dimensional processing
November 21, 2018
Mining Unusual Patterns in Data Streams

4. Stream Data Applications
Telecommunication calling records
Business: credit card transaction flows
Network monitoring and traffic engineering
Financial market: stock exchange
Engineering & industrial processes: power supply & manufacturing
Sensor, monitoring & surveillance: video streams
Security monitoring
Web logs and Web page click streams
Massive data sets (even saved but random access is too expensive)
November 21, 2018
Mining Unusual Patterns in Data Streams

5. Challenges of Stream Data Mining
11/21/2018
Challenges of Stream Data Mining
Multiple, continuous, rapid, time-varying, ordered streams
Main memory computation
Mining queries are either continuous or ad-hoc
Mining queries are often complex
Involving multiple streams, large amount of data, and history
Finding patterns, models, anomaly, differences, …
Mining dynamics (changes, trends and evolutions) of data streams
Multi-level/multi-dimensional processing and data mining
Most stream data are at pretty low-level or multi-dimensional in nature
November 21, 2018
Mining Unusual Patterns in Data Streams

6. Stream Data Mining Tasks
Multi-dimensional (on-line) analysis of streams
Clustering data streams
Classification of data streams
Mining frequent patterns in data streams
Mining sequential patterns in data streams
Mining partial periodicity in data streams
Mining notable gradients in data streams
Mining outliers and unusual patterns in data streams ……
November 21, 2018
Mining Unusual Patterns in Data Streams

7. Multi-Dimensional Stream Analysis: Examples
Analysis of Web click streams
Raw data at low levels: seconds, web page addresses, user IP addresses, …
Analysts want: changes, trends, unusual patterns, at reasonable levels of details
E.g., Average clicking traffic in North America on sports in the last 15 minutes is 40% higher than that in the last 24 hours.”
Analysis of power consumption streams
Raw data: power consumption flow for every household, every minute
Patterns one may find: average hourly power consumption surges up 30% for manufacturing companies in Chicago in the last 2 hours today than that of the same day a week ago
November 21, 2018
Mining Unusual Patterns in Data Streams

8. A Key Step—Stream Data Reduction
Challenges of OLAPing stream data
Raw data cannot be stored
Simple aggregates are not powerful enough
History shape and patterns at different levels are desirable: multi-dimensional regression analysis
Proposal
A scalable multi-dimensional stream “data cube” that can aggregate regression model of stream data efficiently without accessing the raw data
Stream data compression
Compress the stream data to support memory- and time-efficient multi-dimensional regression analysis
November 21, 2018
Mining Unusual Patterns in Data Streams

9. Regression Cube for Time-Series
Initially, one time-series per base cell
Too costly to store all these time-series
Too costly to compute regression at multi-dimensional space
Regression cube
Base cube: only store regression parameters of base cells (e.g., 2 points vs points)
All the upper level cuboids can be computed precisely for linear regression on both standard dimensions and time dimensions
For quadratic regression, we need 5 points
In general, we need:
where k = 2 for quadratic.
November 21, 2018
Mining Unusual Patterns in Data Streams

10. Basics of General Linear Regression
n tuples in one cell: (xi , yi), i =1..n, where yi is the measure attribute to be analyzed
For sample i , a vector of k user-defined predictors ui:
The linear regression model:
where η is a k × 1 vector of regression parameters
November 21, 2018
Mining Unusual Patterns in Data Streams

11. Linearly Compressed Representation (LCR)
Stream data compression for multi-dimensional regression analysis
Define, for i, j = 0,…,k-1:
The linearly compressed representation (LCR) of one cell:
Size of LCR of one cell:
quadratic in k, independent of the number of tuples n in one cell
November 21, 2018
Mining Unusual Patterns in Data Streams

12. Stock Price Example—Aggregation in Standard Dimensions
Simple linear regression on time series data
Cells of two companies
After aggregation:
November 21, 2018
Mining Unusual Patterns in Data Streams

13. Stock Price Example—Aggregation in Time Dimension
Cells of two adjacent
time intervals:
After aggregation
November 21, 2018
Mining Unusual Patterns in Data Streams

14. A Stream Cube Architecture
A tilted time frame
Different time granularities
second, minute, quarter, hour, day, week, …
Critical layers
Minimum interest layer (m-layer)
Observation layer (o-layer)
User: watches at o-layer and occasionally needs to drill-down down to m-layer
Partial materialization of stream cubes
Full materialization: too space and time consuming
No materialization: slow response at query time
Partial materialization: what do we mean “partial”?
November 21, 2018
Mining Unusual Patterns in Data Streams

15. A Tilted Time-Frame Model
Up to 7 days:
24hrs
4qtrs
15minutes
7 days
Time
Now
25sec.
Up to a year:
31 days
24 hours
4 qtrs
12 months
Time
Now
Logarithmic (exponential) scale:
16t 8t 4t 4t 2t 1t
November 21, 2018
Time
Now
Mining Unusual Patterns in Data Streams

16. Two Critical Layers in the Stream Cube
(*, theme, quarter)
o-layer (observation)
(user-group, URL-group, minute)
m-layer (minimal interest)
(individual-user, URL, second)
(primitive) stream data layer
November 21, 2018
Mining Unusual Patterns in Data Streams

17. On-Line Materialization vs. On-Line Computation
Materialization takes precious resources and time
Only incremental materialization (with slide window)
Only materialize “cuboids” of the critical layers?
Some intermediate cells that should be materialized
Popular path approach vs. exception cell approach
Materialize intermediate cells along the popular paths
Exception cells: how to set up exception thresholds?
Notice exceptions do not have monotonic behaviour
Computation problem
How to compute and store stream cubes efficiently?
How to discover unusual cells between the critical layer?
November 21, 2018
Mining Unusual Patterns in Data Streams

18. Stream Cube Structure: from m-layer to o-layer
(A1, *, C1)
(A1, *, C2)
(A1, *, C2)
(A1, *, C2)
(A1, B1, C2)
(A1, B2, C1)
(A2, B1, C1)
(A2, *, C2)
(A2, B1, C2)
A2, B2, C1)
(A1, B2, C2)
(A2, B2, C2)
November 21, 2018
Mining Unusual Patterns in Data Streams

19. Stream Cube Computation
Cube structure from m-layer to o-layer
Three approaches
All cuboids approach
Materializing all cells (too much in both space and time)
Exceptional cells approach
Materializing only exceptional cells (saves space but not time to compute and definition of exception is not flexible)
Popular path approach
Computing and materializing cells only along a popular path
Using H-tree structure to store computed cells (which form the stream cube—a selectively materialized cube)
November 21, 2018
Mining Unusual Patterns in Data Streams

20. An H-Tree Cubing Structure
root
Observation layer
entertainment
sports
politics
uic
uic
uiuc
uiuc
Minimal int. layer
jeff
Jim
jeff
mary
Regression:
Sum: xxxx
Cnt: yyyy
Quant-Info
Q.I.
Q.I.
Q.I.
November 21, 2018
Mining Unusual Patterns in Data Streams

21. Partial Materialization Using H-Tree
Introduced for computing data cubes and iceberg cubes
J. Han, J. Pei, G. Dong, and K. Wang, “Efficient Computation of Iceberg Cubes with Complex Measures”, SIGMOD'01
Compressed database, fast cubing, and space preserving in cube computation
Using H-tree for partial stream cubing
Space preserving:
Intermediate aggregates can be computed incrementally and saved in tree nodes
Facilitate computing other cells and multi-dimensional analysis
H-tree with computed cells can be viewed as “stream cube”
November 21, 2018
Mining Unusual Patterns in Data Streams

22. Time and Space vs. Number of Tuples at the m-Layer
(Dataset D3L3C10T400K)
a) Time vs. m-layer size
b) Space vs. m-layer size
November 21, 2018
Mining Unusual Patterns in Data Streams

23. Mining Unusual Patterns in Data Streams
Time and Space vs. the Number of Levels
a) Time vs. # levels
b) Space vs. # levels
November 21, 2018
Mining Unusual Patterns in Data Streams

24. Mining Other Unusual Patterns in Stream Data
Clustering and outlier analysis for stream mining
Clustering data streams (Guha, Motwani et al )
History-sensitive, high-quality incremental clustering
Classification of stream data
Evolution of decision trees: Domingos et al. (2000, 2001)
Incremental integration of new streams in decision-tree induction
Frequent pattern analysis
Approximate frequent patterns (Manku & Motwani VLDB’02)
Evolution and dramatic changes of frequent patterns
November 21, 2018
Mining Unusual Patterns in Data Streams

25. Mining Unusual Patterns in Data Streams
Conclusions
Stream data mining: A rich and largely unexplored field
Current research focus in database community:
DSMS system architecture, continuous query processing, supporting mechanisms
Stream data mining and stream OLAP analysis
Powerful tools for finding general and unusual patterns
Effectiveness, efficiency and scalability: lots of open problems
Our philosophy:
A multi-dimensional stream analysis framework
Time is a special dimension: tilted time frame
What to compute and what to save?—Critical layers
Very partial materialization/precomputation: popular path approach
Mining dynamics of stream data
November 21, 2018
Mining Unusual Patterns in Data Streams

26. Mining Unusual Patterns in Data Streams
References
B. Babcock, S. Babu, M. Datar, R. Motawani, and J. Widom, “Models and issues in data stream systems”, PODS'02 (tutorial).
S. Babu and J. Widom, “Continuous queries over data streams”, SIGMOD Record, 30: , 2001.
Y. Chen, G. Dong, J. Han, J. Pei, B. W. Wah, and J. Wang. “Online analytical processing stream data: Is it feasible?”, DMKD'02.
Y. Chen, G. Dong, J. Han, B. W. Wah, and J. Wang, “Multi-dimensional regression analysis of time-series data streams”, VLDB'02.
P. Domingos and G. Hulten, “Mining high-speed data streams”, KDD'00.
M. Garofalakis, J. Gehrke, and R. Rastogi, “Querying and mining data streams: You only get one look”, SIGMOD'02 (tutorial).
J. Gehrke, F. Korn, and D. Srivastava, “On computing correlated aggregates over continuous data streams”, SIGMOD'01.
S. Guha, N. Mishra, R. Motwani, and L. O'Callaghan, “Clustering data streams”, FOCS'00.
G. Hulten, L. Spencer, and P. Domingos, “Mining time-changing data streams”, KDD'01.
November 21, 2018
Mining Unusual Patterns in Data Streams

27. Mining Unusual Patterns in Data Streams
Thank you !!!
November 21, 2018
Mining Unusual Patterns in Data Streams