Categories and Concepts - Spring 2019Prototype and exemplar theories

PSYCH-GA 2207

Brenden Lake

What is a chair?

What is a chair?

What is a game?

Are concepts well-defined?(Labov, 1973)

Are concepts well-defined? Some of Labov’s results

The Classical View

• Concepts can be defined: there are necessary and sufficient conditions for category membership

• Membership is all-or-nothing. All members of a category are equally good members.?

Are all members of a category equally good?

green

Are all members of a category equally good?Multi-dimensional scaling solutionderived from people’s similarity ratings

(Rips, Shoben, & Smith, 1973)

atypical birds

typical birdsprototype

Goodness ratings are highly reliable across participant

Instructions:

...‘Which breeds of dogs are real “doggy dogs”? To me, a German Shepard is very doggy, but a Pekinese is not. “Rate the extent to which each instance represents your idea or image of the meaning of the category”’ (1-7 scale)

(Rosch, 1975)

COGNITIVE REPRESENTATIONS OF SEMANTIC CATEGORIES

APPENDIXTABLE Al: NORMS FOR GOODNESS-OF-EXAMPLE RATING FOR NINE SEMANTIC CATEGORIES

229

Member

Goodne

Rank

>s of exampleSpecific

score Member

Goodnes

Rank

3 of exampleSpecific

score

Furniture

chairsofacouchtableeasy chairdresserrocking chaircoffee tablerockerlove seatchest of drawersdeskbedbureaudavenportend tabledivannight tablechestcedar chestvanitybookcaseloungechaise loungeottomanfootstoolcabinetchina closetbenchbuffet

1.51.53.53.556.56.589

101112131415.515.51718192021222324252627282930

1.041.041.101.101.331.371.371.381.421.44.48.54.58.59.61.61.70

1.831.982.112.132.152.172.262.432.452.492.592.772.89

lampstoolhassockdrawerspianocushionmagazine rackhi-ficupboardstereomirrortelevisionbarshelfrugpillowwastebasketradiosewing machinestovecounterclockdrapesrefrigeratorpictureclosetvaseashtrayfantelephone

313233343536373839404142434445464748495051525354555657585960

2.943.133.433.633.643.704.144.254.274.324.394.414.464.525.005.035.345.375.395.405.445.485.675.705.755.956.236.356.496.68

Fruit

orangeapplebananapeachpearapricottangerineplumgrapesnectarinestrawberrygrapefruitberrycherrypineappleblackberrymelonblueberryraspberrylemonblack raspberryboysenberrywatermeloncantaloupelimetangelo

123456.56.589

1011121314151617181920212223242526

1.071.081.151.171.181.361.361.371.381.521.611.771.821.861.192.052.092.142.152.162.212.382.392.442.452.50

papayahoneydewfigmangoguavapomegranatecranberrypassion fruitprunesgooseberrydatekumquatraisinmuskmelonpersimmonpawpawcoconutavocadopumpkintomatonutgourdolivepicklesquash

27282930313233.533.53536373839404142434445464748495051

2.582.732.862.883.033.053.223.223.303.333.353.393.423.483.634.304.505.375.395.586.016.026.216.346.55

COGNITIVE REPRESENTATIONS OF SEMANTIC CATEGORIES

APPENDIXTABLE Al: NORMS FOR GOODNESS-OF-EXAMPLE RATING FOR NINE SEMANTIC CATEGORIES

229

Member

Goodne

Rank

>s of exampleSpecific

score Member

Goodnes

Rank

3 of exampleSpecific

score

Furniture

chairsofacouchtableeasy chairdresserrocking chaircoffee tablerockerlove seatchest of drawersdeskbedbureaudavenportend tabledivannight tablechestcedar chestvanitybookcaseloungechaise loungeottomanfootstoolcabinetchina closetbenchbuffet

1.51.53.53.556.56.589

101112131415.515.51718192021222324252627282930

1.041.041.101.101.331.371.371.381.421.44.48.54.58.59.61.61.70

1.831.982.112.132.152.172.262.432.452.492.592.772.89

lampstoolhassockdrawerspianocushionmagazine rackhi-ficupboardstereomirrortelevisionbarshelfrugpillowwastebasketradiosewing machinestovecounterclockdrapesrefrigeratorpictureclosetvaseashtrayfantelephone

313233343536373839404142434445464748495051525354555657585960

2.943.133.433.633.643.704.144.254.274.324.394.414.464.525.005.035.345.375.395.405.445.485.675.705.755.956.236.356.496.68

Fruit

orangeapplebananapeachpearapricottangerineplumgrapesnectarinestrawberrygrapefruitberrycherrypineappleblackberrymelonblueberryraspberrylemonblack raspberryboysenberrywatermeloncantaloupelimetangelo

123456.56.589

1011121314151617181920212223242526

1.071.081.151.171.181.361.361.371.381.521.611.771.821.861.192.052.092.142.152.162.212.382.392.442.452.50

papayahoneydewfigmangoguavapomegranatecranberrypassion fruitprunesgooseberrydatekumquatraisinmuskmelonpersimmonpawpawcoconutavocadopumpkintomatonutgourdolivepicklesquash

27282930313233.533.53536373839404142434445464748495051

2.582.732.862.883.033.053.223.223.303.333.353.393.423.483.634.304.505.375.395.586.016.026.216.346.55

Member Rank Score(1 [typical]...

7 [not typical])

...

Category: furniture

Typicality ratings are highly reliable and predict many aspects of categorization.

400

488

575

663

750

high medium low

birds insect fruit vegetable

typicality

(Smith, Rips, & Shoben, 1974)

reactiontime

Prompt (True or False):“A X [item] is a member of category Y”

Typicality predicts sentence verification

Task: “Name as many examples of Category X as you can...”

Result: The earlier the object is named, the more “typical” it is

(e.g., Rosch, Simpson, & Miller, 1976)

Typicality predicts category production

Example task, “Name as many birds as you can”: robin,

sparrow,canary,

…., ostrich, emu, etc.

typical birds

atypical birds

Typicality affects…• RT in sentence verification tasks

• “A robin is a bird”• Picture identification RT (robin vs. duck)• Learning

People learn typical items firstLearning is better if you teach with typical items

• Order of production in a list• Order in speech production (“apples and lemons” more

likely than “lemons and apples”)• Category-based induction

• Actually, typicality affects every task that uses categories

PP1 (5).max

PP1 (5).max

(Armstrong, Gleitman, & Gleitman, 1983)

Should we throw out the classical view? Cautionary note: Even definitional concepts

show typicality effects

typicality

These typicality ratings also affect sentence verification tasks, just like graded concepts.

The Classical View

• Concepts can be defined: there are necessary and sufficient conditions for category membership

• Membership is all-or-nothing. All members of a category are equally good members.

If not “classical,” then what?Prototype theory

Bird? Birds You’ve Seen Prototypical

Bird

• There are different versions of the theory, which go like this: Concepts are a summary representations based on typical properties or central tendency of a category, or an ideal image

• Earliest alternative, but now not the only, or the most popular theory

1. Instructions: You will see stimuli from Category A or B. Please indicate which category you think is correct.

2. Training phase: Participants see stimuli one at a time. For each item, they respond “A” or “B”. Usually, feedback (the correct answer) is received during training.

3. Test phase (optional): Participants may respond to additional stimuli. No feedback is given.

(Posner & Keele, 1968)

An example artificial category learning task, supporting the notion of learning a prototype

or “ideal image”

Category A or B?

A

B

Category A or B?

B

Category A or B?

A

Category A or B?

A

Category A or B?

B

Category A or B?

Training period is done. Now for testing…

(Posner & Keele, 1968)Prototype A: (not seen) Prototype B: (not seen)

Distortions of A: Old Distortions of B: Old

Distortions of A: New Distortions of B: New

Items seen during test period (after training)

After training, participants were tested on:-- the prototypes (new)-- some pattern distortions (old)-- some pattern distortions (new)

Result:( Accuracy for prototype =

Accuracy for old distortions )

> Accuracy for new distortions

Suggests that some form of abstract representation is learned, like an “ideal image” or prototype

PP1 (5).max

(image from Armstrong, Gleitman, & Gleitman, 1983)

Prototype theory and the Rosch and Mervis family resemblance view

“Many features in common, but no feature is shared by everyone”

Rosch & Mervis’s (1975) family resemblance view

Typicality rests on two main factors:

• having features frequently found in the category; and• not having features frequently found in other

categories

TABLE 1 SUPERORDINATE CATEGORIES AND ITEMS USED IN EXPERIMENTS 1 AND 2

Category

Item Furniture Vehicle Fruit Weapon

2 3 4

6

8 9

10 11 12 13 14 15 16 17 18 19 20

Chair Sofa Table Dresser Desk Bed Bookcase Footstool Lamp Piano Cushion Mirror Rug Radio Stove Clock Picture Closet Vase Telephone

Car Orange Gun Truck Apple Knife Bus Banana Sword Motorcycle Peach Bomb Train Pear Hand grenade Trolley car Apricot Spear Bicycle Plum Cannon Airplane Grapes Bow and arrow Boat Strawberry Club Tractor Grapefruit Tank cart Pineapple Teat-gas Wheelchair Blueberry whip Tank Lemon Icepick Raft Watermelon Fists Sled Honeydew Rocket Horse Pomegranate Poison Blimp Date Scissors Skates Coconut Words Wheelbarrow Tomato Foot Elevator Olive Screwdriver

Vegetable

Peas Carrots String beans Spinach Broccoli Asparagus Corn Cauliflower Brussel sprou Lettuce Beets Tomato Lima beans Eggplant Onion Potato Yam Mushroom Pumpkin Rice

ts

Clothing - Pants Shirt Dress 7

s Skirt Jacket z Coat Sweater E

kz Underpants 3 Socks F Pajamas Bathing suit x Shoes m WY Vest Tie Mittens Hat Apron Purse Wristwatch Necklace

Attribute listing experiment

FAMILY RESEMBLANCES

25

581

1 2 3 4 5 6 7 8 3 IO II 12 13 14 15 16 17 18 1520 Number of Items per coteqory lo which attributes apply

FIG. 1. Frequency distribution for number of attributes applied to each number of items/category.

Those attributes unique to a single member are not of primary interest for the present study since they do not contribute to the structure of the category per se. In actual fact, the number of unique attributes appli- cable to items was evenly distributed over members of the categories; for none of the six categories was the number of unique attributes signi- ficantly correlated with prototypicality. Of the attributes applicable to two or more members, Fig. 1 shows that the number of attributes de- creases as the number of items to which the attribute is applicable in- creases. In summary: the majority of attributes listed for items in the six categories demonstrated a family resemblance. relationship; that is, they were common to only some of the category members.

The major hypothesis of the experiment was that this family resem- blance structure would prove significantly correlated with the prototypi- cality of items. Correlations were computed separately for each of the two measures of family resemblance and separately for each category. The measure of prototypicality was the mean rating on a 7-point scale of the extent to which items fit subjects’ idea or image of the meaning of the category names (Rosch, 1975a). The basic measure of degree of family resemblance for an item was the sum of the weighted raw scores of each of the attributes listed for the item. The logarithmic measure of family resemblance was the sum of the natural logarithms of the scores of each of the attributes that had been listed for an item. Items in each category were ranked l-20 on the basis of prototypicality and were ranked l-20 on the basis of each of the measures of family resemblance. Spearman rank-order correlations between the ranks of items on family resemblance and their ranks on prototypicality were performed sepa- rately for each of the measures of family resemblance and for each of the categories. These correlations, for the basic measure of family resem-

Family resemblance

Most attributes are unique to just one category item, andvery few apply across all items (max of 20)

Family resemblance

582 ROSCH AND MERVIS

TABLE 2 NUMBER OF ATTRIBUTES IN COMMON TO FIVE MOST AND FIVE LEAST

PROTOTYPICAL MEMBERS OF SIX CATEGORIES

Category Most typical members Least typical members

Furniture 13 2 Vehicle 36 2 Fruit 16 0 Weapon 9 0 Vegetable 3 0 Clothing 21 0

blance, were: furniture, 0.88; vehicle, 0.92; weapon, 0.94; fruit, 0.85; vegetable, 0.84; clothing, 0.91. These correlations for the logarithmic measure of family resemblance were: furniture, 0.84; vehicle, 0.90; weapon, 0.93; fruit, 0.88; vegetable, 0.86; clothing, 0.88. All were signifi- cant (p < .OOl).

Such results strongly confirm our hypothesis that the more an item has attributes in common with other members of the category, the more it will be considered a good and representative member of the category. Furthermore, the similarity in results obtained with the basic and the logarithmic measures of family resemblance argues that this relationship is not dependent upon the properties of the particular scale used in mea- surement. Specifically, items in a category tended to be credited with approximately equal numbers of attributes, but the less prototypical the item, the fewer other items in the category tended to share each attri- bute. Thus, the ranks for the basic and logarithmic measures of family resemblance were almost identical, and the correlations between family resemblance and prototypicality were scarcely affected by the change in measure. The relationship between degree of family resemblance and prototypicality for these categories, thus, appears to be a robust one.

A corollary of this finding may account for one of the persistent illu- sions concerning superordinate categories. Subjects, upon receiving feedback from the experiment, and audiences, upon being told of it, gen- erally argue that they feel positive that there are many attributes com- mon to all members of the category even when they cannot think of any specific attributes for which there are not counterexamples. If the more prototypical members of a category are those which have most at- tributes common to other members of the category it is probable that they are most likely to have attributes in common with each other. To investigate this possibility, the number of attributes common to the five most and five least prototypical items in each category were compared. The number of attributes are shown in Table 2. It is clear from this count

The most typical category members share more attributes than the least typical members.

Rosch & Mervis category structure - Exp 5TABLE 3

ARTIFICIAL CATEGORY STRUCTURES USED IN EXPERIMENTS 5 AND 6

Type of category structure

Control set Symmetric experimental set

Asymmetric experimental

set

Use of the Item in category category

Letter string

Family resemblance

score Overlap

score Letter string

Family resemblance

score Overlap

score

Basic category 1 structure 2

3 4 5 6

HPNWD 12 0 HPNSJ 12 2 GKNTJ 12 4 4KCTG 12 5 4KC6D 12 3 HPC6B 12 1

JXPHM 15 0 XPHMQ 19 1 PHMQB 21 2 HMQBL 21 3 MQBLF 19 4 QBLFS 15 5

Letter string

DLT83 DLTIA DLTPM DLGKI D9H60 3YH7V

Family resemblance

score

16 15 14 z

12 E 10 tz 7 8

Nonoverlap 1 R7QUM 12 CTRVG 15 SXB25 16 F

contrast 2 R7QXV 12 TRVGZ 19 SXBZQ 15 category 3 Z5Q2V 12 RVGZK 21 SXBRE 14 ij (Experiment 5) 4 L5F27 12 VGZKD 21 SXVFW 12 v) 5 LSFlM 12 GZKDW 19 S4Zl& 10 6 R7F19 12 ZKDWN I5 SJZCN 7

Overlapped 1 8SJKT 40 GVRTC 0 contrast 2 8SJ3G 3 VRTCS 1 category” 3 9UJCG 3 RTCSF 2 (Experiment 6) 4 4uzc9 2 TCSFL 3

5 4UZRT 3 CSFLB 4 6 MSZRS 3 SFLBQ 5

’ Overlap is with the basic category structure not the nonoverlap contrast category. s b Contrast strings in control do not have same structure as initial category strings and were not analyzed in Experiment 6.

w

Artificial category learning results (Exp 5)- non-overal contrast

FAMILY RESEMBLANCES 595

Results and Discussion There were three dependent variables of interest; rate of learning,

reaction time, and rankings of prototypicality. Rate of learning was mea- sured by the total number of errors subjects made in classifying an item; reaction time was the time a subject took to respond to an item in his last run; and rankings of prototypicality were the subjects’ rankings of the prototypicality of the items.

The two structural types of experimental stimuli were each divided into three parts: the two stimuli with greatest family resemblance, the two with middle degree of family resemblance, and the two with least family resemblance. (For the symmetric group, the two items within each of the three parts possessed equal degree of family resemblance.) For the control set, no such division was possible, and the six items of the set were analyzed separately. Table 4 shows the means for all three experimental variables for the three types of category structures.

A one-way analysis of variance (ANOVA) for correlated scores was performed on the high, medium, and low family resemblance items for the two experimental sets and on all six of the items for the control set. For the control group, results were not significant for any of the three variables. For both experimental groups, however, the results were sig- nificant for all three variables: Symmetric categories-rate of learning, F(2,9) = 7.09, p < .05; reaction time, F(2,9) = 6.41, p < .05; proto- typicality rating, F(2,9) = 11.35, p < .Ol; Asymmetric categories-rate of learning, F(2,9) = 9.48, p < .Ol; reaction time, F(2,9) = 7.91, p < .05; prototypicality rating, F(2,9) = 14.66, p < .Ol. Thus, the pre- dicted results were obtained. In artificial family resemblance sets, when no single attribute is common to all members of the set, even when con- trast sets have no elements in common with each other, items that have greater degree of family resemblance with the members of their own set

TABLE 4 EFFECT OF DEGREE OF FAMILY RESEMBLANCE ON RESPONSE MEASURES

Response measures

Stimulus type Number of errors Reaction time

(msec) Prototypicality

rating

Symmetric experimental

Asymmetric experimental

Control

Hi” Med Lo Hi Med Lo Hi Med Lo 2.8 4.4 5.5 560 617 692 5.0 3.4 2.1

2.4 6.8 9.5 532 619 765 5.5 3.5 1.6

6.5 6.4 6.7 670 6.51 644 3.7 3.4 3.4

a Hi, Med, and Lo refer to family resemblance scores.

High family resemblance items have fewer errors, faster RT, and higher typicality ratings.

TABLE 3 ARTIFICIAL CATEGORY STRUCTURES USED IN EXPERIMENTS 5 AND 6

Type of category structure

Control set Symmetric experimental set

Asymmetric experimental

set

Use of the Item in category category

Letter string

Family resemblance

score Overlap

score Letter string

Family resemblance

score Overlap

score

Basic category 1 structure 2

3 4 5 6

HPNWD 12 0 HPNSJ 12 2 GKNTJ 12 4 4KCTG 12 5 4KC6D 12 3 HPC6B 12 1

JXPHM 15 0 XPHMQ 19 1 PHMQB 21 2 HMQBL 21 3 MQBLF 19 4 QBLFS 15 5

Letter string

DLT83 DLTIA DLTPM DLGKI D9H60 3YH7V

Family resemblance

score

16 15 14 z

12 E 10 tz 7 8

Nonoverlap 1 R7QUM 12 CTRVG 15 SXB25 16 F

contrast 2 R7QXV 12 TRVGZ 19 SXBZQ 15 category 3 Z5Q2V 12 RVGZK 21 SXBRE 14 ij (Experiment 5) 4 L5F27 12 VGZKD 21 SXVFW 12 v) 5 LSFlM 12 GZKDW 19 S4Zl& 10 6 R7F19 12 ZKDWN I5 SJZCN 7

Overlapped 1 8SJKT 40 GVRTC 0 contrast 2 8SJ3G 3 VRTCS 1 category” 3 9UJCG 3 RTCSF 2 (Experiment 6) 4 4uzc9 2 TCSFL 3

5 4UZRT 3 CSFLB 4 6 MSZRS 3 SFLBQ 5

’ Overlap is with the basic category structure not the nonoverlap contrast category. s b Contrast strings in control do not have same structure as initial category strings and were not analyzed in Experiment 6.

w

Rosch & Mervis category structure - Exp 6

Artificial category learning results (Exp 6)- overlap contrast category

FAMILY RESEMBLANCES 597

ment 5 were constructed in an ad hoc manner in order to provide overlap scores O-5 for the strings of the initial category. These contrast category strings did not possess the same structure or same overlap scores as the initial category strings. Contrast categories for the symmet- rical groups were constructed with the same symmetric structure and same degree of overlap as the initial categories. The overlap scores for each string in the initial category and the overlap contrast category are shown in Table 3. (To understand better the derivation of the overlap score, the reader might wish to count the number of letters in a string which occur in at least one string of the contrast category and sum the number of such letters.)

Procedures were identical to those of Experiment 5.

Results and Discussion The control and experimental sets of Experiment 5 had different struc-

tures. For the control set, the items had shown no difference in learning, reaction time, or prototypicality ratings when learned in conjunction with nonoverlapping contrast sets. By the method of measuring amount of overlap described under Method above, the contrast sets in the present experiment changed this set into one in which items ranged from zero attributes of overlap to all five attributes overlapped (only the initial category and not the contrast category itself was analyzed for this set-see Table 3).

Table 5 shows learning, reaction time, and prototypicality scores for the greatest, middle range, and least overlapped items. A one-way ANOVA for correlated scores was performed for these measures for the three dependent variables. All three were significant: rate of learning, F(2,9) = 8.36, p < .Ol; reaction time, F(2,9) = 10.75, p < .Ol; proto- typicality,F(2,9) = 11.19,p < .Ol.

For the symmetric experimental set, overlap is in conflict with the family resemblance structure internal to the category. There are two hypotheses which we wished to test with the analysis: The first was that, with internal family resemblance held constant by the analysis, extent of overlap with the contrast category would show a significant effect on

TABLE 5 EFFECT OF DEGREE OF OVERLAP ON RESPONSE MEASURES FOR CONTROL SET

Response measure

Number of errors Reaction time (msec) Prototypicality rating

Low 7.1 909 5.3

Degree of overlap

Medium 9.4 986 3.4

High 12.6 1125

1.8

Low overlap items have fewer errors, faster RT, and higher typicality ratings.

Prototypicality can be induced purely by overlap with contrast categories

Typicality is based on both• An item’s similarity to other category members

(increasing)• An item’s similarity to members of other categories

(decreasing)

For some reason, many later accounts ignore #2, in spite of correlational and experimental evidence for it in this paper

Overall conclusion, Rosch & Mervis

Basic assumptions of Prototype Theory

• A conceptual representation is a summary representation of the category

• It represents the typical properties or central tendency of the category

• Items that differ in their closeness to the representation vary in typicality

Is a prototype enough?

dog prototype my dog

Consider the feature, “Needs to be brushed occasionally, not every day”

This feature would be true for most dogs, but certainly not my dog.

I may have a separate exemplar-based representation for my dog

Is a prototype enough?“apple”

summary representation, where typicality is the sum weights of the present features:- “round” (weight 1.0)- “edible” (weight 0.8)- “sweet” (weight 0.7)- ….- “green” (weight 0.5)?- “red” (weight 0.5)?

Would an apple be best if it is both green and red at the same time? what if features are contradictory?

what would the prototype look like?

What is an alternative? Exemplars

• No summary representation

• Concepts are represented by remembered category members: “exemplars”

exemplars are labeled by their category membership

• Categorization is done by retrieving similar exemplars, and noting their category membership (simplifying greatly)

• Can account for good performance on unseen prototypes, since they are similar to many exemplars

Exemplar vs. prototype theories

Bird? Birds You’ve Seen Prototypical

Bird

prototype theoryexemplar theory

What is a chair? a set like this…

D1(shape)

D2(size)

D3(color)

D4(position)

1 1 1 1

1 1 1 0

0 0 0 1

Category A

Medin & Schaffer (1978) Example(what do these feature table mean?)

(abstract table) (what people actually see)

D1 D2 D3 D4

1 1 1 1

1 1 1 0

0 0 0 1

D1 D2 D3 D4

0 0 0 0

0 0 1 1

1 1 0 0

0 1 0 1

Category A Category B

Transfer item

Medin & Schaffer Example

0 1 0 1

Category A Category B

Transfer item

Similarity between two items x and y

D1 D2 D3 D4

1 1 1 1

1 1 1 0

0 0 0 1

0.09

D1 D2 D3 D4

0 0 0 0

0 0 1 1

1 1 0 0

x

y

sim(y, x) = ∏Di

m1[xi≠yi] = m ⋅ 1 ⋅ m ⋅ 1 = 0.09

“mismatch” free parameter such that m = 0.3

sim(y, x)

Medin and Schaffer’s Context Model

0 1 0 1

Category A Category B

Transfer item

D1 D2 D3 D4

1 1 1 1

1 1 1 0

0 0 0 1

0.09

0.027

0.3

D1 D2 D3 D4

0 0 0 0

0 0 1 1

1 1 0 0

0.09

0.09

0.09

sim(y, x) sim(y, x)

y

sim(y, C) = ∑x∈ C

sim(y, x)

sim(y, A) = 0.417 sim(y, B) = 0.27

Similarity between item y and category C

for one of the classes C

0 1 0 1

Category A Category B

Transfer item

D1 D2 D3 D4

1 1 1 1

1 1 1 0

0 0 0 1

0.09

0.027

0.3

D1 D2 D3 D4

0 0 0 0

0 0 1 1

1 1 0 0

0.09

0.09

0.09

sim(y, x) sim(y, x)

y

P(y ∈ A) = sim(y, A)sim(y, A) + sim(y, B) = 0.417

0.417 + 0.27 = 0.61

Probability of response

sim(y, A) = 0.417 sim(y, B) = 0.27

P(y ∈ B) = sim(y, B)sim(y, A) + sim(y, B) = 0.27

0.417 + 0.27 = 0.39

Context model of classification

sim(y, x) = ∏Di

m1[xi≠yi] “mismatch” free parameter m

Item similarity

Category similarity

Bird? Birds You’ve Seen

ysim(y, C) = ∑x∈ C

sim(y, x)

x ∈ C

P(y ∈ C) = sim(y, C)∑C′ �sim(y, C′�)

Probability of classification

“classification is based on similarity to all exemplars in a class”(Medin & Schaffer, 1978)

Close similarity is critical

Compare two items (m = .3)• Item Y overlaps with 2 features for each of 3 items• Item Z perfectly matches 1 item, but for 2 items not at all• Similarity of Y to category = .09 + .09 + .09 = .27• Similarity of Z to category = 1 + 0 + 0 = 1

• Z is much more similar to the category, even though it has only 4 matching features compared to 6 for Y

critically, Y would likely be favored in prototype models• Configural similarity is important

The mismatch parameter m

A bit of a “catch all” for various factors:• The intrinsic mismatch between the stimulus feature and

the exemplar’s feature;red vs. green could have lower m than red vs. maroon

• Attention to the dimension (due to learning)• (M&S also suggest forgetting; if you don’t remember the

feature, mismatch will have little effect)

Another worry is that the context model is only defined for discrete features

• Other models have separated some of these into different variables, and work for continuous features (Nosofsky’s Generalized Context Model, and ALCOVE)

Medin & Schaffer Experiment 2famous “5-4” category structure

Key comparison is stimulus 4 vs stimulus 7• Prototype model would predict stimulus 4 is easier to learn

It’s more similar to the prototype• Exemplar model would predict stimulus 7 is easier to learn

Has two near neighbors, 15 and 4• Results favor exemplar model: stimulus 7 had fewer error

(FE) and higher confidence rating

222 DOUGLAS L. MEDIN AND MARGUERITE M. SCHAFFER

"A" STIMULI

STIMULUSNUMBER DIMENSION VALUES

C F S N

47

1513

5

1 1 11 0 11 0 11 1 0O i l

STIMULUSNUMBER

13689

1116

00111

43344

TRAINING STIMULI"R" STTMIII i

Et,9,3,2,8.5

NEW

STIMULUSRAT_ NUMBER DIMENSION VALUESING C F S N FE

4 , 8 1 2 1 1 0 0 5 , 55 . 4 2 0 1 1 0 5 , 25 , 1 1 4 0 0 0 1 3 , 95 , 2 1 0 0 0 0 0 3 , 15,2

TRANSFER STIMULI

RAT-

5,05,15,25.5

DIMENSION VALUES RATINGC F S N A-PREDICTED E-PREDICTED

1110000

0010101

0011010

1 3.70 4,41 5,30 4,11 3,31 4.10 4,9

Figure 4. Design of Experiment 2. (C, P, S, and N refer to the dimensions of color, form, size, andnumber, respectively. The stimulus numbers are carried over from Experiment 1. Fe refers to averageerrors during learning. Rating scores may vary from 1 to 6, with 3.5 representing chance [nohdifferential]classification.)

eter values that would alter this predictionwould place numerous other testable con-straints on the data.

Method

Subjects. Thirty-two volunteers were solicitedthrough ads in local newspapers. The subjects, men andwomen ranging in ages from 17 to 30 years, were paid$2.50 for the experimental session. The subjects had notparticipated in the first experiment.

Stimuli, Sixteen stimulus cards with geometricforms drawn on them were used. Nine cards were usedin training and seven additional cards were used intransfer. The geometric forms were like those from thepreceding experiment, except that the dimension ofnumber was substituted for the dimension of position.The number dimension was represented by either asingle geometric form centered on the card or by twogeometric forms each centered on their respectivehalves of the card.

The assignment of abstract notation to individualstimulus cards varied from subject to subject exactlyas in the first experiment. That is, the assignment of

stimulus cards to conditions and category labels wasexactly counterbalanced.

Procedure. The procedure followed that used inthe first part of Experiment 1: initial training, followedby a S-10-minute interpolated activity, followed by atransfer task involving both training and new transferstimuli.

The instructions for training were those used inExperiment 1. Training consisted of up to 16 runsthrough the list of 9 training stimuli with a learningcriterion of 1 errorless run. Other procedural detailsfollowed those of Experiment 1, including the inter-polated activity and the transfer test instructions andprocedure.

Results

Learning. The learning task was of moder-ate difficulty; 19 of the 32 subjects learned theclassification task within the maximum limitof 16 runs. Overall, subjects averaged 18%errors on the last run through the list, butvirtually all subjects showed some improve-

Prototype: 1 1 1 1 Prototype: 0 0 0 0

What is an exemplar?

• Nosofsky (1998, JEP:LMC) asks what IS an exemplar? Is it an item or is it an experience?

e.g., is your dog an exemplar?or is each experience of encountering your dog?

• He presented items with varying frequency.If each item is an exemplar, then the frequency shouldn’t have any effectIf each experience is an exemplar, then typicality and classification accuracy should be slanted towards more frequent exemplars

What is an exemplar?56 ROBERT M. NOSOFSKY

COCOLU

XorrCQ

SATURATION

Figure 1. Category structure tested in Experiments 1 and 2. (Stimulienclosed by triangles = members of Category I; Stimuli enclosed bycircles = members of Category 2)

to allow for a precise quantification of similarity relations.Furthermore, there appear to be varying degrees of category"goodness" associated with the individual exemplars. Forexample, Colors 2, 4, and 7 clearly are good exemplars ofCategory 2, whereas Colors 3, 6, and 9 are relatively poorexemplars, lying close to the category boundary.

In Experiment 1 presentation frequencies of good Exem-plars 2 and 7 were manipulated. Condition B was a baselinecondition in which all exemplars were presented with equalfrequency, whereas in Condition E2 (E7), Exemplar 2 (7) waspresented approximately five times as often as each of theother exemplars.

If differential frequency information is reflected in people'scategory representations in the manner suggested earlier, thenthe first main prediction is that classification accuracy andtypicality ratings for the manipulated exemplars should in-crease with their presentation frequency. A second mainprediction stemming from the frequency-sensitive exemplarmodel is that classification accuracy and typicality ratingsshould also increase for members of Category 2 that are verysimilar to the high-frequency exemplars. As can be seen inFigure 1, Exemplar 4 is a close neighbor of Exemplar 2, andExemplar 9 is a close neighbor of Exemplar 7. The expectationis that category "goodness" will increase primarily for Exem-plars 2 and 4 in Condition E2 and for Exemplars 7 and 9 inCondition E7.

Method

Subjects150 subjects were hired for participation in the experiment. Most

subjects were undergraduates at Indiana University. 50 subjects par-ticipated in Conditions B, E2, and E7, respectively.

Stimuli

The stimuli were 12 color chips manufactured by the Munsellcolor company. According to the Munsell color system, the colorswere of a constant red hue (5R) but varied in brightness (value) andsaturation (chroma). The Munsell value/chroma specifications forColors 1-12 shown in Figure 1 were 7/4, 7/8, 6/6, 6/10, 5/4, 5/8, 5/12, 4/6, 4/10, 3/4, 3/8, and 3/10.

The colors were mounted behind 5/16-in. (0.79-cm) diametercircles punched in the middle of white index cards. To ensure thatsubjects were attending to the actual colors and not to incidentalmarkings on the cards, four different tokens were used for each color.A total of 19 tokens of Color 2 (7) were used in Condition E2 (E7).

Procedure

Learning phase. On any given trial, a subject viewed a color andguessed its category assignment (Figure 1). The subject entered theresponse on a score sheet and then turned over the card to view thecorrect answer. A code number was also entered on the back of thecard to identify the stimulus for the experimenter. The subject enteredthis code number on the score sheet next to the category responseand then restudied the stimulus-response mapping.

Subjects were tested for three blocks of trials. There were 48 trialsin each block of Condition B and 63 trials in each block of ConditionsE2 and E7. The experimenter shuffled the deck of cards between eachblock.

Transfer phase. Subjects were presented with each of the 12 colorsin a random order. The subject classified the color into either Category1 or 2, rated on a scale from I (lowest) to 10 (highest) how confidenthe or she was about being correct, and then rated on a scale from 1to 10 how typical or how good an example the color was of itscategory. The instructions emphasized that even if a subject washighly confident that a color belonged to a given category, one couldstill judge it as a poor example of the category. It was hoped that thedistinction between classification confidence and judged typicalitywould be reinforced by collecting both types of ratings. Subjects werethen presented with all pairs of colors from Category 2 and wereinstructed to choose the better example of Category 2 in each pair.Presentation order of the pairs and left-right placement of the colorswithin each pair were randomized.

ResultsClassification Learning

Table 1 shows the mean proportion of classification learn-ing errors for each color in each condition. The distributionsof errors were similar across conditions, with colors closest tothe category boundary (1, 3, 6, 8, 9, and 12) having the mosterrors, and colors far from the boundary (2, 4, and 10) theleast. Color 2 had a smaller proportion of errors in ConditionE2 than in the other conditions, average /(98) = 4.10, p <.001, whereas Color 7 had a smaller proportion of errors inCondition E7, average f(98) = 4.08, p < .001. The trends forColors 4 and 9 were in the predicted directions but were smallin magnitude and not statistically significant.

Typicality Ratings

The results for confidence and typicality ratings were essen-tially identical and so I report only the typicality data. The

Either item 2, or item 7 (depending on condition), was manipulated to appear 5x more often

What is an exemplar? It seems to be an experience

• Nosofsky found each experience was in fact “an exemplar.” That is, the frequency that individual exemplars occurred strongly influenced typicality

• Classification accuracy and typicality ratings increased for high-frequency exemplars, and also increased category memory that were similar to high-frequency exemplars

Issues with exemplar experiments

Artificial category structures tested are unrealistic• e.g., example from Medin & Schaffer

People are smart — if you give them categories that aren’t captured well by prototypes, they may do something else…

D1 D2 D3 D4

1 1 1 1

1 1 1 0

0 0 0 1

D1 D2 D3 D4

0 0 0 0

0 0 1 1

1 1 0 0

Category A Category B

How much is learned? Medin & Schaffer’s experiments

• 6 items, 20 blocks of learning16% didn’t learn categories

• 9 items (famous “5-4” structure) 16 blocks44% didn’t learn!!

• Same as Exp. 2, but with facesno one learns a damn thing

• 11 items, 16 blocks50% didn’t learn

• Exercise: Can you think of any real-world, pair of categories that you need more than 1 feature to discriminate?

Acknowledgements

Thanks Greg Murphy for the first version of many of these slides