Categorization Classical View – Defining properties E.g. Triangles have 3 sides and 3 angles adding up to 180 degrees – Unquestioned for most of time.

Categorization

• Classical View–Defining properties• E.g. Triangles have 3 sides and 3 angles adding

up to 180 degrees

–Unquestioned for most of time

Challenge to Classical View: Wittgenstein (1953)

– Some categories don’t have necessary and sufficient properties (e.g. a game)

– Family Resemblances• Members of a category may be related to each other

but have no common property (a cloud of point in space)

– Centrality: some members are better than others– Gradience - some categories have degrees of

membership

Challenge: Typicality

• If classical view is right, then all members should be equally “good”, but they’re not

Rosch’s Typicality Effects– Typicality varies (e.g. sparrow vs. ostrich)– Typicality associated with how often a member’s

properties occur in category– Typical members categorized faster– Generated first and more often– Learned first by kids– Similarity asymmetries– Generalization asymmetries

Prototype Theory

• Most typical member is basis of the category

• Prototype is explicitly stored• Category membership determined from

similarity to prototype• Not classical - no defining properties

Demonstration of Prototype Effect

• Franks and Binford

Prototype

DistortionsLow High

Experiment

• Phase 1: View instances (no prototype)• Phase II: View new instances and rate

old/new confidence–Old Distortions–New Distortions–Prototypes

Results of Prototype Experiment

• Subjects were more confident of having seen prototypes

• More distorted from prototype = less confidence (regardless of actually having seen or not)

Problems with Prototypes• Too limited– Contains only central tendency of category– Lose info about• Variance (how much tolerance for distortion is ok)• Correlations among properties (e.g. only small birds

sing)• Category size

– An instance may be closer to prototype of one category but still belong in another

Exemplar-based Theories

• Store individual instances rather than prototypes

• How do you classify a new stimulus?–Compare to all instances of all categories–Assign it to category belonging to best-

matching instance

Problems with Similarity as Category Basis

• Drawback of prototype and exemplar-based categories

• Both of these use “similarity” which is hard to define

• Similarity is “features”? Which ones?

Similarity Depends on Context

• Tversky Faces Demonstration: Split Class Demo

Similarity Depends on Context

• Tversky Faces Demonstration: Split Class Demo

Similarity is Especially Bad at Certain Categories

• Superordinate – How is car similar to boat?– How is amoeba similar to elephant?

• Ad-hoc – What is this category?• Children, money photographs, jewelry, pets ?

– On-the-fly categories - what would you take on a camping trip?

Theory-based Categories• Animal started out with bird-like features• Due to accident, had insect features• Animal mated and produced bird-like

offspring• Animal judged as “bird”, even with insect

features• Judgment based upon some internal

“birdness” not related to appearance

Hierarchical (Taxonomic Categories)

• Thing - Living Thing - Animal - Mammal - Dog - Schnauzer - “Smokey”

Basic Level (Rosch)

• Most natural• Middle level (not too specific, not to general)• Let’s be more specific– Maximizes within-category perceptual similarity– Minimizes between category perceptual similarity

Hierarchical Categories Examples

• Superordinate – Vehicles, furniture

• Basic– Cars, boats

• Subordinate– Accord, Camry

• Instance– Sean’s Camry, Sue’s Camry

Similarity and Hierarchical Categories

Within Category Between Category

Similarity Similarity

Super- Low Low

Ordinate (Car vs. Boat) (Vehicle vs. furniture)

Basic High Low

(Accord vs. Camry) (Car vs. Boat)

Sub- High High

Ordinate (Sean's Camry vs. (Accord vs. Camry)

Sue's Camry)

Basic-Level Effects

• Generated fastest and first• Learned first by kids• Shorter words (“dog” vs. “Schnauzer”)• Relatively universal across cultures• Biederman’s RBC theory is mostly basic

level recognition

Semantic Memory: Concepts

Geometric Approach: Concepts and items are representedas points in a high-dimensional space. Similarity between itemsis the inverse of distance between the points. Categorization isthe task of finding which concept point is closest to the point thatrepresents the item in question (i.e. “is it a cat?” is a question ofwhether the point representing “it” is close to the “cat” point than any other point in the space).

• cat• dog• horse

• pig

• duck

closer together =

more similar

Semantic Memory: Concepts

Geometric Axioms:

• Minimality: Similarity between an object and itself is always maximum ( d[A,A] = 0 )

• Symmetry: Similarity between A and B is the same as between B and A ( d[A,B] = d[B,A] )

• Triangle Inequality: If A is similar to B and B is similar to C, then A can’t be too dissimilar to C. ( d[A,C] d[A,B + d[B,C] )

S(apple,apple) > S(pomogranite, pomogranite)

Familiar things are moresimilar to themselves thanunfamiliar things.

Unfamiliar things are moresimilar to familiar things than vice-versa.

S(pomogranite,apple) > S(apple, pomogranite)Things can be similarto for different reasons.

(Jamaica, Cuba, North Korea example)

DON’T WORK FOR PEOPLE!!!...

Semantic Memory: Concepts

Featural Approach: Concepts and items are representedas lists of features. Similarity between items is given by:

S(A,B) = a features(A&B) - b features(AnotB) - c features(BnotA)

So similarity increases as two items have more in common,and decreases as each has it’s own non-shared features.

Notice there can be biases: coefficients a, b, and c can beweighted differently, so that features in each category canhave different effects.

So, this model can account for the violations of the metric axioms...

Semantic Memory: ConceptsFeature apple orange banana pomograniteedible + + + +has a skin + + + +round + + +red + +edible skin +edible seeds + +good for pies +good for juice + +

Suppose the equation is: S(A,B) = 1*(A&B) - 1*(A~B) - 0.5*(B~A)S(apple,apple) = 7-0-0 = 7S(pomagranite,pomagranite) = 5-0-0 = 5

S(apple,pomogranite) = 4-3-0.5*1 = 0.5S(pomograntite,apple) = 4-1-0.5*3 = 1.5

violation of minimality

violation of symmetry

Semantic Memory: Concepts

How can we implement the featural model in a network?• Units represent concepts and features, with links for connecting concepts that are related, and features that describe them.• Assume spreading activation: when one unit is activated, it automatically spreads to all of the connected units over time• Assume the fan effect: the more units activation has to spread across, the weaker it becomes.

When we compare two things, both units are activated, and activation spreads outward from them. Their similarity isinversely proportional to how long it takes for a certain amountof activation from the two sources to overlap.

Semantic Memory: Concepts

How can we implement the featural model in a network?• Units represent concepts and features, with links for connecting concepts that are related, and features that describe them.• Assume spreading activation, and the fan effect.

apple pomogranite

ediblehas a skinroundrededible skinedible seedsgood for piesgood for juices

Units not shared decrease overlapping

activation, by spreading it thinner

(fan effect)

The more units are shared,

the more activation will overlap

Semantic Memory: Concepts

This model can also account for categorization andtypicality effects:• Categorization: It takes longer to verify “A dog is an animal” than “A dog is a mammal”, because it has farther to travel.

• Weights between units can indicate how typical an instance is of a superordinate category, changing how strongly activation from one is spread to the other.

animal

birdmammal

dog cat

animal

birdmammal

robinpenguin

Semantic Memory: Concepts

What do feature lists leave out?• Causal relations (e.g. the fact that fertilizer tends to grow plants)• Relational dependencies (e.g. the fact that only small birds sing)• In short: Feature lists leave out structured information.

We recall from our discussion of Episodic Memory, this problemca be solved with the use of schemata: complex structured frameworks.

Thus, schemata can be used to semantic memory, too, to tell uswhat kinds of items are typically found in offices, what kinds ofevents typically happen in a restaurant, and so on.

Modeling Schemata?Challenge for the future: How to represent structuredrelational information in a network?• Relational information (e.g. “Chris loves Pat”) has a problemin networks with distributed representation, similar to thebinding problem: the catastrophic superposition problem.

Suppose this pattern:and this pattern:and this pattern:and this pattern:and this pattern:

Then this pattern:and this pattern:and this pattern:

represents “Chris”represents “Pat”represents “Harry”represents “Sally”represents “loves”

represents “Chris loves Pat”represents “Pat loves Chris”represents “Harry loves Sally”

There is no way to tell the difference!

Modeling Schemata?

One Answer: Temporal synchrony•

Suppose this pattern:

and this pattern:

and this pattern:

represents “Chris”

represents “Sally”

represents “loves”

But how do we distinguish between “Chris loves Sally” and “Sally loves Chris”?•

Modeling Schemata?Need to combine structural and semantic information

LISA (Learning and Inference with Schemas and Analogies) – Hummel & Holyoak

Binds semantic information (e.g. “Chris”) to roles (e.g., “loves” Agent)

Can then make inferences like we do

Chris loves Mary. Chris gives flowers to MaryBill likes Sally. Bill gives candy to ??? Sally

•

1 – retrieve info from memory

Remembered info is a subtle visual property

Property not explicitly considered

Property not easily deduced from other stored info

e.g., what is the shape of Snoopy’s ears?2 – anticipating navigation (what if I move my arm this way?)

Mental imageryWhat’s it good for?

Image generation

Image maintenance

Image Transformation

Mental imageryWhat are it’s parts?

Retain perceptual input

Generate from memory

Images with more parts take longer to generateIdentity of image separate from location

(Imagine Bush on a rocket ship heading into space)Global image versus parts image

Parts need left hemipshere Left hemisphere better at categorical (above, below)Right hemisphere better at metric (precise distance)

Mental imageryImage Generation

Can generate images by selectively attending to bathroom tiles

Visual memory parts of brains not active during this task

Mental imageryImage Generation

Holding visual image impairs visual detection but not auditory

Smaller images harder inspect

Hemispatial neglect affects imagery as well as perception

Evidence generally supports idea that imagery may use perceptual mechanisms – BUT

d.f. can do imagery fine although perceptual system is mangled

Mental imageryImage Inspection

Can only hold small number of “Chunks” in visual memory

Fades fast without active attention

Mental imageryImage Maintenance

Shepard and MetzlerShowed rotation of cuboid objects strongly related to

Time to accomplish

Argue that process mimics real worldBut introspection seems against this (don’t rotate whole object)

Appears to be right hemisphere function

Mental imageryImage Transformation

Propositional vs. Depictive

Each has syntax and semantics

Mental imagesWhat are they?

SyntaxON(BALL,BOX)Need relation to connect (BALL,BOX) has no meaning

SemanticsMeaning of individual symbols is arbitraryRepresentation is unambiguousAbstract

Can refer to non-picturable entititesCan refer to classes of objectsNot tied to specific modaility

Is this fair?

Mental imagesPropositional?

SyntaxPoints and empty space (pixel-like)Points arranged to make continuous pictures

(i.e. comic strip dots)Points placed in spatial relation to each other

SemanticsMeaning of individual symbols is actual objectDistance is maintained

Mental imagesDepictive?

SCANNING results favors depictive?

Experiments showing things further away from center of object took longer to “See”

YES – BUT..

What if propositions are linked spatially (see page 285)This would produce same result..

Mental imagesDepictive or propositional?

SCANNING: The SEQUEL results favors depictive?

Experiments of island map showing distances between map items took longer to process. In a network, same distance between nodes would predict no effect.

YES – BUT..

What if dummy nodes are inserted for space between? (Starting to look more and more depictive to me)

Mental imagesDepictive or propositional?

SCANNING: The TRIQUEL results favors depictive?

Experiments of island map showing verification of other objects does not depend on time (which is predicted byPropositional)

YES – BUT..

What if verification of other objects uses anothermechanism

Mental imagesDepictive or propositional?

The effect of demand characteristicsExperiment showed effect of experimenter expectancy

on results. Subjects told image distance would affect scanning time

showed an effect of distance on scan timesSubjects told image distance would NOT affect scanning

time showed NO effect of distance on scan times

Follow up study by another experimenter showed when subjects expected a “U” curve (and others), scanning time was always related to distance

Mental imagesDepictive or propositional?

Cognitive Neuroscience

Connections go from topographic areas e.g. VI) to non-topographic areas (e.g. object recognition) which do notcare about location

Presumably – image is generated in particular location through backward connections to topographic areas

Mental imagesDepictive or propositional?

FMRI to the rescue?

Larger images activated larger topographic areas of visual areas in cortex (e.g. fovea projects to posterior of visual areas

while parafovea projects to anterior portions)

YES BUTIs this epiphemonal (concurrent but not causal)?

Perhaps not because damage to these areas inhibits imagery

Mental imagesDepictive or propositional?

Final YES BUT

Back to d.f. – why can she do imagery fine if her early visual areas are so damaged?

IF YOU HAVE THE ANSWER TO THIS – LET ME KNOW AND WE WILL BOTH BECOME FAMOUS

Mental imagesDepictive or propositional?