ANALYSIS AND VISUALIZATIONOF TIME-VARYING DATA

USING ‘ACTIVITY MODELING’

BySalil R. Akerkar

AdvisorDr Bernard P. Zeigler

ACIMS LAB (University of Arizona)

Presentation Outline

Introduction Activity – A DEVS Concept Activity Modeler System Stage1 - Preprocessing Stage2 - Activity Engine Stage3 - Visualization Results Implications for Discrete Event Simulation Future Work

Introduction

Data Source and Problem under study Current trends Unexplored area Motivation – Discrete Events vs. Discrete Time

Activity – A DEVS Concept

Definition of Activity

||)( 1 ii mmTActivity

t1 0ti

m1

mi

mn

q

T

TActivityTyAvgActivit /)( qTActivityqTssresholdCroNumberOfTh /)(),(

Activity – A DEVS Concept

Coherency (Space and Time) Instantaneous Activity

Accumulated Activity (same as DEVS Activity)

Activity Domain

)1()() tValuetValue(IA(t)Activity ousInstantane

t

i

tValuetValuetAAdActivityAccumulate )1()())((

Activity Modeler System

RawData

RawData

FORMATTED DATA

FORMATTED DATA

RESULTS

RESULTS

Stage-1

RESULTS

RESULTS

ACTIVITY DATA

ACTIVITY DATA

Stage-2 Stage-3

PERLFORMATTER ACTIVITY

ENGINE

(OPTIONAL)PERL

FORMATTER

GNUPLOT

MODULES

GNUPLOT

MODULES

AVS- EXPRESS

MODULES

Stage 1 – Pre Processing

Why do we need pre-processing? Regular Structure format PERL formatter

Functions Extract Information Format Correction Logic Analyze part of information 2D formatter

decrease IO operations standardization

Stage 2 – Activity Engine

ACTIVITY GENERATOR

PATTERNPREDICTOR

STATISTICANALYZER

ACTIVITYTIME-

SERVICES

ACTIVITY LOG

THE ACTIVITY ENGINE

PERL

Formatter

--------------------

--------------------

GNUPLOT

SCRIPTS

AVS-EXPRESS

MODULES

--------------------

--------------------

--------------------

--------------------

--------------------

--------------------

--------------------

--------------------

DATA-FILEPATTERN

INFORMATION

STATISTICAL INFORMATION

ACTIVITY DATA

DATA ENGINE

Stage 2 – Data Engine

Functions File handling

Sequential / Random access Standardization of filenames for automation

Memory Allocation Transformation between domains

Cellular and Temporal

Transformation between dimensions Val2D[i][j] = Val1D[i*Cols+j]

Independent of spatial dimension

Stage 2 - Activity Generator

Instantaneous Activity Accumulated Activity Time Advances Activity Factor (AF)

Cellular domain

Threshold (AF)

],0[))((

TttepsTotalTimeS

thresholdtIAnTimeSteps

NT

txIAt x ),(

Cells

Activity

factor

Stage 2 – Statistic Analyzer

Extract Statistics in terms of groups Group1: Maximum, Minimum, Range, Average Group2: Standard deviation, Mean Group3: Living Factor (Temporal domain) Group4: Histogram of Time Advances

Static in nature

Provides meaningful threshold to Activity Factor Living Factor

Stage 2 – Statistic Analyzer

Group 3: Living Factor (LF) Temporal domain

Group 4: Histogram of Time Advances Temporal domain Logarithmic in scale

],0[))((

TtTotalCells

thresholdtIAnCells

910)( tadvMintadvMax

Time

Tim

e

Stage 3 – Pattern Predictor

Spatial and Temporal Coherency Peaks and Max Analyze activity pattern Predict activity pattern

Stage 3 – Pattern Predictor

•Max Locator

•Peak Locator

Difference in Peak and Max

•False Peak problem

•Eliminated by ROI

(Region of Imminence)

Stage 3 – Region Of Imminence (ROI)

Definition Steps

Peak Detection in IA Scanning algorithm

Boundary conditions Threshold conditions ()

Significance Imminence Factor

Cells

Stage 3 – Pattern Predictor

1D scanning algorithm 2 neighbors Binary visualization

Cells

Threshold condition

Boundary condition

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Peak Under consideration: 2 Location of cell: 10

Initial Values:Left-neighbor = right- neighbor = 10

Final Values:Left-neighbor = 7Right-neighbor = 13

Stage 3 – Sphere Of Imminence

2D scanning algorithm

3 types of tuning Coarse Normal Fine

Stage 3 – Sphere Of Imminence

Type Of Tuning

Computation time (ms)

Imminence Factor

(t= 5)

Imminence

Factor (t=10)

Coarse 5393 0.0709 0.0974

Normal 6224 0.0985 0.1395

Fine 6456 0.1505 0.3327

Coarse Tuning

Normal Tuning

Fine Tuning

Stage 3 – Region Of Imminence

ROI: Overcome the False Peak problem

)1&(&)1( cellValcellValcellValcellVal 1&&1 cellValcellValcellValcellVal

1&&1 cellValcellValcellValcellVal 1&&1 cellValcellValcellValcellVal

Stage 3 – Predict Pattern

1D space Linear Span Module [0.9 – 0.95] Order of Pattern Pattern attributes

Offset Direction Difference

Steps Recognizing pattern t[n,n+1]

5 1st order pattern 2 2nd order

Predicting pattern t[n+2,T]

1 1 1 0 1 0 0 0

0 0 1 1 0 1 0 0

t = ta

t = tb

3 0 0 0 1 0 0 0

0 0 2 0 0 1 0 0

t = ta

t = tb

ROI

Linear span

2nd Order 1st

Stage 3 - Visualization

Softwares GNUPLOT AVS-Express

Visualization Stages Reader (Import data) Visualization modules Writing stage

Reader

VIZ modules

Writer

Stage 3 - Visualization

Zero Padding Binary Visualization Advantages

Eliminating unwanted data Reduction in file size

Implementation set zrange [0.5:]

Stage 3 - Visualization

Domain Types Of Result Visualization Techniques

1D 2D

Spatio-Temporal

Instantaneous Activity, Accumulated Activity, Time

Advances

Surface Plot Images (GNUPLOT)

Surface Plot / Contour movies (GNUPLOT

scripts/ AVS-Express)

Region Of Imminence, Peak Locator, Max Locator

Binary Visualization, Zero Padding (GNUPLOT)

Binary Visualization, Zero Padding

(GNUPLOT scripts)

Cellular Statistics, Activity Factor 1D single / multi graphs

(GNUPLOT)

Surface Plot Images (GNUPLOT)

Temporal Living Factor, Histogram of time advances

1D single / multi graphs

(GNUPLOT)

Surface Plot Images (GNUPLOT)

Results

1D space 1D heat diffusion process Robot Activity

2D space 2D heat diffusion process Fire-Front model

Results – 1D Heat diffusion

• 1D space ,T=100

• N=10, 100, 200

N 100

10 200

Cel

ls

Cells

Time

Results – Robot Activity

1D space Robots modeled as cells Simulation time steps – 2357 Data (Value domain)

1- Robot moving 0- Robot stopped

Activity domain 1- State transition 0- Same state

Robots

Time

Results – Robot Activity

Living Factor Activity Factor Imminent groups

Results – 2D diffusion

2D space (100 x 100 cells) T = 50 Cellular domain results (2D)

Activity Factor Statistics Surface plot images

IA surface characterized by concentric circles tadv histogram lower end

Activity Factor

Histogram of Time Advances

Results – 2D diffusion

Movie of IA / AA (activity domain) and output values (value domain)

Results – Fire Front model

2D space (100 x 100 cells) T = 297

Movie for Value domain

Results – Fire Front model

Living Factor 20% maximum t=180 boundary

Imminence Factor = 0.7 t [50-150]

Time

Results – Fire Front model

Instantaneous Activity

Peak Bars

Accumulated Activity

Region Of Imminence

Implications for Discrete Event Simulation

DEVS transitions:

DTSS transitions:

Maximum Slope:

DEVS v/s DTSS

Implications for Discrete Event Simulation

MODEL CELLS TIME MAX(IA) TOTAL AA DEVS

DTSS

1D diffusion

(N=10)

10 100 0.26318 2.4283 0.0093

1D diffusion

(N=100)

100 100 0.9069 3.8296 0.00042

1D diffusion

(N=200)

200 100 0.9635 3.9285 0.0002

2D diffusion 10000 50 0.2583 2048.77 0.819

Fire Front 10000 297 213.995 5321979 0.0083

DEVS v/s DTSS

Results – Predict Pattern

Test data - 3 1D diffusion (N=100)

Results

Results for 1D process Test data 1D diffusion

Percentage Error decreases as

N increases ROI characterized by

linear curves

Conclusion

New perspective for data analysis – Activity domain ROI – Spatial Coherency in Temporal domain Analyze process behavior in terms of Activity Compute and Predict – activity pattern Results – process specific Predict Pattern - % Error decreases as

N increases ROI curves are characterized by linear curves

DEVS found to be more efficient than DTSS

Future Work

Extending system to data in 3D space

Extending system to UNIX platform

Enhancing the Pattern predictor module

Efficiently Detecting the ‘new Imminent Cells’ in DEVS simulation

ACKNOWLEDGEMENTS

Dr. Bernard Zeigler Dr. Salim Hariri Dr. James Nutaro Dr. Xiaolin Hu, Alex Muzy Hans-Berhard Broeker Cristina Siegerist ACIMS LAB

QUESTIONS ?