A Survey on Soft Subspace Clustering

Subspace clustering (SC) is a promising clustering technology to identify clusters based on their associations with subspaces in high dimensional spaces. SC can be classified into hard subspace clustering (HSC) and soft subspace clustering (SSC). While HSC algorithms have been extensively studied and well accepted by the scientific community, SSC algorithms are relatively new but gaining more attention in recent years due to better adaptability. In the paper, a comprehensive survey on existing SSC algorithms and the recent development are presented. The SSC algorithms are classified systematically into three main categories, namely, conventional SSC (CSSC), independent SSC (ISSC) and extended SSC (XSSC). The characteristics of these algorithms are highlighted and the potential future development of SSC is also discussed.Comment: This paper has been published in Information Sciences Journal in 201

OPTIMASI ATURAN FUZZY DALAM SISTEM FUZZY SUGENO ORDE NOL DENGAN FUZZY C-MEANS CLUSTERING PADA DIAGNOSIS KANKER OTAK

Kanker otak adalah salah satu jenis kanker yang terjadi di Indonesia dengan tingkat kematian yang cukup tinggi dengan angka kejadian 1,9 per 100.000 penduduk pada tahun 2012, sedangkan angka mortalitas kanker otak sebanyak 1,3 per 100.000 penduduk. Oleh karena itu, diperlukan adanya deteksi dini dan diagnosis kanker otak. Salah satu cara untuk mendeteksi kanker otak adalah dengan magnetic resonance images (MRI). Tujuan dari penelitian ini adalah menjelaskan langkah-langkah penerapan fuzzy c-means clustering pada sistem fuzzy sugeno orde nol untuk diagnosis kanker otak dan mengetahui tingkat ketepatan dari sistem fuzzy sugeno orde nol. Penelitian ini menggunakan 114 data hasil ekstraksi data MRI yang terdiri dari 90 data latih dan 24 data uji. Sistem fuzzy yang digunakan adalah sistem fuzzy sugeno orde nol dengan 14 variabel input, yaitu contrast, correlation, dissimilarity, energy, entropy, homogeneity, max. probability, sum of squares, sum average, sum variance, sum entropy, diff. variance, diff. entropy, IDM. Sedangkan outputnya terbagi menjadi dua, yaitu otak normal dan otak kanker. Untuk mengoptimalkan keakurasian sistem maka digunakan fuzzy c-means clustering dalam membangun aturan fuzzy dan metode weight average untuk proses defuzzifikasi. Data latih dikelompokkan menjadi 50 cluster menggunakan fuzzy c-means clustering, kemudian hasil keluarannya berupa pusat cluster digunakan untuk membangun aturan fuzzy. Tingkat keakurasian, sensitivitas, dan spesifikasi dari sistem fuzzy sugeno orde nol masing-masing 92,22%, 93,33%, dan 91,11% untuk data latih. Untuk data uji dihasilkan keakurasian 75%, sensitivitas 50%, dan spesifikasi 100%. Keakurasian, sensitivitas, dan spesifikasi menggunakan Radial Basis Function Neural Network (RBFNN) untuk data latih masing-masing 83,33%, 82,9789%, 86,0465%, sedangkan pada data uji dihasilkan keakurasian 91,66%, sensitivitas 85,7142%, dan spesifikasi 100%. Bila dibandingkan dengan penelitian sebelumnya, hasil yang diperoleh untuk data latih dapat dikatakan lebih baik, sedangkan untuk data uji hasil yang diperoleh dengan metode RBFNN lebih baik dan untuk sistem sugeno orde nol masih diperlukan perbaikan guna meningkatkan keakurasian

Graph ambiguity

In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved

Dealing with non-metric dissimilarities in fuzzy central clustering algorithms

Clustering is the problem of grouping objects on the basis of a similarity measure among them. Relational clustering methods can be employed when a feature-based representation of the objects is not available, and their description is given in terms of pairwise (dis)similarities. This paper focuses on the relational duals of fuzzy central clustering algorithms, and their application in situations when patterns are represented by means of non-metric pairwise dissimilarities. Symmetrization and shift operations have been proposed to transform the dissimilarities among patterns from non-metric to metric. In this paper, we analyze how four popular fuzzy central clustering algorithms are affected by such transformations. The main contributions include the lack of invariance to shift operations, as well as the invariance to symmetrization. Moreover, we highlight the connections between relational duals of central clustering algorithms and central clustering algorithms in kernel-induced spaces. One among the presented algorithms has never been proposed for non-metric relational clustering, and turns out to be very robust to shift operations. (C) 2008 Elsevier Inc. All rights reserved