Semantically Segmented Clustering Based on Possibilistic and Rough Set Theories

Abstract

This paper reports the application of a possibility and rough set based clustering to semantically segmented real-world databases. The approach is an improved version of the well-known kmodes algorithm. It is a soft clustering method that clusters instances with uncertain categorical values to different clusters using their membership degrees. The possibility theory is used for dealing with uncertainty in the values of attributes and in the memberships of clusters. Rough sets are used to detect clusters with rough boundaries. We demonstrate the effectiveness of the proposed approach with the help of two real-world databases: a retail store or transactions data set and a mobile phone data set. The numeric values of attributes are segmented into semantically meaningful linguistic values using a novel discretization method. These linguistic values can lead to more natural interpretation of knowledge using possibilistic degrees. The possibilistic degrees describe our knowledge relative to the values of attributes (fully plausible to occur, may occur, or rejected) and identify the level of uncertainty in memberships to different clusters. In addition, our method deduces peripheral objects by calculating the approximate sets as defined in the rough set theory. The k-modes enhanced with rough set and possibility theories can provide semantically meaningful information for decision making to the store owners (retails data set) and telecommunication companies (mobile phone data set). C 2015 Wiley Periodicals, Inc.This section reports an overview of the possibility and rough set theories used in our study. Possibility theory is characterized by the use of dual set functions, namely possibility (Equation 5) and necessity (Equation 6) measures.N (E) = min ω / ∈ (1 − π (ω)) ,where E is an event.Here y ∈ U , and B(y) is a subset of U such that ∀x ∈ B(y) values of attributes in B are the same.

Categorical Data Clustering: A Bibliometric Analysis and Taxonomy

“…MVA [84] the concept of a number of automated clusters (NoACs) with a rough value set MDA [103], MSA [179], ITDR [62] Moreover, Ammar et al integrate possibility theory with RST, aiming to manage uncertainty in attribute values by utilizing possibility degrees and uncertain clusters through possibilistic membership degrees. This approach extends their prior work [180] by employing a discretization method to convert numeric values into semantically more meaningful linguistic variables with possibilistic memberships based on the K-modes algorithm [167].…”

Encoding the Law of the Household and the Standardisation of Uncertainty

“…In the history of statistics and particularly its computations, the practice of clustering arose as a means to combine entities deemed to be not of the same property but of approximate resemblance (Ammar et al 2015), or: more like than unlike, rather than the same. Cluster analysis involves the explicit use of logical steps (algorithms), and is often used in machine learning, pattern recognition and information retrieval systems.…”

An Efficient Segmentation and Classification System in Medical Images Using Intuitionist Possibilistic Fuzzy C-Mean Clustering and Fuzzy SVM Algorithm

“…Proper segmentation is required for better feature extraction and classification. References [ 7 , 8 , 9 ] addresses many algorithms for the early detection of breast cancer detection. The evaluation of segmentation based on detection rate and accuracy gave the result of breast cancer detection cases [ 10 , 11 , 12 ].…”

“…Figure 2 shows a classification task related to the medical images as output. Classifiers methods like rough set data analysis, support vector machine (SVM), decision tree, neural network and linear discriminant analysis (LDA) were extensively used for medical image detection approaches [3,7,29,30]. The major contributions of the proposed method are the following:…”