International Journal of Granular Computing, Rough Sets and Intelligent Systems http://www.inderscience.com/browse/index.php?journalID=315&year=2011&vol=2&issue=2 Inderscience Publishers Ltd en-uk International Journal of Granular Computing, Rough Sets and Intelligent Systems 1757-2703 1757-2711 © 2011 Inderscience Publishers Ltd editor@inderscience.com https://www.inderscience.com/images/files/coverImgs/ijgcrsis_scoverijgcrsis.jpg http://www.inderscience.com/browse/index.php?journalID=315&year=2011&vol=2&issue=2 http://www.inderscience.com/link.php?id=43365 The notions of indiscernibility and discernibility are the core concept of classical rough sets to cluster similarities and differences of data objects. In this paper, we use a new method of clustering data based on the combination of indiscernibility (quantitative indiscernibility relation) and its indiscernibility level. The indiscernibility level quantify the indiscernibility of pair of objects among other objects in information systems and this level represent the granularity of pair of objects in information system. For comparison to the new method, the following four clustering methods were selected and evaluated on a simulation dataset: average-, complete- and single-linkage agglomerative hierarchical clustering and Ward's method. The result of this paper shows that the four methods of hierarchical clustering yield dendrogram instability that gives different solution under permutation of input order of data object while the new method reduces dendrogram instability. Reducing dendrogram instability using clustering based on indiscernibility and indiscernibility level
R.B. Fajriya Hakim; Subanar Seno; Edi Winarko
International Journal of Granular Computing, Rough Sets and Intelligent Systems, Vol. 2, No. 2 (2011) pp. 87 - 106
The notions of indiscernibility and discernibility are the core concept of classical rough sets to cluster similarities and differences of data objects. In this paper, we use a new method of clustering data based on the combination of indiscernibility (quantitative indiscernibility relation) and its indiscernibility level. The indiscernibility level quantify the indiscernibility of pair of objects among other objects in information systems and this level represent the granularity of pair of objects in information system. For comparison to the new method, the following four clustering methods were selected and evaluated on a simulation dataset: average-, complete- and single-linkage agglomerative hierarchical clustering and Ward's method. The result of this paper shows that the four methods of hierarchical clustering yield dendrogram instability that gives different solution under permutation of input order of data object while the new method reduces dendrogram instability.

]]> 10.1504/IJGCRSIS.2011.043365 International Journal of Granular Computing, Rough Sets and Intelligent Systems, Vol. 2, No. 2 (2011) pp. 87 - 106 R.B. Fajriya Hakim; Subanar Seno; Edi Winarko Statistics Department, Faculty of Mathematics and Natural Sciences, Universitas Islam Indonesia, Jalan Kaliurang KM 14.5 Sleman, Jogjakarta 55584, Indonesia. ' Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Jogjakarta 55528, Indonesia. ' Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Jogjakarta 55528, Indonesia rough sets hierarchical clustering indiscernibility level dendrogram instability. 2011-10-26T23:20:50-05:00 2 2 87 106 2011-10-26T23:20:50-05:00 http://www.inderscience.com/link.php?id=43366 A pattern discovered from a collection of data is usually considered potentially interesting if its information content can assist the user in their decision making process. To that end, we have defined the concept of potential interestingness of a pattern based on whether it provides statistical knowledge that is able to affect one's belief system. In this paper, we introduce two algorithms, referred to as All-Confidence based Discovery of Potentially Interesting Patterns (ACDPIP) and ACDPIP-Closed, to discover patterns that qualify as potentially interesting. We show that the ACDPIP algorithm represents an efficient alternative to an algorithm introduced in our earlier work, referred to as Discovery of Potentially Interesting Patterns (DAPIP). However, results of experimental investigations also show that the application of ACDPIP is limited to sparse datasets. In response, we propose the algorithm ACDPIP-Closed designed to effectively discover potentially interesting patterns from dense datasets. Algorithms for discovering potentially interesting patterns
Raj Singh; Tom Johnsten; Vijay V. Raghavan; Ying Xie
International Journal of Granular Computing, Rough Sets and Intelligent Systems, Vol. 2, No. 2 (2011) pp. 107 - 122
A pattern discovered from a collection of data is usually considered potentially interesting if its information content can assist the user in their decision making process. To that end, we have defined the concept of potential interestingness of a pattern based on whether it provides statistical knowledge that is able to affect one's belief system. In this paper, we introduce two algorithms, referred to as All-Confidence based Discovery of Potentially Interesting Patterns (ACDPIP) and ACDPIP-Closed, to discover patterns that qualify as potentially interesting. We show that the ACDPIP algorithm represents an efficient alternative to an algorithm introduced in our earlier work, referred to as Discovery of Potentially Interesting Patterns (DAPIP). However, results of experimental investigations also show that the application of ACDPIP is limited to sparse datasets. In response, we propose the algorithm ACDPIP-Closed designed to effectively discover potentially interesting patterns from dense datasets.

]]> 10.1504/IJGCRSIS.2011.043366 International Journal of Granular Computing, Rough Sets and Intelligent Systems, Vol. 2, No. 2 (2011) pp. 107 - 122 Raj Singh; Tom Johnsten; Vijay V. Raghavan; Ying Xie School of Science and Computer Engineering, University of Houston Clear Lake, Houston, TX 77058, USA. ' School of Computer and Information Sciences, University of South Alabama, Mobile, AL 36688, USA. ' Center of Advanced Computer Studies, University of Louisiana, Lafayette, LA 70504, USA. ' Deptartment of Computer Science and Information Systems, Kennesaw State University, Kennesaw, GA 30144, USA data mining potential interesting patterns positive patterns negative patterns association rules closed frequent itemsets pattern discovery. 2011-10-26T23:20:50-05:00 2 2 107 122 2011-10-26T23:20:50-05:00 http://www.inderscience.com/link.php?id=43367 Feature selection refers to the problem of selecting the set of most relevant features which produces the most predictive outcome. Rough set theory has been one of the most successful methods used for feature selection. However, this method is still not able to find the optimal subsets. This paper proposes a new feature selection method based on rough set theory hybrid with a weighted bee colony optimisation (WBCO) in an attempt to combat this. This proposed work is applied in the medical domain to find the minimal reducts and experimentally compared with the existing rough set methods, rough set methods with computational intelligence and non-rough set methods. The performance is analysed with a novel genetic algorithm-based k-nearest neighbour (GkNN) classifier. The experiments and results show that our proposed method could find optimum reducts than the other algorithms. A weighted bee colony optimisation hybrid with rough set reduct algorithm for feature selection in the medical domain
N. Suguna; K. Thanushkodi
International Journal of Granular Computing, Rough Sets and Intelligent Systems, Vol. 2, No. 2 (2011) pp. 123 - 140
Feature selection refers to the problem of selecting the set of most relevant features which produces the most predictive outcome. Rough set theory has been one of the most successful methods used for feature selection. However, this method is still not able to find the optimal subsets. This paper proposes a new feature selection method based on rough set theory hybrid with a weighted bee colony optimisation (WBCO) in an attempt to combat this. This proposed work is applied in the medical domain to find the minimal reducts and experimentally compared with the existing rough set methods, rough set methods with computational intelligence and non-rough set methods. The performance is analysed with a novel genetic algorithm-based k-nearest neighbour (GkNN) classifier. The experiments and results show that our proposed method could find optimum reducts than the other algorithms.

]]> 10.1504/IJGCRSIS.2011.043367 International Journal of Granular Computing, Rough Sets and Intelligent Systems, Vol. 2, No. 2 (2011) pp. 123 - 140 N. Suguna; K. Thanushkodi Akshaya College of Engineering and Technology, Coimbatore, Tamil Nadu, India. ' Akshaya College of Engineering and Technology, Coimbatore, Tamil Nadu, India feature selection rough sets quick reduct genetic algorithms ant colony optimisation ACO PSO particle swarm optimisation weighted BCO bee colony optimisation rough set theory k-nearest neighbour classifier. 2011-10-26T23:20:50-05:00 2 2 123 140 2011-10-26T23:20:50-05:00 http://www.inderscience.com/link.php?id=43369 Covering-based rough set theory is a generalisation of rough set theory. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. In this paper, we introduce matroid theory to covering-based rough sets, and explore the matroidal structure and properties of covering-based rough sets. Specifically, we define the upper approximation number to establish the matroidal structure of covering-based rough sets. So many important concepts and methods in matroid theory can be employed to investigate covering-based rough sets. The rank plays a very important role in a matrix, so we use the rank function of the matroid induced by a covering to measure the covering. With the rank function, a pair of approximation operators, namely, matroid approximation operators, are constructed. This type of approximation operators not only inherits the properties of those traditional ones which are defined from the perspective of set theory, but also presents some new properties. Finally, the matroid upper approximations are compared with the second upper approximations in covering-based rough sets. Matroidal structure of covering-based rough sets through the upper approximation number
Shiping Wang; William Zhu
International Journal of Granular Computing, Rough Sets and Intelligent Systems, Vol. 2, No. 2 (2011) pp. 141 - 148
Covering-based rough set theory is a generalisation of rough set theory. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. In this paper, we introduce matroid theory to covering-based rough sets, and explore the matroidal structure and properties of covering-based rough sets. Specifically, we define the upper approximation number to establish the matroidal structure of covering-based rough sets. So many important concepts and methods in matroid theory can be employed to investigate covering-based rough sets. The rank plays a very important role in a matrix, so we use the rank function of the matroid induced by a covering to measure the covering. With the rank function, a pair of approximation operators, namely, matroid approximation operators, are constructed. This type of approximation operators not only inherits the properties of those traditional ones which are defined from the perspective of set theory, but also presents some new properties. Finally, the matroid upper approximations are compared with the second upper approximations in covering-based rough sets.

]]> 10.1504/IJGCRSIS.2011.043369 International Journal of Granular Computing, Rough Sets and Intelligent Systems, Vol. 2, No. 2 (2011) pp. 141 - 148 Shiping Wang; William Zhu School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China. ' Lab of Granular Computing, Zhangzhou Normal University, Zhangzhou, 363000, China covering based rough sets matroid theory matroids upper approximation number approximation operator rank function rough set theory. 2011-10-26T23:20:50-05:00 2 2 141 148 2011-10-26T23:20:50-05:00 http://www.inderscience.com/link.php?id=43370 Advances in non-linear dimensionality reduction provide a way to understand and visualise the underlying structure of complex datasets. The performance of large-scale non-linear dimensionality reduction is of key importance in data mining, machine learning, and data analysis. In this paper, we concentrate on improving the performance of non-linear dimensionality reduction using large-scale datasets on the GPU. In particular, we focus on solving problems including k-nearest neighbour (KNN) search and sparse spectral decomposition for large-scale data, and propose an efficient framework for local linear embedding (LLE). We implement a k-d tree-based KNN algorithm and Krylov subspace method on the GPU to accelerate non-linear dimensionality reduction for large-scale data. Our results enable GPU-based k-d tree LLE processes of up to about 30-60× faster compared to the brute force KNN (Hernandez et al., 2007) LLE model on the CPU. Overall, our methods save O(n²-6n-2k-3) memory space. Parallel non-linear dimension reduction algorithm on GPU
Tsung Tai Yeh; Tseng Yi Chen; Yen Chiu Chen; Hsin Wen Wei
International Journal of Granular Computing, Rough Sets and Intelligent Systems, Vol. 2, No. 2 (2011) pp. 149 - 165
Advances in non-linear dimensionality reduction provide a way to understand and visualise the underlying structure of complex datasets. The performance of large-scale non-linear dimensionality reduction is of key importance in data mining, machine learning, and data analysis. In this paper, we concentrate on improving the performance of non-linear dimensionality reduction using large-scale datasets on the GPU. In particular, we focus on solving problems including k-nearest neighbour (KNN) search and sparse spectral decomposition for large-scale data, and propose an efficient framework for local linear embedding (LLE). We implement a k-d tree-based KNN algorithm and Krylov subspace method on the GPU to accelerate non-linear dimensionality reduction for large-scale data. Our results enable GPU-based k-d tree LLE processes of up to about 30-60× faster compared to the brute force KNN (Hernandez et al., 2007) LLE model on the CPU. Overall, our methods save O(n²-6n-2k-3) memory space.

]]> 10.1504/IJGCRSIS.2011.043370 International Journal of Granular Computing, Rough Sets and Intelligent Systems, Vol. 2, No. 2 (2011) pp. 149 - 165 Tsung Tai Yeh; Tseng Yi Chen; Yen Chiu Chen; Hsin Wen Wei Institute of Information Science, Academia Sinica, 128 Academia Road, Section 2, Nankang, Taipei, Taiwan. ' 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan. ' Computer Science Department, National Tsing Hua University, 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan. ' Institute of Information Science, Academia Sinica, 128 Academia Road, Section 2, Nankang, Taipei, Taiwan nonlinear dimension reduction dimensionality reduction GPU complex datasets memory space graphics processing unit. 2011-10-26T23:20:50-05:00 2 2 149 165 2011-10-26T23:20:50-05:00 http://www.inderscience.com/link.php?id=43371 In modern day crimes and terrorism, it has become imperative to identify by features the criminals who are involved and who have caused such a disaster. The current work is a basic step towards such an important identification process. In this direction, we begin our work with the identification of fuzzy geometric shapes, which resemble with the actual geometric shapes fuzzily. Zadeh proposed computing with words (CW) which deals with perceptions, where the perceptions are mostly fuzzy, while the measurements are always found to be crisp. On the similar lines, sketching with words (SW) is a technique in which the objects of sketching are the perceptions described in uncertain, vague, imprecise words and prepositions described in natural language (NL). We propose SW here to represent geometric figures using membership functions to estimate f-geometry. Elements of sketching with words
B. Mohammed Imran; M.M. Sufyan Beg
International Journal of Granular Computing, Rough Sets and Intelligent Systems, Vol. 2, No. 2 (2011) pp. 166 - 178
In modern day crimes and terrorism, it has become imperative to identify by features the criminals who are involved and who have caused such a disaster. The current work is a basic step towards such an important identification process. In this direction, we begin our work with the identification of fuzzy geometric shapes, which resemble with the actual geometric shapes fuzzily. Zadeh proposed computing with words (CW) which deals with perceptions, where the perceptions are mostly fuzzy, while the measurements are always found to be crisp. On the similar lines, sketching with words (SW) is a technique in which the objects of sketching are the perceptions described in uncertain, vague, imprecise words and prepositions described in natural language (NL). We propose SW here to represent geometric figures using membership functions to estimate f-geometry.

]]> 10.1504/IJGCRSIS.2011.043371 International Journal of Granular Computing, Rough Sets and Intelligent Systems, Vol. 2, No. 2 (2011) pp. 166 - 178 B. Mohammed Imran; M.M. Sufyan Beg Department of Computer Engineering, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi 110025, India. ' Department of Computer Engineering, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi 110025, India sketching with words fuzzy images fuzzy geometry f-principle f-theorem fuzzy geometric objects geometric shapes geometric figures sketching automation perceptions fuzzy sketches image retrieval feature identification. 2011-10-26T23:20:50-05:00 2 2 166 178 2011-10-26T23:20:50-05:00