Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


case1121454398.pdf (2.65 MB)

ETD Abstract Container

Abstract Header

Formal Concepts and Applications

Shen, Gongqin
http://rave.ohiolink.edu/etdc/view?acc_num=case1121454398

Abstract Details

2005, Doctor of Philosophy, Case Western Reserve University, Computing and Information Science.
Formal Concept Analysis (FCA) is a powerful tool for symbolic data analysis using a mathematical structure called lattice. FCA has novel applications in areas such as data mining and information retrieval. In this thesis, we study the theory and applications of FCA. This thesis consists of three parts. The first part introduces a new notion of formal concept, called approximable concept, and connect this notion to semantic domain theory. FCA has been traditionally focused on finite contexts and finite concept lattices, therefore neglecting the full power of the theory. After a thorough investigation, we developed a new definition of concept, inspired by the ideas of partial information and successive approximation in domain theory, to provide computationally meaningful alternative. Domain theory is a branch of order theory invented by Scott for the denotational semantics of programming languages. The theoretical contribution of this part amounts to a systematic connection, in the form of a categorical equivalence, between formal concept analysis and domain theory. The second part presents a tool for automatic concept lattice layout and visualization. Concept lattices are normally represented by a list of string pairs instead of a lattice diagram. Currently, there are no standard rules for the visualization of concept lattices. We develop a tool which creates balanced and well-built lattice diagrams for finite contexts, automatically. The diagram layout of concept lattices help us understand the whole structure of concept lattices. The third part shows a method for web-menu layout design and describes a user evaluation study comparing the resulting menu layout of an existing real world web site with the one derived from our method. Most of today's web sites' menu layouts are created by the intuition of the web designers. We propose a new FCA-based semi-automatic web-menu design methodology, called FcAWN (Formal Concept Analysis for Web Navigation), to construct more consistent and reasonable layouts of web sites. In FcAWN, hyper-link hierarchies are considered as part of a lattice structure instead of a tree structure. We apply our method to Case University's EECS departmental web site to obtain a new design and implementation. A user evaluation study was conducted to compare the differences between the original site and the new one generated by FcAWN. By restricting to the data on users giving up answering questions of our carefully designed questionnaire, the FcAWN site has already shown a statistically significant advantage over the existing one in terms of usability.
Guo-Qiang Zhang (Advisor)
Computer Science
formal concept analysis; approximable concepts; domain theory; lattice; category theory; visualization; user evaluation.

Recommended Citations

Citations

  • Shen, G. (2005). Formal Concepts and Applications [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1121454398

    APA Style (7th edition)

  • Shen, Gongqin. Formal Concepts and Applications. 2005. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1121454398.

    MLA Style (8th edition)

  • Shen, Gongqin. "Formal Concepts and Applications." Doctoral dissertation, Case Western Reserve University, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=case1121454398

    Chicago Manual of Style (17th edition)

case1121454398
6,805
© 2005, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.