1. Mulugeta H Tedla University of Cincinnati, April 22, 2008
Application & emperical Analysis of Extended multidimensional conceptual space
Mulugeta H Tedla
University of Cincinnati, April 22, 2008

2. Overview Project Description Motivation
Objective
Results
Motivation
Introduction to Conceptual Space
Project Methodology
Key Findings/Results
Results 1
Results 2
Conclusion

3. Project Description Objective Results
Apply the Extended Multidimensional Conceptual Space (EMCS) as a framework for Knowledge Representation and Knowledge Discovery
demonstrate effectiveness
address dimensionality issue for properties in data-rich environments
Results
(work in progress)

4. Motivation Real world problems Content based information retrieval
Automatic document indexing
Context sensitive search

5. Introduction
Concept – an object/abstraction with features or properties
Conceptual Space
Pioneers in cognitive science – Peter Gardenfor – put conceptual space
representation of information geometrically by extending quality dimensions/domains and properties as integral into the notion of Conceptual space
E.g. concept “apple”
Dimensions – capture qualities of objects, form the frame work help us assign properties to objects and relation between them.
Domains: Color, Shape, Texture, Test etc.
Properties for Domain Color – RGB, i.e. Red, Green, and Blue
bridge between a Symbolic and Connectionist models
Symbolic – too coarse ( )
Connectionist – too fine (neural net – association of low level data - weights)

6. E.g Concept Space Ci=<C1,C2,C3,…>
E.g. Color Domain
E.g Concept Space Ci=<C1,C2,C3,…>
Red
Green
Blue
Color
Orange c2 c1
Texture
Test

7. Procedure/Methodology
Data or Document Preprocessing
Conversion of words into numerical representation
How?
Removing non essential words (stop words)
E.g. ‘the’, ‘of’, ‘at’…
Extract stem words (Porter Stem Algorithm)
E.g. ‘definition’ , ‘defining’ = ‘defin’
Feature Extraction
Compute word or term frequency in a document (TF)
Compute document frequency of term (DF)
Feature Selection
Compute and identify ‘Best Features’ of a concept using
TF * IDF

8. Procedure/Methodology cont’d
Concept Representation
Aggregation of object properties on different dimensions over different domains . [MA01]
Aggregation using co-occurrence (edges in the concept graph) two attributes (on dimensions) , domain properties(nodes in concept graph). [MA01]
Connection matrix C, is defined as follows:
Cij =0 if i, j belong to the same domain if i = j ∈ [0, 1] if i, j belong to different domains [MA01]
E.g. Apple
Co-occurrence of Gree, Rough and Sweet

9. Procedure/Methodology cont’d
Conection Matrix
Then the connection matrix is computed by [1]:
Cij =∑min(qij,qik)/ ∑qij
Extended Multi-dimensional Concept Representation [MA01]
Cij =∑min(qij,,…..,qik)

10. Procedure/Methodology cont’d
Fix the instance j,
Compute degree to which the properties Pi1…Pi occur: U{i1,…,i}= min(qji,,…..,qji1)
The Fuzzy set : U{i1,…,i} over all the instance is interpreted as Cardinality – the number of instance in which the properities Pi1…Pi co-occur
μCardA(i) = min{μ(i), 1 − μ(i+1)}
Do 1, and 2 for all possible co-occurences for a given window K [upto 3 in my case]
K=3=p1, p1p2, p1p2p3

11. Procedure/Methodology cont’d
Build the summary – Connection Matrix
111
1 0 0
0 1 0
0 0 1
131
1 3 1
0 1 0
0 0 1

12. Core Concept Examples Example Documens for Skin Cancer Doc-1 Doc-2
Breast
Skin
Sunburn
brain
Doc-1
0.3
0.8
0.9
0.0
Doc-2
0.5
0.6
0.2
D0c-3
0.1

13. Conclusion
Add your conclusion here

14. Questions and Discussion