Categorization Classical View – Defining properties E.g. Triangles have 3 sides and 3 angles...
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Transcript of Categorization Classical View – Defining properties E.g. Triangles have 3 sides and 3 angles...
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
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 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?
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
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?