Lecture #10 (Feb 26)

Central Role of Similarity + its Complexity

Plays a central role in prototype + exemplar theories; Very subjective + can mean dif things in dif situations

Ex. Bear vs teddy bear

Ex. Apple vs baseball

Ex. Time vs river

Ugly Duck Theory

We equally share the same features with everyone else if we can def the features

Without subjective bias, any two distinct objects in a, system share the same number of properties, making them equally similar; Implies that classification requires prior bias

Similarity as a Construct

An essential idea in categorization but not objectively definable; Categories as classes of objects that max within class similarity + minimize between class similarity

Both prototype + exemplar models use similarity in evaluating category membership; Induction is also sensitive to similarity

Categories

Classes of objects that maximize within class similarity + minimize between class similarity

Within Class Similarity

How similar the members of the same category are to each other

High within-class similarity =

• Category members share many features

• They “feel like they belong together”

Ex. Within class similarity is high here

Category: Bird

Sparrows, robins, finches

→ All have wings, feathers, beaks, similar body plans

Between Class Similarity

How similar members of different categories are to each other

Low between-class similarity =

• Categories are easy to tell apart

• There’s little overlap in features

Ex. B/w class similarity is low here

Bird vs. Fish

→ feathers vs. scales, wings vs. fins

Is induction sensitive to similarity?

Yes

Ex. More similar ex → Narrower induction

Is similarity objectively definable?

No

Geometric Model of Similarity

Says that similarity is analogous to proximity in some mental space (dissimilarity ←→ distance); Mental rep of the perceptual features takes the form of a mental space analogous to a physical space

Mental Space

An internal, psychological feature space where objects are represented as points based on their properties

Multidimensional Scaling (MDS)

A stat technique for visualizing the geometric model of similarity; Given a set of items + judgements of dissimilarity among the items, the MDS finds positions in an imaginary space such that inter-item distances match judged dissimilarity as closely as possible

Used to reconstruct the corresp distances in mental space

How is similarity measured in MDS?

Subjects asked to rate the similarity of pairs of objects

Questions about the Geometric Model

Does mental dissimilarity actually obey the mathematical laws of distance (metric axioms/distance axioms):

• Symmetry

• Triangle Inequality

Metric Axioms/Distance Axioms Def

Mathematical laws of distance; Questioned if this aligns with mental dissimilarity

Metric Axioms/Distance Axioms Parts

Symmetry and Triangle Inequality

Symmetry

d(a,b) = d(b,a)

d is a distance measurement

d(a,b) is the distance between a and b

d (b,a) is the distance between b and a

Metric Axioms/Distance Axioms Parts

Triangle Inequality

d(a,b) + d(b,c) greater/equal to d(a,c) → the shortest distance between 2 points is a straight line

Distance between a + b PLUS the distance between b + c is greater/equal to distance between a + c (cannot be shorter)

d is a distance measurement

Metric Axioms/Distance Axioms Parts

Is there more than 1 way to measure distance?

Yes → euclidean distance and city block distance; Both obey distance axioms

Does similarity obey the distance axioms? (symmetry + triangle inequality)

Symmetry → No (failed to replicate)

• An apple is similar to a pomegranate (less pref) vs

• A pomegranate is similar to an apple (more pref)

Triangle Inequality → No

• Jamaica is similar to Cuba (very similar)

• Cuba is similar to North Korea (very similar)

• Is Jamaica similar to North Korea? (very dissimilar)

Not physical possible with a triangle

Features

Discrete attributes of objects

Contrast Model of Similarity

sim(A,B) = w1 f(A∩B) - w2 f(A-B) - w3 f(B-A)

bolded = common features (middle of venn diagram)

A-B = distinctive features of A

B-A = distinctive features of B

Featural similarity can be asymmetric + can violate the triangle inequality - like human similarity judgements

Can featural similarity asymmetric?

Yes, can be asymmetric + can violate the triangle inequality → like human similarity judgements

Holism

Concept cant be understood in isolation

Conceptual Coherence

Why is dog a reasonable category, but women, fire and dangerous and this is not?