Rough clustering

Lingras, Pawan; Peters, Georg

doi:10.1002/widm.16

Cited by 51 publications

(19 citation statements)

References 38 publications

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“…A significant number of researchers have enhanced rough set theory in studies such as Refs. , , . This theory is considered a valuable tool to solve problems such as representation of uncertain or imprecise knowledge, data mining, and knowledge analysis.…”

Section: Possibility and Rough Set Theoriesmentioning

confidence: 99%

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Semantically Segmented Clustering Based on Possibilistic and Rough Set Theories

Ammar

Elouedi

Lingras

2015

Int. J. Intell. Syst.

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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.

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Section: Possibility and Rough Set Theoriesmentioning

confidence: 99%

“…This situation can be remedied by representing these soft clusters as rough sets. Rough set based methods allow an object to belong to multiple clusters without assigning a numeric membership. The use of rough sets makes it possible to represent a cluster with lower and upper approximations.…”

Section: Introductionmentioning

confidence: 99%

Semantically Segmented Clustering Based on Possibilistic and Rough Set Theories

Ammar

Elouedi

Lingras

2015

Int. J. Intell. Syst.

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“…Lingras et al. proposed RKM . RKM calculates cluster centers and belongingness of each object to a lower or upper approximation of each cluster by iterative process.…”

Section: Rough Sets and Rkmmentioning

confidence: 99%

“…However, it is pointed out that the fuzzy degree sometimes may be too descriptive for interpreting clustering results . In such cases, rough‐set representation becomes a useful and powerful tool .…”

Section: Introductionmentioning

confidence: 99%

“…The lower approximation means that “an object surely belongs to the set” and the upper one means that “an object possibly belongs to the set”. Clustering based on rough set could provide a solution that is less restrictive than conventional clustering and less descriptive than fuzzy clustering, and therefore the rough set based clustering has attracted increasing interest of researchers …”

Section: Introductionmentioning

confidence: 99%

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Objective-Based Rough c-Means Clustering

Endo

Kinoshita

2013

Int. J. Intell. Syst.

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Conventional clustering algorithms classify a set of objects into some clusters with clear boundaries, that is, one object must belong to one cluster. However, many objects belong to more than one cluster in real world since the boundaries of clusters generally overlap with each other. Fuzzy‐set representation of clusters makes it possible for each object to belong to more than one cluster. On the other hand, the fuzzy degree is sometimes regarded as too descriptive for interpreting clustering results. Rough‐set representation could deal with such cases. Clustering based on rough set could provide a solution that is less restrictive than conventional clustering and less descriptive than fuzzy clustering. This paper proposes a rough clustering algorithm which is based on optimization of an objective function and the calculation formula of cluster centers is the same as one by Lingras et al. Moreover, it shows effectiveness of our proposed clustering algorithm in comparison with other algorithms.

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Soft clustering

Ferraro

Giordani

2019

WIREs Computational Stats

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Clustering is one of the most used tools in data analysis. In the last decades, due to the increasing complexity of data, soft clustering has received a great deal of attention. There exist different approaches that can be considered as soft. The most known is the fuzzy approach that consists in assigning objects to clusters with membership degrees, depending on the dissimilarities between each object and all the prototypes, ranging in the unit interval. Closely related to the fuzzy approach, there is the possibilistic one that, differently from the previous one, relaxes some constraints on the membership degrees. In particular, the objects are assigned to clusters with degrees of typicalities, depending just on the dissimilarities between each object and the closest prototype. A further soft approach is the rough one. In this case, there are not degrees ranging between 0 and 1 but objects with intermediate features belong to the boundary region and are assigned to more than one cluster. Even if it is not universally recognized in the scientific community as an approach of soft clustering, from our point of view, the model-based approach can also be considered as such. Model-based clustering methods also produce a soft partition of the objects and the posterior probability of a component membership may play a role similar to the membership degree. The four approaches are critically described from a theoretical point of view and an empirical comparative analysis is carried out.

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Rough clustering

Cited by 51 publications

References 38 publications

Semantically Segmented Clustering Based on Possibilistic and Rough Set Theories

Semantically Segmented Clustering Based on Possibilistic and Rough Set Theories

Objective-Based Rough c-Means Clustering

Soft clustering

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