Browsing by Subject "Set Theory"

Now showing 1 - 5 of 5

Open Access
Hypergraph models and algorithms for data-pattern-based clustering
(Springer, 2004) Ozdal, M. M.; Aykanat, Cevdet
In traditional approaches for clustering market basket type data, relations among transactions are modeled according to the items occurring in these transactions. However, an individual item might induce different relations in different contexts. Since such contexts might be captured by interesting patterns in the overall data, we represent each transaction as a set of patterns through modifying the conventional pattern semantics. By clustering the patterns in the dataset, we infer a clustering of the transactions represented this way. For this, we propose a novel hypergraph model to represent the relations among the patterns. Instead of a local measure that depends only on common items among patterns, we propose a global measure that is based on the cooccurences of these patterns in the overall data. The success of existing hypergraph partitioning based algorithms in other domains depends on sparsity of the hypergraph and explicit objective metrics. For this, we propose a two-phase clustering approach for the above hypergraph, which is expected to be dense. In the first phase, the vertices of the hypergraph are merged in a multilevel algorithm to obtain large number of high quality clusters. Here, we propose new quality metrics for merging decisions in hypergraph clustering specifically for this domain. In order to enable the use of existing metrics in the second phase, we introduce a vertex-to-cluster affinity concept to devise a method for constructing a sparse hypergraph based on the obtained clustering. The experiments we have performed show the effectiveness of the proposed framework.
Open Access
Maximizing benefit of classifications using feature intervals
(Springer, Berlin, Heidelberg, 2003) İkizler, Nazlı; Güvenir, H. Altay
There is a great need for classification methods that can properly handle asymmetric cost and benefit constraints of classifications. In this study, we aim to emphasize the importance of classification benefits by means of a new classification algorithm, Benefit-Maximizing classifier with Feature Intervals (BMFI) that uses feature projection based knowledge representation. Empirical results show that BMFI has promising performance compared to recent cost-sensitive algorithms in terms of the benefit gained.
Open Access
Nonstandard set theories and information management
(Springer/, 1996) Akman, V.; Pakkan, M.
The merits of set theory as a foundational tool in mathematics stimulate its use in various areas of artificial intelligence, in particular intelligent information systems. In this paper, a study of various nonstandard treatments of set theory from this perspective is offered. Applications of these alternative set theories to information or knowledge management are surveyed.
Open Access
A rule-based video database system architecture
(Elsevier, 2002) Dönderler, M. E.; Ulusoy, Özgür; Güdükbay, Uğur
We propose a novel architecture for a video database system incorporating both spatio-temporal and semantic (keyword, event/activity and category-based) query facilities. The originality of our approach stems from the fact that we intend to provide full support for spatio-temporal, relative object-motion and similarity-based object-trajectory queries by a rule-based system utilizing a knowledge-base while using an object-relational database to answer semantic-based queries. Our method of extracting and modeling spatio-temporal relations is also a unique one such that we segment video clips into shots using spatial relationships between objects in video frames rather than applying a traditional scene detection algorithm. The technique we use is simple, yet novel and powerful in terms of effectiveness and user query satisfaction: video clips are segmented into shots whenever the current set of relations between objects changes and the video frames, where these changes occur, are chosen as keyframes. The directional, topological and third-dimension relations used for shots are those of the keyframes selected to represent the shots and this information is kept, along with frame numbers of the keyframes, in a knowledge-base as Prolog facts. The system has a comprehensive set of inference rules to reduce the number of facts stored in the knowledge-base because a considerable number of facts, which otherwise would have to be stored explicitly, can be derived by rules with some extra effort. © 2002 Elsevier Science Inc. All rights reserved.
Open Access
Solving equations in the universe of hypersets
(1993) Pakkan, Müjdat
Hyperset Theory (a.k.a. ZFC~/AFA) of Peter Aczel is an enrichment of the classical ZFC set theory and uses a graphical representation for sets. By allowing non-well-founded sets, the theory provides an appropriate framework for modeling various phenomena involving circularity. Z F C /A F A has an important consequence that guarantees a solution to a set of equations in the universe of hypersets, viz. the Solution Lemma. This lemma asserts that a system of equations defined in the universe of hypersets has a unique solution, and has applications in areas like artificial intelligence, database theory, and situation theory. In this thesis, a program called HYPERSOLVER, which can solve systems of equations to which the Solution Lemma is applicable and which has built-in procedures to display the graphs depicting the solutions, is presented.