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Discovering Tendency Association between Objects with Relaxed Periodicity and its Application in Seismology Changjie. TANG 1 Rynson W. H. LAU 2 H. YIN 1 Qing LI 2 L. YANG 1 Z. YU 1 L. XIANG 1 T. ZHANG 1 1 Computer Department, Sichuan University, Chengdu, China
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Discovering Tendency Associationbetween Objects with Relaxed Periodicity and its Application in Seismology • Changjie. TANG1Rynson W. H. LAU2H. YIN1Qing LI2 • L. YANG 1Z. YU1L. XIANG1T. ZHANG 1 • 1 Computer Department, Sichuan University, Chengdu, China • chjtang@scu.edu.cn • 2 Department of Computer Science, City University of Hong Kong, Hong Kong • {rynson,csqli}@cityu.edu.hk
Outline • Introduction, Background • Main Idea ( • Concepts ( Relaxed periodicity ) • Algorithms • Theoretical results • Implementation and App. in Seismic Research • Summary
Background • Periodic phenomena , ( repetitive phenomena) • Correlation between objects with periodicity, • such as: • Climate and its premonitions • Earthquake (Seismology )and its premonitions • Example : Earthquake magnitude and the Radon • concentration in the groundwater).
Background Correlation between objects with periodicity, • earthquake • magnitude • Radon • groundwater • The repetitious is not in the mathematical sense • because noises and inflation /deflation, or stretching unevenly on the time axis. Relaxed Periodicity
Background : Project RADIUS • Project RADIUS ( UN, To reduce the losses of natural disaster ,1990-1999) • Sichuan Province : Earth quake --intensive active. • Use new techniques in research of Earth quake : • such as: Internet techniques , KDD/DM,... • Hundreds researchers are working in Sichuan
Background : (SCEQIS) • Sichuan Earth Quake Infor. System (SCEQIS) This work S1 Web DB KDD s2 DW Decision s3 station
1748-1998 =History, 1999-2048 =prediction( Earthquake magnitude for Area Anning River)
Outline • Introduction, Background • Main idea of this work • Algorithms • Concepts ( Relaxed periodicity ) • Theoretical results • Implementation and App in Seismic Research of Annin River • Summary
Main Idea : Tendency With Inertia Down Peak Up Valley
Main Idea : Peak-Valley Array (Series) with Inertia • By the concept of Inertia, we can overcome • Small noise, • inflation /deflation, • Stretching unevenly on the time axis. • Peak-Valley Array (Series) with Inertia
Evaluate n-Peaks length ( 110 days) • For magnitude of Anning Area, 110 days = Stable 3-Peaks length in peak-Valley series: Relaxed Periodicity
Evaluate n-Peaks length ( 110 days) • Idea :Use the N-Peaks as time measure unit for life cycle of Earthquake. ( Relative time ). Ignore the uneven stretching on the time axis
! Correlation between objects with periodicity, • earthquake • magnitude • Earth • deform • (observable) • Our Task: Confidence= ? Support=?
Outline • Introduction, Background • Main Idea • Concepts ( Relaxed periodicity ) • Algorithms • Theoretical results • Implementation and App in Seismic Research of Annin River • Summary
Concepts : (Tendency with inertia ) • Tendency • TendencyType={Up, Peak, Down, Valley, Unknown}. • ObjTendency: [t, t’] →TendencyType • t1, t2, t3 adjacent time points • ObjTendency(t2, obj) the tendency of obj at time t2. • defined by checking the obj value, Tab. 1
Tendency With Inertia Peak Down Up Valley
Definition 4 (Candidate periodicity with n peaks). • Definition 5 ( Relaxed confidence of candidate periodicity) CP(n) • Definition 6 ( Relaxed periodicity with • Confidence> C0 ). • C0 is specified min value
Evaluate n-Peaks length ( 4 peks = 110 days ) • For magnitude of Anning Area, 110 days = Stable 3-Peaks length in peak-Valley series • 4-Peaks =110 daysRelaxed Periodicity with C > 72%
Outline • Introduction, Background • Main Idea • Concepts ( Relaxed periodicity ) • Algorithms • Theoretical results • Implementation and App in Seismic Research of Annin River • Summary
Algorithm 1. Get Tendency Series with inertia • Input: Database, inertia of the object. • Output: Tendency Series. • Steps: • (1) Retrieve the time series from database, stored in {a1, a2, ...,am}. • (2) Decide the tendency of a1 by comparing a1 and a2.The value falls in {Peak, Valley}. • (3) For ( i=2; i<m; i++) • {Left=ai; Middle=ai+1; Right=ai+2; • Determine the tendency of middle according to the Table-1.} • (4) Decide the tendency of am by comparing am-1 and am. The values falls in {Peak, Valley}.
Algorithm 2 Get Peak-Valley Series • Input: Tendency Series. • Output: Peak _Valley series. • Steps: • (1) Result = Input; • (2) Scan Result for adjoining peak (valley). If there are k adjacent peaks (valleys), keep the middle peak (valley), i.e. the [k/2]-th peak(valley), and delete rest (k-1) peaks(valleys). • (3) Delete all Up and Down from Result. ▍
Algorithm 3. Mine the relaxed periodicity • .Input: (1)Peak_Valley_Series; • (2) MaxSpan, //the maximum span for candidate periodicity - a positive integer • (3) MinSpan , //the minimum span for candidate periodicity - a positive integer • (4) MaxTimeLength, // It is a multiple of logical Chronon • (5) Min_Confidence, Gap, // two predefined numbers • Output: Relaxed Periodicity P and its confidence C.
Algorithm 3. ( Continue) • Procedure GetRelaxedPeriods( ) • for (i= 2;MinSpan<=i<MaxSpan; i ++) • for (TimeLength=1; TimeLength <= MaxTimeLenth; TimeLength++) { • scan Peak_Valley_Series calculate total_Peaks; • Total_i_span = total_Peaks – i + 1; // number of i-span; see Definition 3 and • // Lemma 1. • Valid_i_Span = number of i-Span that satisfying |RP(i)- TimeLength| <= Gap; • confid = Valid_i_Span /Total_i_Span; • } • if (confid >= Min_Confidence) { • C = confid; P = TimeLength; // output • Output “P as relaxed periodicity of i peaks, confidence = C”; • }. ▍
Result of GetRelaxedPeriods( ) in Earthquake Magnitude at Annin
Algorithm 4 ( Association of two Obj with relaxed Periodicity) • Input: Two peak-valley series S1 and S2, Correlation • Cond1, Cond2, Logical Chronon, Gap, which is a non-negative number. • Output: Relaxed match confidence. • Steps: ( SQL-like) • (1) Select TimeStamp, attribute concerned into TempR1 • (2) From peak-valley Series S1 • (3) Where Cond1 is true. • (4) Select TimeStamp, Attribute concerned into TempR2 • (5) From peak-valley Series S2
Algorithm 4 ( Continue) • (6) Where Cond2 is true. • (7) Select TimeStamp, Attribute concerned • (8) From R1, R2 • (9) Where Correlation match error is not greater than gap.
Outline ! • Introduction, Background • Main Idea • Concepts ( Relaxed periodicity ) • Algorithms • Theoretical results • Implementation and App in Seismic Research of Annin River • Summary
Theoretical results • Lemma 1. Let Peaks={P1,P2,...,Pr} be the peak series of object obj and n<=r. The number of candidate periodicity with n peaks is r-n+1. • As loop control number in algorithm • Theorem 1. the complexity of Algorithm 4 is O(m*n+m+n), where m and n are the sizes of two time series
Outline • Introduction, Background • Main Idea • Concepts ( Relaxed periodicity ) • Algorithms • Theoretical results • Implementation and App in Seismic Research of Annin River • Summary
Environment and Data • Annin River Area , geometric fault structure , in Sichuan province. • Covers 150 KM2 , E-quake intensely active status. • DB1: “Earthquake catalog from 1970 to 1995 at Annin”, • DB2: “Earth deform database from 1986 to 1996 at Annin”. • After data cleaning, the total number of records in DW is about 12,000.
Mining relaxed periodicity for earthquake magnitude • By Algorithm 1, mine out the Tendency series for each time point related to the seismic catalog. • By Algorithm 2, mine out the peak-valley Series from Tendency series. • By Algorithm 3, mine out the relaxed periodicity of earthquake and their complete support ratio from peak-valley series. The results are as shown in Fig.2.
Figure 2. The relaxed periodicity of earthquake and relaxed confidence.
Table 3. Peak_valley Series for Earthquake magnitude (Min_Sup=25%).
Peak-valley Series for Earthquake magnitude (Min_Support = 40%)
Performance • CPU: Pentium II 200 with 32MB RAM. • Test data: “earthquake catalog from 1970 to 1995”, 6000 records., “ earth deform database from 1986 to 1996”, 6000 records. • Algorithms: 1 2 3 4 • Execution time: 60sec. 70sec 10sec. 10s. • Not very fast, but acceptable.
Summary • Mining association between objects with relaxed periodicity is useful. • Propose concepts : such as relaxed periodicity • Four algorithms, Acceptable performance. • Theorem 1 shows that Algorithm 4 is still naive, • Efficiency remains to be improved. • Much further research needs to be done.
请各位专家同行指正! Thank you !!!