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8/12/2019 Aks-Memory Across Eye-Movements 1f Dynamic in Visual Search
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Memory across Eye-Movements:1/f Dynamic in Visual Search
Aug 5, 2001Madison, Wisconsin
---------------------------------- Society for Chaos Theory in
Psychology & the Life Sciences
Deborah J. AksUW-Whitewater
Gregory ZelinskySUNY- Stonybrook
Julien C. Sprott UW-Madison
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What guides eye-movements during complicated
visual search?
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Deterministic rules?
Simple set of neuronal interaction rules (e.g.,SOC) ?
Memory?
Are there correlations across sequence of
fixations?
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Find:
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Do we keep track of where we look?
Is there memory in search?
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Horowitz, T.S. & Wolfe, J. M. (1998). Visual Search has no memory . Nature, 357, 575-577.
Finding: Random repositioning of stimulidoes not affect search RTs
No memory?
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Overview QUESTIONS .
What guides complicated eye movements? Random or non-random process? Is there memory across fixations?
METHOD OF TESTING . Challenging visual search task
KEY ANALYSES Power law relation? Coloring of noise --> Memory across eye-movements
Fourier analysis Iterated Functions Systems (IFS) Test
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RESULTS
Raw fixations --> short term memory (1/f 2 brown noise) Fixation differences --> long term memory (1/f pink noise)
MODEL . Self-organized criticality (SOC)(Bak, Tang, & Wiesenfeld, 1987)
CONCLUSION There is memory across eye-movements! SOC model predicts relative eye movements.
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Horowitz, T.S. & Wolfe, J. M. (1998). Visual Search has no memory . Nature, 357, 575-577.
Finding: Random repositioning of stimulidoes not affect search RTs
Key Press RTsvs.Eye Movements
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What does visual search teach us? Cognitive processes!
Speed & Accuracy
Mechanisms Automatic or Attention
Search strategy Parallel, Serial, random or ?
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Features... Find the odd item Discriminate by..
Color xxxx xxx
Size xxxxxxx Orientation ------l---
Depth
Movement xxxx--> x
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Look for the red L
L
L
L L
L
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L
L
L L
L
L L L
L
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Conjunction Search
Find...combination of features
2 orientations (particular arrangement) Find: L among Ts
T
T
T
L T
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T
T
T
T
T
T T
L T
T T
T
T
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+
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T
T
T
T
T
T T
T
T T
T
T
L
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300
400
500
# of items
R T ( m s e c
)
5 10 15
0 ms/item
Feature search is easy!
Fast (300ms) Parallel (0-10ms/item) No attention needed
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300
500
700
# of items
R T ( m s e c )
5 10 15
40 ms/item
0 ms/item Feature
Conjunction
Conjunction search is hard! Slow er Sequential Focused attention needed
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Feature search is easy Fast (300ms) Parallel (500ms) Serial (>10ms/item)
Attention needed
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What guides search?
Environmental information.
Internal cognitive process Attention.
Memory? Deterministic Process:Self-Organized Criticality (SOC)?
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Memory in visual search?
Memory for locations in
search (Kristjansso,2000)
Identity of objectsaccumulates over time(Treisman & Gelade, 1980)
Random repositioning ofstimuli does not affectsearch RTs(Horowitz & Wolfe, 1998)
Inattentional amnesia insearch (Wolfe, 1999)
Evidence for Evidence against
We are able to keep track of
where we look! Inhibition of return(Klein, 1982)
Failure to replicate
inhibition of return(Wolfe & Pokorny, 1990)
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Non-systematic eye-movements
Engle, 1977; Ellis & Stark, 1988;Scinto & Pillalamarri, 1986;
Krendel & Wodinsky, 1960; Groner & Groner, 1982
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Visual Search Task
T
T
T
T
T
T
T
Find the upright T
T
T
T
T T
T
T
T
T
T
T
T T
T
T
T
T
T
T
T
T
TT
T
T
T
T
T
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Map trajectory of eyes :
Duration & x,y coordinates for each fixation.----------------------------------------------------------
Differences between fixationsxn xn+1 & yn yn+1
Distance = (x2 + y 2)1/2
Direction = Arctan (y/x).
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Analyses
Power spectra (FFT)
Descriptive & Correlational Statistics
Iterated Function Systems (IFS) test
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Results 24 fixations per trial (on average)
7.6 seconds (SD =6.9 sec) per trial (316 ms/item).
Mean fixation duration = 212 ms (SD = 89 ms)
10,215 fixations across complete search experiment.
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Series of Fixation Differences(yn+1- yn)
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Scatter plot of 10,215 eye fixations forthe entire visual search experiment.
Eye Fixations
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Delay Plot of Fixationsyn -vs- y n+1
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Across 8 sessions we see scaling properties:
Fixation frequency decreased from 1888 to 657
Fixation duration increased from 206 to 217 ms.
Fixation differences xn xn+1 decreased yn yn+1 increased
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Spectral analysisFast-Fourier Transform (FFT)
Power vs. FrequencyRegression slope = power exponent
f a
f -2 = 1/ f 2
Brown noise
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Power law indicates
Adaptive fractal properties: Scale invariance Flexible system
Strength of memory Steepness of the slope (on a log-log scale) reflects..
correlation across data points duration of memory
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White Noise
Pink Noise
Brown Noise
1/f 0 noise -- flat spectrum= nocorrelation across data points
1/f noise --shallow slope =extremely long term correlation
1/f 2 noise-- steep slope = short-term correlation.
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Power Spectra on raw fixations
a
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Power Spectra of first differencesacross fixations
a = -.6
Di fi i
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Distance across eye fixations(x2 + y 2) 1/2
a = -.47
a = -0.3
a = -1.8
Iterated Function Systems
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Iterated Function Systems--IFS Test--
(Peak & Frame, 1994 ; Stewart, 1989 ).Fixation Series
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1
2 3
4
Start
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PinkNoise
Brown Noise
White Noise
1/f
1/f
1/f
Raw Fixations
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Brown noise pattern
Clustering along diagonals reveals short-term, highly correlated consecutive data points
Fixation differences
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Fixation differences
Pink noise
Triangular microstructure associated w/ long-term, loosely correlated consecutive data points
IFS Test: Fixation direction
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Clustering indicates correlated fixations. Direction of fixations show
anti-correlated movements a indicated by absence of main diagonals.
IFS Test: Fixation direction
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IFS tests yields patternsconsistent w/ FFT results
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Summary of results :
Sequence of
Absolute eye positions --> 1/f brown noise Short-term memory.
Differences-between-fixations --> 1/f pink noise Longer-term memory.
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ModelHebb, 1969; Rummelhardt & McClelland, 1985
Neuronal interactions --->
implicit guidance
Could eye movements be described by a simple set ofneuronal interaction rules (e.g., SOC) that produce 1/f
behavior?
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Increasing Neural Activation --->
0 4
SOC Network(Adapted from Bak, Tang, & Wiesenfeld, 1987)
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Stimulate 1 neuron
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Z(x,y)= initiallystimulated site
As individual neurons are activated beyond a threshold (of 3), activity (4) is
dispersed to surrounding cells.
Threshold rule: For Z(x,y) > Zcr =3
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Activity in theoriginal site is
depleted to zero.
Z(x,y) -> Z(x,y) - 4
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0 4
Neural SOC
l SOC il
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Neural SOC w/ eye movements trails
Eye movements are pulled to the
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site(s) of greatest activation
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For Z(x,y) > Zcr
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Complex & effective search
( ,y) Z(x,y) -> Z(x,y) - 4 Z(x + 1,y)-> Z(x + 1,y) + 1
Z(x,y+
1) -> Z(x,y+
1) + 1Simple set of SOC rules..
{
can produce:
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CONCLUSIONS
There is memory across eye-movements!
Neural SOC model --> 1/f relative eye-movements.
Simple self-organizing system--> effective search
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http://psychology.uww.edu/Aks/papers/AZS01.ppt
Aks, D. J. Zelinsky G. & Sprott J. C. (2002). Memory Across Eye-Movements: 1/f Dynamic in Visual Search. Nonlinear
Dynamics, Psychology and Life Sciences, 6 (1).
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Bluebird contributed bywww.Sierra foothill.org
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And thanks to Bob Goodman for,among a # of things,
getting me to reduce the # of slides in this talk.
Phew, Debs down to 93 slides
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References
Aks, D.J., Nokes, T. Sprott, J.C. & Keane, E. (1998). Resolvingperceptual ambiguity in the Necker Cube: A dynamical systemsapproach Abstracts of the Psychonomics Society 3 38
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approach. Abstracts of the Psychonomics Society, 3, 38.Allport, D.A. (1987). Selection-for-action: Some behavioral and
neurophysiological considerations of attention and action. In H.Heuer & A.F. Sanders, (Eds.), Perspectives on Perception andAction. Hillsdale, N.J.: Erlbaum.
Bak, P. (1996). How nature works: the science of self-organizedcriticality. New York: Springer-Verlag.
Bak, P., & Tang, C. (1989). Earthquakes as a self-organizedcritical phenomenon. Journal of Geophysics Research - Solar.Earth Planet, 94, 15635-15637.
Bak, P., Tang, C., & Wiesenfeld, K. (1987). Self-organizedcriticality: An explanation of 1/f noise. Physical ReviewLetters, 59, 381-384.
Bak, P., Tang, C., & Wiesenfeld, K. (1988). Self-organizedcriticality. Physical Review A, 38, 364-374.
Daugman, J. G. (1991). Self-similar oriented wavelet pyramids:Conjectures about neural non-orthogonality. In A. Gorea (Ed.),Representations of Vision. Cambridge: Cambridge University Press.
Ellis, S. R., & Stark, L. (1986). Statistical dependency in visualscanning. Human Factors, 28(4), 421-438.
Gilden, D. L. (1996). Fluctuations in the time required forelementary decisions. Psychological Science, 8 (4), 296 302.
Gilden, D. L., Thornton, T., & Mallon, M. (1995). 1/f noise inhuman cognition. Science, 267, 1837-1839.
Hilborn, R. C. (1994). Chaos and Nonlinear Dynamics: Anintroduction for Scientists and Engineers. Oxford: OxfordUniversity Press.
Hochberg, J. (1968). In the minds eye. In R. N. Haber (Ed.),