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An Efficient Algorithm for Mining Time Interval-based Patterns in Large Databases

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### An Efficient Algorithm for Mining Time Interval-based Patterns in Large Databases

Yi-Cheng Chen, Ji-Chiang Jiang, Wen-ChihPeng and Suh-Yin Lee

Department of Computer Science

National Chiao Tung University

Hsinchu, Taiwan 300

{ejen.cs95g, perrys0620.cs96g}@nctu.edu.tw [email protected] [email protected]

CIKM, 2010

OUTLINE

- 1.INTRODUCTION
- 2.PROBLEM DEFINITION
- 3.INCISION STRATEGY
- 4.COINCIDENCE REPRESENTATION
- 5.CTMiner ALGORITHM
- 6.EXPERIMENTAL RESULTS
- 7.CONCLUSION AND FUTURE WORK

1.INTRODUCTION

- All related researches in this domain are based on Allen’s temporal logics.
- Which there are 13 temporal relations between any two event intervals .

1.INTRODUCTION

Compare with previous works：

- Kam et al. - hierarchical representation.
- Hoppner - scan database by sliding window.
- Papapetrou - Hybrid-DFS algorithm.
- Wu et al. - TPrefixSpan.
- Patel et al. - Augmented Representation(By additional counting information ), and IEMiner.

1.INTRODUCTION

Propose ：

- Incision strategy
- Coincidence representation
- CTMiner (Coincidence Temporal Miner)

2.PROBLEM DEFINITION

Event interval and event sequence

- E = {e1, e2,…, ek} be the set of event symbols.
- (ei, si, fi), ei∈ E, si , fi,are time points, si < fi
- Event start：ei.tsEvent finish：ei.tf
- {(e1, s1, f1), (e2, s2, f2), …, (en, sn, fn)} where si≤si+1 and si< fi

2.PROBLEM DEFINITION

Temporal database

- Database D = {r1, r2, …, rm}, each record ri, where 1≤ i≤ m
- A record riconsists of a sequence-id and an event interval(start time and finish time).
- Records in the database D with the same client-id are grouped together.
- Database D can be viewed as a collection of event sequences.

2.PROBLEM DEFINITION

Time set and time sequence

- An event sequence q = {(e1, s1, f1), (e2, s2, f2), …, (en, sn, fn)}
- The set T ={s1, f1, s2, f2, …, si, fi,…, sn, fn} is called a time set corresponding to sequence q.
- Order all the elements in T and eliminate redundant element, we got sequence Ts.sequence Ts = {t1, t2, t3, …, tk}where ti∈ T , ti< ti+1.

2.PROBLEM DEFINITION

- Event slice

2.PROBLEM DEFINITION

- Event slice

(en, sn, fn)(B,1,5),(D,8,4),(E,10,13),(F,10,13)

4 event intervals in sequence 2

Corresponding time set T={1,5,8,14,10,13,10,13}{s1, f1, s2, f2, s3, f3, s4, f4 }

Time sequence Ts ={1,5,8,10,13,14}{t1, t2, t3, …, tk}

2.PROBLEM DEFINITION

Event slice

- Let set L = { +, -, *, Φ}, a set of event sequences Q = {q1, q2, …, qi,…}, qi= {(e1, s1, f1), …, (ej, sj, fj) , … (en, sn, fn)}

2.PROBLEM DEFINITION

- Event slice

start slice D＋= (D, 8, 10)intermediate slice D*= (D, 10, 13)finish slice D－= (D, 13, 14)

The event interval B has only one intact slice B = (B, 1, 5)

3.INCISION STRATEGY

- Incision example

3.INCISION STRATEGY

- Incision example

The incision strategy can totally avoid the generation of intermediate slices. By trimming the intermediate slices, we can still express the relationship between any two intervals correctly.

4.COINCIDENCE REPRESENTATION

- Group simultaneously occurring slices together to form the coincidences.
- Concatenation with all coincidences can describe an event sequence effectively.
- Simplify the processing of complex pairwise relationships between all intervals efficiently.

4.COINCIDENCE REPRESENTATION

- Good scalability
- Nonambiguity
- Simple is good
- Compact space usage

5.CTMiner ALGORITHM

min_sup = 2

6.EXPERIMENTAL RESULTS

- Runtime performance on synthetic data sets

6.EXPERIMENTAL RESULTS

- Real world dataset analysis

7.CONCLUSION AND FUTURE WORK

- Coincidence representation is nonambiguous and has several advantages over existing representations .

7.CONCLUSION AND FUTURE WORK

- Further：mining closed and maximal temporal patterns, incremental temporal patterns mining, and the research of method toward data stream.

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