Matrix Profile II: Exploiting a Novel Algorithm and GPUs to - PowerPoint Presentation

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Matrix Profile II: Exploiting a Novel Algorithm and GPUs to - PPT Presentation

Yan Zhu Zachary Zimmerman Nader Shakibay Senobari ChinChia Michael Yeh Gareth Funning Abdullah Mueen Philip Brisk Eamonn Keogh httpwwwcsucredueamonnMatrixProfilehtml ID: 561562

profile time qti series time profile series qti matrix stomp min algorithm distance subsequence 000 motif update 1qti window

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Slide1

Matrix Profile II: Exploiting a Novel Algorithm and GPUs to break the one Hundred Million Barrier for Time Series Motifs and Joins

Yan Zhu, Zachary Zimmerman, Nader

Shakibay

Senobari

Chin-Chia Michael Yeh, Gareth Funning, Abdullah Mueen,

Philip Brisk, Eamonn Keogh

http://www.cs.ucr.edu/~eamonn/MatrixProfile.html

Or, how to do four hundred ninety-nine quadrillion, nine hundred ninety-nine trillion, nine hundred ninety-nine billion, five hundred million pairwise comparisons very fast.Slide2

Definition Review: Distance Profile

1,1

2,1

…

n-m+1,1

A seismology time series, with two repeated earthquake patterns

Query,

the 1

subsequence in the time series

Obtain the z-normalized Euclidean distance between

Query

and each window (subsequence) in the time series. We would obtain a vector like this:

i,j

is the

distance between the

subsequence and the

subsequence.

We can obtain

, D

, … D

n-m+1

similarly.

Slide3

Definition Review: From Distance Profile to Matrix Profile

Note: this distance matrix is symmetric!

Matrix

Profile:

a vector of distance between each subsequence and its nearest neighbor

i,j

is the distance between the

window and the

window of the time series

1,1

1,2

…

1,n-m+1

2,1

2,2

…

2,n-m+1

…

i,1

i,2

…

i,j

…

i,n-m+1

…

n-m+1,1

n-m+1,2

…

n-m+1,n-m+1

Min(

)

Min(D

)

Min(D

n-m+1

)

Min(D

)P1

P1……...Pn-m+1Slide4

From Matrix Profile to Motif

The Matrix Profile has two minimum points. This pair of minimum points correspond to the 1

motif in the time series.

(

the closest pair of subsequences in the time series

)

A pair of minimum points

ime series

atrix profileSlide5

Question: How to compute Matrix Profile

very fast

Answer

: We have an

O(n2) time, O(n)

space algorithm called STOMP to evaluate it.

To see how it works, let us first introduce an important formula:

ot product of the

window and the

window. Once we know

, it takes

O(1)

time to compute

We precompute and store the means and stds in O(n) space. Slide6

The relationship between

and

…

… time complexity! …

……

……………

……

………Slide7

STOMP Algorithm: Computing the

ith line

…

n-m+1

i,1

i,2

i,3

…

i,n-m+1

i,1

i,2

QTi,3…QTi,n-m+1

QTi-1,1QTi-1,2…QTi-1,n-mQTi-1,n-m+1Update if Smaller

Matrix ProfileDistance ProfileWe pre-calculate QTx,1

and QT1,x (x=1,2,3,…,n-m+1).Then iterate through i=2, 2, 3, …, n-m+1.d1,1d1,2…d1,n-m+1d2,1

d2,2…d2,n-m+1………

…di,1di,2…di,n-m+1……

……dn-m+1,1dn-m+1,2…dn-m+1,n-m+1

…

n-m+1

min

minSlide8

i+1

…

n-m+1

i,i

i,i+1

…

i,n-m+1

i,i

i,i+1

…

i,n-m+1

i-1,i-1QTi-1,i

…QTi-1,n-mQTi-1,n-m+1di,i+1di,i+2…

di,n-m+1dmin

…Second Kernel Launch: Evaluate Final Value of Pi minUpdate if SmallerFirst Kernel Launch: Update Pi

to Pn-m+1

P1P2P3…Pn-m+1di,1

di,2di,3…di,n-m+1QTi,1

QTi,2QTi,3…QTi,n-m+1QTi-1,1QTi-1,2

…QTi-1,n-mQTi-1,n-m+1

…

Porting the algorithm to GPU

OptimizeUpdate if SmallerUpdate if SmallerSlide9

Comparison of STAMP, STOMP and GPU-STOMP

Algorithm

STAMP15.1 min1.17 hours

5.4 hours24.4 hours

STOMP

4.21 min

0.3 hours

1.26 hours

5.22 hours

GPU-STOMP

10 sec

18 sec46 sec2.5 minFor a fix subsequence length m=256: timeAlgorithm m | n2000 | 17,279,800400 | 100,000,000

STAMP (estimated)

36.5 weeks25.5 years

STOMP (estimated)8.4 weeks5.4 yearsGPU-STOMP9.27 hours12.13 daysFor large data, and for the very first time in the literature, 100,000,000Slide10

Comparing the speed of STOMP with existing algorithms

Algorithm m

512

1,024

2,048

4,096

STOMP

501s (14MB)

506s (14MB)

490s (14MB)

Quick-Motif

27s (65MB)

151s (90MB)

630s (295MB)

695s (101MB)

2040s (1.1GB)

N/A (>2GB)

For a time series of length : CPU time(memory usage) Note: the time and space cost of STOMP is independent of how the data looks.Slide11

Case Study I: Parameter Setting

There is only one parameter to set: the subsequence length m, however, the result is not sensitive to it…

aw seismograph data

matrix profiles

0min

30min

m=1000

m=2000

m=4000Slide12

Case Study II: The Benefit of Using Matrix Profile for Motif Discovery

1000

2000

3000

1996

2009

1996,

ID:30104990

2009, ID:371327705

motif is a pair of sensor defects

motif is a pair of matching seismology patternsSlide13

Case Study III: Earthquake Swarms

The matrix profile of a seven-minute snippet from a seismograph recording at Mount St Helens

“

... so regularly that we dubbed them ‘drumbeats’. The period between successive drumbeats shifted slowly with time, but was 30–300 seconds

”

* We are not only providing a linear-space algorithm that is much faster than all existing motif-discovery algorithms; we are actually providing much more information than just the top

motifs in the time series with STOMP.Slide14

514,000

524,000

-0.1

0.1

0.2

Y-axis

magnetometry

1000

2000

Case Study III: Penguin Telemetry

7.5 hours of recording at 40Hz took GPU-STOMP only 2.5 minute to run.Slide15