Asma Ammar

Iterative meta-clustering through granular hierarchy of supermarket customers and products

This paper proposes a novel iterative meta-clustering technique that uses clustering results from one set of objects to dynamically change the representation of another set of objects. The proposal evolves two clustering schemes in parallel influencing each other through indirect recursion. The proposal is based on the emerging area of granular computing, where each object is represented as an information granule and an information granule can hierarchically include other information granules. The paper describes the theoretical and algorithmic formulation of the iterative meta-clustering algorithm followed by its implementation. The proposal is demonstrated with the help of a retail store dataset consisting of transactions involving customers and products. A customer granule is represented by static information obtained from the database and dynamic information obtained from clustering of products bought by the customer. Similarly, the product granule augments the static representation from the database with clustering profiles of customers who buy these products. The algorithm is tested for a synthetic dataset to explore various nuances of the proposal, followed by an extensive experimentation with a real-world retail dataset.

A New Possibilistic Clustering Method: The Possibilistic K-Modes

This paper investigates the problem of clustering data pervaded by uncertainty. Dealing with uncertainty, in particular, using clustering methods can be of great interest since it helps to make a better decision. In this paper, we combine the k-modes method within the possibility theory in order to obtain a new clustering approach for uncertain categorical data; more precisely we develop the so-called possibilistic kmodes method (PKM) allowing to deal with uncertain attribute values of objects where uncertainty is presented through possibility distributions. Experimental results show good performance on well-known benchmarks.

RPKM: the rough possibilistic k-modes

Clustering categorical data sets under uncertain framework is a fundamental task in data mining area. In this paper, we propose a new method based on the k-modes clustering method using rough set and possibility theories in order to cluster objects into several clusters. While possibility theory handles the uncertainty in the belonging of objects to different clusters by specifying the possibilistic membership degrees, rough set theory detects and clusters peripheral objects using the upper and lower approximations. We introduce modifications on the standard version of the k-modes approach (SKM) to obtain the rough possibilistic k-modes method denoted by RPKM. These modifications make it possible to classify objects to different clusters characterized by rough boundaries. Experimental results on benchmark UCI data sets indicate the effectiveness of our proposed method i.e. RPKM.

K-Modes Clustering Using Possibilistic Membership

This paper describes an extension of the standard k-modes method (SKM) to cluster categorical objects under uncertain framework. Our proposed approach combines the SKM with possibility theory in order to obtain the so-called k-modes method based on possibilistic membership (KM-PM). This latter makes it possible to deal with uncertainty in the assignment of the objects to different clusters using possibilistic membership degrees. Besides, it facilitates the detection of boundary objects by taking into account of the similarity of each object to all clusters. The KM-PM also overcomes the numeric limitation of the existing possibilistic clustering approaches (i.e. the dealing only with numeric values) and easily handles the extreme cases of knowledge, namely the complete knowledge and the total ignorance. Simulations on real-world databases show that the proposed KM-PM algorithm gives more meaningful results.

Incremental Rough Possibilistic K-Modes

In this paper, we propose a novel version of the k-modes method dealing with the incremental clustering under uncertain framework. The proposal is called the incremental rough possibilistic k-modes I-RPKM. First, possibility theory is used to handle uncertain values of attributes in databases and, to compute the membership values of objects to resulting clusters. After that, rough set theory is applied to detect boundary regions. After getting the final partition, the I-RPKM adapts the incremental clustering strategy to take into account new information and update the cluster number without re-clustering objects. I-RPKM is shown to perform better than other certain and uncertain approaches.

The K-Modes Method under Possibilistic Framework

In this paper, we develop a new clustering method combining the possibility theory with the standard k-modes method (SKM). The proposed method is called KM-PF to express the fact that it is a modification of k-modes algorithm under possibilistic framework. KM-PM incorporates possibilistic theory in two distinct stages in application of the SKM combining the possibilistic k-modes (PKM) and the k-modes using possibilistic membership (KM-PM). First, it deals with uncertain attribute values of instances using possibilistic distributions. Then, it computes the possibilistic membership degrees of each object to all clusters. Experimental results show that the proposed method compares favourably to the SKM, PKM and KM-PM.

Decremental Rough Possibilistic K-Modes

This paper proposes decremental rough possibilitic k-modes (D-RPKM) as a new clustering method for categorical databases. It distinguishes itself from the conventional clustering method in four aspects. First, it can deal with uncertain values of attributes by defining possibility degrees. Then, it handles uncertainty when an object belongs to several clusters using possibilistic membership degrees. It also determines boundary regions through the computing of the approximation sets based on the rough set theory. Finally, it accommodates gradual changes in datasets where there is a decrease in the cluster number. Such a dynamically changing dataset can be seen in numerous real-world situations such as changing behaviour of customers, or popularity of products or when there is, for example, an extinction of some species or diseases. For experiments, we use UCI machine learning repository datasets with different evaluation criteria. Results highlight the effectiveness of the proposed method compared to different versions of k-modes method.

Meta-clustering of possibilistically segmented retail datasets

This paper proposes a possibilistic meta-clustering algorithm. The possibility theory is used for possibilistic segmentation of the input data as well as for determining the possibilistic membership of objects to multiple clusters. The meta-clustering uses connections between information granules to send clustering knowledge from one granule to another. The approach is demonstrated with the help of the k-modes clustering algorithm for a real-world retail store, where a customer is connected to the products bought, and products are connected to customers who buy them. The meta-clustering approach uses the results from clustering of customers as an input to cluster the products, and recursively uses clustering of products as input to the clustering customers. The customer granule is represented using static information from the database and dynamic information from the clustering of the products bought. Similarly, a product granule is represented by static information from the database and dynamic part from the clustering of the customers who buy the product. The static information from the database is represented using possibilistic segments.

Semantically Segmented Clustering Based on Possibilistic and Rough Set Theories

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 k‐modes 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).

The k-modes method using possibility and rough set theories

This paper investigates rough clustering of objects from uncertain databases using possibility and rough set theories. Real databases can contain both certain and uncertain attribute values. To properly cluster such instances into different clusters, it is necessary to take into account such uncertainty. When clustering objects with uncertain values, we have to consider the similarities between each object and all clusters in order to provide more accurate clustering results. To this end, we propose a new approach based on the k-modes method to cluster categorical objects using possibility and rough set theories to deal with uncertainty. First, possibility theory is applied to handle uncertain attribute values of instances and to specify membership degrees of each instance to all clusters. Then, rough set theory is used to detect peripheral objects and to form clusters with rough boundaries. The results of the proposed approach compare favourably with other certain and uncertain approaches based on different evaluation criteria.