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Concepts & Categorization

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Concepts & Categorization

- Many prototype and exemplar models assume that similarity is inversely related to distance in some representational space

B

C

A

distance A,B small psychologically similar

distance B,C large psychologically dissimilar

- Represent observed similarities by a multidimensional space – close neighbors should have high similarity
- Multidimensional Scaling (MDS): iterative procedure to place points in a (low) dimensional space to model observed similarities

- Suppose we have N stimuli
- Measure the (dis)similarity between every pair of stimuli (N x (N-1) / 2 pairs).
- Represent each stimulus as a point in a multidimensional space.
- Similarity is measured by geometric distance, e.g., Minkowski distance metric:

- Tversky argued that similarity is more flexible than can be predicted by distance in some psychological space
- Distances should obey metric axioms
- Metric axioms are sometimes violated in the case of conceptual stimuli

- Psychological distance should obey three axioms
- Minimality
- Symmetry
- Triangle inequality

“North-Korea” is more similar to “China” than vice versa

“Pomegranate” is more similar to “Apple” than vice versa

Violates symmetry

- Spatial representations predict that if A and B are similar, and B and C are similar, then A and C have to be somewhat similar as well (triangle inequality)
- However, you can find examples where A is similar to B, B is similar to C, but A is not similar to C at all violation of the triangle inequality
- Example:
- RIVER is similar to BANK
- MONEY is similar to BANK
- RIVER is not similar to MONEY

- Model addresses problems of geometric models of similarity
- Represent stimuli with sets of discrete features
- Similarity is a flexible function of the number of common and distinctive features

# shared features

# features unique to X

#features unique to Y

Similarity(X,Y) = a( shared) – b(X but not Y) – c(Y but not X)

a,b, and c are weighting parameters

Similarity(X,Y) = a( shared) – b(X but not Y) – c(Y but not X)

`LemonOrange

yelloworange

ovalround

soursweet

treestrees

citruscitrus

-ade-ade

\

Similarity(X,Y) = a( shared) – b(X but not Y) – c(Y but not X)

`LemonOrange

yelloworange

ovalround

soursweet

treestrees

citruscitrus

-ade-ade

Similarity( “Lemon”,”Orange” ) = a(3) - b(3) - c(3)

If a=10, b=6, and c=2 Similarity = 10*3-6*3-2*3=6

Suppose weighting parameter b > c

Then, pomegranate is more similar to apple than vice versa because pomegranate has fewer distinctive features

If weighting parameters are: a > b > c (common feature weighted more)

Then, model can predict that while Lemon is similar to Orange and Orange is similar to Apricot, the similarity between Lemon and Apricot is still low

- In similarity data, “Fruit” is nearest neighbor in 18 out of 20 items
- In 2D solution, “Fruit” can be nearest neighbor of at most 5 items
- High-dimensional solutions might solve this but these are less appealing

- Typicality Demo
- will see X --- Y.
- need to judge if X is a member of Y.
- finger --- body part
- pansy --- animal

pants – furniture

turtle – precious stone

robin – bird

dog – mammal

turquoise --- precious stone

ostrich -- bird

poem – reading materials

rose – mammal

whale – mammal

diamond – precious stone

book – reading material

opal – precious stone

- typical
- robin-bird, dog-mammal, book-reading, diamond-precious stone

- atypical
- ostrich-bird, whale-mammal, poem-reading, turquoise-precious stone

Is this a “cat”?

Is this a “dog”?

- Similarity-based models: A new exemplar is classified based on its similarity to a stored category representation
- Types of representation
- prototype
- exemplar

- Central Tendency

P

Learning involves abstracting a set of prototypes

- Typical items are similar to a prototype
- Typicality effects are naturally predicted

atypical

P

typical

- If there is a prototype representation
- Prototype should be easy to classify
- Even if the prototype is never seen during learning
- Posner & Keele

- All information about individual exemplars is lost
- category size
- variability of the exemplars
- correlations among attributes

- category representation consists of storage of a number of category members
- New exemplars are compared to known exemplars – most similar item will influence classification the most

dog

??

cat

dog

dog

cat

dog

cat

- It is hard to distinguish between exemplar models and prototype models
- Both can predict many of the same patterns of data
- Graded typicality
- How many exemplars is new item similar to?

- Prototype classification effects
- Prototype is similar to most category members

- Sometimes similarity does not help to classify.
- Daredevil

- 20 Questions:http://20q.net/
- Google Sets:http://labs.google.com/sets