Cognitive modelling based on Prototype Theory

1. Ingrid O'Keane Ingrid.OKeane@gmail.com Cognitive modellingbased on Prototype Theory

2. I approached this by figuring out how I would learn the test sets, then taking the test and verifying if the results matched what I would expect Recorded results showed that I grouped items rather than memorising each test set, hence new test sets were categorised according to similiarity to those groups – one aspect of the Gestalt Theory Proximity, similiarity & continuity of items are grouped together, so for Category A, I looked for A entries in particular in the 1st dimension, similiarly for Conjunction AB, I looked for an AB entry Introduction

3. Pattern Matching I did not intend memorising the test sets, instead I looked at each Category and grouped similiar items together: Category A test sets should have at least 1 A, pref in dimension 1 Category B test sets should have at least 1 B, pref in dimension 3 Category C test sets should have at least 1 C, pref in dimension Category AB test sets should have at least 1 AB entry

4. Why prototype? • Chunking of items or pattern matching within the categories led me to use a prototype rather than the exemplar model • Weights for each category & conjunction were calculated according to test item & the dimension it occured in, eg Cat A gave higher weight to an A entry in dim1 than to a B or C entry • Also, as this experiment had a small number of test sets for the particpants to categorise, I felt the prototype would be more appropriate

5. Results for ABY Test Set A theory is a general account of how (someone thinks) a given cognitive process or area works. Theories are usually ‘informal’, stated in natural language (english), and leave details unspecified. A model is a specific instantiation of a theory. Models are formally stated, in equations, computer code, or similar. Models must specify enough details to work independently. Models make quantitative predictions (e.g. the degree to which something will happen in different situations). Models often have parameters representing different biases or preferences. By changing the values of these parameters the model may be able to account for different people’s responses. • Actual(orange) vs Predicted(blue) show that there was confidence that ABY was part of category A, less so for AB and even less for B • Results for category B were poorer due to only 1 entry matching rather than 2 for both A & AB

6. Results for CYB Test Set • Actual(orange) vs Predicted(blue) show that there was confidence that CYB was part of category C & BC, less so for B and even less for A, AB & AC. • Results interesting as it reflects the higher weight assigned to a C entry in dim1 than a B in dim3

7. Results for YAC Test Set • In this case, predicted vs actual results were quite mismatched. • Both trends are similar in orientation but the actual trend (orange line) shows that people were not confident with this test set, prehaps because Y as leading item was only in 1 of the learned test sets.

8. Results for XBC Test Set • Both trends are similar and show most confidence in XBC being in category C, then less so in B and less again in BC. • This reflects the weigh factor that C has in the prototype model as well as ease of recalling C's grouped in dim3 as part of the experiment test sets

9. Results for XXB Test Set • Trends are mismatched for category C but both show confidence in XXB being in B above all others. • This set had the most occurrences of under-confidence from participants for the conjuctions even though items occurred in 2/3 dims for both B & C

10. Conclusion • The prototype model does match up really well where there is a clear pattern established in the test set, results from actual and predicted followed very similiar trends for ABY, CYB & XXB • However when the new test set did not have a clear pattern, participants were not as confident when categorising as the model so improvements would need to be made to calculate this uncertanty