Similarity & Analogy Flashcards
Similarity: Spatial Model
We represent things in mental space - distance as f/n of similarity
- RT confirms these distances
Spatial Model: Latent-semantic analysis (Landauer & Dumais, 1997)
Columns = Encyclopedia with words, Rows = Every word in encyclopedia
More similar = more times two words appear in the same entry over the times they don’t appear together in the same entry.
Similarity: Feature Model
Spatial model can’t be right (violated) - similarity distances are asymmetrical.
e.g. “Canada is like USA” is not the same distance as “USA is like Canada”
- Metric spaces should show Triangle Inequality: distance AC cannot be longer than AB + BC
But similarity can: e.g. Russia and Jamaica are more dissimilar than would be expected when comparing USSR to Cuba, and Cuba to Jamaica
- Similarity and difference should be metrical inverse
Similarity: Structural Model
Similarities perceived between objects as defined by their roles and relations to other objects, not just their individual features
- Features are represented in a structured/coherent manner
- Objects bound by relations to others
Similarity: Structural Model: Alignable differences
E.g. Differences between hotel & motel vs hotel & coconut
When objects have highly alignable differences, similarity ratings are higher than for objects with low alignability
When dimensions of relevance aren’t shared, it is difficult to represent differences
How do similarity judgements highlight relations?
E.g. with picture of squirrel
People who are asked to rate similarity between two pictures first more readily align the pics based on the depicted relational role
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Structured relational representations: Terminology for:
- big(sun)
- bigger(sun, planets)
- CAUSE [bigger(sun, planets), revolves around (planet, sun)]
Predicate = the part of a sentence or clause containing a verb and stating something about the subject (e.g. “went home” in “John went home”).
predicate(one argument) = big(sun)
attribute predicates argument?
predicate(multiple arguments/roles) = bigger(sun, planets)
Higher-order relation = predicate that has lower-order relations as its arguments
What is an analogy?
Analogy = Two conceptual domains share relational similarity, not feature or object-based similarity
e.g. CAUSE [bigger (sun, planets), revolves around (planet, sun)] is equiv to
CAUSE [bigger (nucleus, electron), revolves around (electron, nucleus)]
Structure-mapping theory of analogy (Gentner, 1983; 2010)
Comparisons involve an alignment of relational structures
- especially in their hierarchies
E.g. alignment between Nucleus-electron and Sun-planets in “CAUSE [bigger (sun, planets), revolves around (planet, sun)] is equiv to CAUSE [bigger (nucleus, electron), revolves around (electron, nucleus)]”
Structure-mapping theory of analogy: Constraints: Structural Consistency
- One-to-one mapping of arguments
E.g. “sun” maps onto “nucleus”, not “nucleus” AND “bigger” in CAUSE [bigger (sun, planets), revolves around (planet, sun)] is equiv to CAUSE [bigger (nucleus, electron), revolves around (electron, nucleus)] - Parallel connectivity between arguments of each concept
E.g. In the analogy above, “sun” –> “nucleus” and “planets” –> “electrons”. Not “sun” –> “electrons”
(So it’s directly parallel across both concepts)
Structure-mapping theory of analogy: Constraints: Systematicity
Deeply nested relational structures make better analogies.
E.g. “US Invasion of Iraq is like WW2”
- some overlap in surface features: dictators were both bad guys who killed their own citizens, and targeted specific ethnic subgroups
- No deep systematic commonality: Leaders use different
Structure-mapping theory of analogy: What can deeply nested relational structures in analogies help us learn?
Make inferences
E.g. Solar system/Atom analogy - If planets follow elliptical orbits of sun, we can infer that electrons follow elliptical orbits of the nucleus?
Highlight alignable differences between both concepts (e.g. gravity in solar system = electro-magnetic forces in atom)
Can abstract commonalities - e.g. common theories that underly both systems (e.g. central force system underlies both solar system and atom)
Structure-mapping vs Feature comparison
Similarities and differences
Similarities between Structure-mapping and Feature comparison:
- One-to-one mapping
- Parallel connectivity
- Systematicity
Differences:
Structure-mapping:
- Computationally expensive! Even for simple scene comparisons (unable to do this under WM load)
— Space & Feature processing less costly
Representational pluralism: Inference vs Memory
Not all info need be represented in a structured format - info can be represented differently depending on the task/cog processes engaged.
- Due to computationally expensive nature of structurally formatted info
Hence, depending on the task & cognitive process, different representational formats better explain data patterns.
Representational pluralism: Inference vs Memory
Study by Gentner, Rattermann, & Forbus (1993):
Participants read stories.
Story A: Bird-hunter and eagle who have conflict, but resolve it
Relational match: One nation wants to invade another, but resolve it
Surface match: Story about hawk raising baby birds
Group 1: Given 2 stories, asked to evaluate inferences from story A to story B, based on shared content
Group 2: Given 1 story and asked what Story A reminded them of.
Inference: Relational match
Memory: Surface match
