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# Psychophysics ECE 51100

Purdue

GPA 3.59

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This 28 page Class Notes was uploaded by Cassidy Casper on Saturday September 19, 2015. The Class Notes belongs to ECE 51100 at Purdue University taught by Hong Tan in Fall. Since its upload, it has received 78 views. For similar materials see /class/207892/ece-51100-purdue-university in Electrical Engineering & Computer Science at Purdue University.

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Date Created: 09/19/15

ECESllPSYSll PSYCHOPHYSICS A Joint Offering by the School of Electrical and Computer Engineering And the Department of Psychological Sciences Purdue University Fall 2007 Topic Information Theory for review only not graded 1 For the stimulusresponse confusion matrix shown below compute IS IR and I Tm Please explain your steps whether you compute them by hand or by using a software package R1 R2 R3 R4 R5 1 15 2 2 0 1 3 2 3 12 2 1 S4 1 0 3 15 1 5 2 1 4 0 13 Ans Te 09467 IS 23219 IR 23096 2 For the stimulusresponse confusion matrix shown in 1 demonstrate that i I Tex remains the same if the role of stimuli and responses were reversed ie by transposing the confusion matrix and Ans I T m 09467 ii I Tex remains the same if rows or columns were switched around e g by exchanging column R2 with column R5 etc Ans ITm 09467 Please do so by both reasoning mathematical proof or essay and by numerical examples 3 What is the interpretation of the quantity 2 In what ways are IT and 2 different in representing the outcome of an AI experiment 4 Explain the issues involved in selecting k the number of alternatives in a stimulus set when designing an absolute identification experiment to measure channel capacity Discuss what happens if k was too small or too large After the completion of an AI experiment how would you determine whether the value of k has been appropriately selected Multidimensional Scaling Hong Z Tan amp Zygmunt Pizlo Outline I Motivation I An Example on Haptic Texture Perception I Summary Hong Z Tan amp Zygmunt Pizlo Motivation I In general multidimensional stimuli lead to higher information transfer I Perceptual dimensionality is related to but not necessarily identical to physical dimensionality I Realworld stimuli are usually complex and multidimensional How do we determine their associated perceptual dimensionality OExample 1 Face recognition OExample 2 Color perception 9 Example 3 Haptic surface texture perception Hong Z Tan amp Zygmunt Pizlo Multidimensional Scaling MDS An Overview I MDS is a technique that lets us investigate the underlying dimensionality associated with a stimulus set I Given a set of 11 objects 0 Obtain dissimilarity measures as for each pair of objects r s 9 Search for a low dimensional perceptual space where each object is represented by a point 9 Ensure that the distances between the points in perceptual space drs match the original dissimilarities 5 Hong Z Tan amp Zygmunt Pizlo MDS The Idea n y intensity 612 0 I I 5561 5 5 O 6 etc 1 2 3 4 0 0 0 frequency z instrument Hong Z Tan amp Zygmunt Pizlo MDS The Results Dissimilarity Judgments 51210 51350 65615 etc Recovered Perceptual Distances Hong Z Tan amp Zygmunt Pizlo An Example Texture Perception I Hollins et al PampP 1993 I Stimuli 17 texture samples I Procedure passive stimulation I Dissimilarity Scores OGrouping ie similarity scores OCooccurrence scores 00 or 10 ODissimilarity 1 Cooccurrence I MDS analysis ALSCAL SAS Hong Z Tan amp Zygmunt Pizlo Cooccurrence Matrix Average over All Subjects Wax Card Slimulus Felt Straw Paper Cork Tile board Fell 100 Straw 00 100 Wax paper 05 00 100 Cork 10 05 30 100 Tile 05 00 60 55 100 Cardboard 05 00 60 60 95 1 00 Hong Z Tan 81 Zygmunt Pizlo cont I Dissimilarity 1 Cooccurrence I MDS analysis ALSCAL SAS Hong Z Tan amp Zygmunt Pizlo How many dimensions I Given 11 objects MDS analysis recovers n I underlying dimensions 1 113 1 quotkg3L in I Dimensionality is determined by examining SStress Stress and 1 R2 as a function of dimensions 10 Hong Z Tan amp Zygmunt Pizlo lR2 Plot from Hollins et a 04 N 03 I 02 01 on Solution dimensionality Hong Z Tan amp Zygmunt Pizlo A 3D Solution Dimension 1 scounnq ad sandpaper sponge loam straw 39 Cube representing the 3dimensional multidimensional scaling solution From Hollins Faldowski Rao amp Young 1993 J Hong Z Tan amp Zygmunt Pizlo Interpreting the MDS Solution I Adjective Rating Smooth l Dimension 1 Rough Hard 39 Dimension 2 39 S0fl Sli er Stick pp y Dimension 3 y Flat Bumpy Warm Cool 13 Hong Z Tan amp Zygmunt Pizlo Summary of MDS I Experimental procedures OKey is to obtain dissimilarity scores OGrouping similarity dissimilarity OOrdering nonmetric Oetc I Data analysis OUse statistical packages such as SAS OFor 11 objects n I dimensional solution Hong Z Tan amp Zygmunt Pizlo I Select solution dimensionality OSStress Stress and I R2 I Interpretation of MDS solutions OAdjective rating I Known problems and limitations olnvariant to translation rotation re ection OMay discover nonexistent perceptual spaces I Veri cation of MDS solution OAdjective rating OMatching experiments Color perception X rR gG bB Hong Z Tan amp Zygmunt Pizlo Readings I T F Cox and M A A Cox Multidimensional Scaling New York Chapman amp Hall 1994 I M Hollins R Faldowski S Rao and F Young Perceptual dimensions of tactile surface texture A multidimensional scaling analysis Perception amp Psychophysics vol 54 pp 697705 1993 Hong Z Tan amp Zygmunt Pizlo Estimation of Gd Hong Z Tan amp Zygmunt Pizlo The Problem I 6d can not be estimated directly from 11 or 21 experiments I We can always nd a cumulative Gaussian curve that goes through 2 points EXACTLY PR2S1 or 2 205 2H zscore Hong Z Tan amp Zygmunt Pizlo I We can always nd a straight line that goes through 1 point EXACTLY zH zF I Therefore we can NOT measure the goodness of t in either case with rms error Hong Z Tan amp Zygmunt Pizlo Two Ways to Estimate ad I 1 When you only collect one pair of H F ONeed assumptions to estimate 6d I 2 When you measure multiple pairs of H F OUse the rms error of ROC curve tting OThere are two ways to estimate ROC Run multiple experiments Ask subjects to use different k in different sessions 01 Rating paradigm Ask subjects to maintain multiple k in the same session Hong Z Tan amp Zygmunt Pizio The Main Idea I Given that aquot ZH ZF I We have 2 2 00139 02H 02F I Therefol e w estimate 6d we need to estimate O39ZH and O39ZF rst Hong Z Tan amp Zygmunt Pizlo Method 1 Estimate ad with One Pair of H F Values I Assumptions OThe only source of variability in d39 is sampling error therefore we are getting a lowerbound estimate OBinomial distribution approximates Gaussian with suf cient number of trials This is true if e p probability of responding yes is not extreme or N number of trials is large when p is extreme Hong Z Tan amp Zygmunt Pizlo I It then follows that the variability of H and F are 0F F1 F N1 0H Ha H N2 Where N1 0139 N2 is the number of times stimulus S1 or S2 has been presented respectively I All we need to do now is to estimate GZH and cm Hong Z Tan amp Zygmunt Pizlo PR2S1 or 82 1 2 ZCF 1 x F e 2 dx Lo x27r NE 52F FGF from gt F 777777 7 7 assumptions ltl F 0 39 ZF B 01 constants ZF52F g E a O F zF 2F zscore NZF9 o2zF based on local linear approximation Hong Z Tan amp Zygmunt Pizlo Summary of Method 1 1 1 zFgt2 zltFF UZltFgt0F27zez fwez N1 1 f zltHgt2 02w 2 27rH1 H 62 N2 FinwllJ 001 022m 022F It should be clear that Cd is inversely proportional to N1 and N2 Hong Z Tan amp Zygmunt Pizlo Method 2 Estimate 6d with ROC I No explicit 0 LAB PGG GYIO assumptlons are 6400 Trials 5134 Trials 6592 Trials needed 2 I Estlmate 62H and i cm as the rms zH 39 v error of straight 0 v Best linear its LSE 1 LAD zd 064 z 134dev0V06 PGG zd 092 21 141 dev012 GYO 26 101 z39 149 dev004 I Then compute 23 2 1 o 1 2 2 B 05139 V 02H 02F Hong Z Tan amp Zygmunt Pizlo Two Ways of Obtaining ROC I Multiple sessions with different k values Osee Pang et al 1991 I Same session with multiple k values 9 Rating Experiment Hong Z Tan amp Zygmunt Pizlo

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