Knowledge Discovery from Categorical Data Based on Structured Partial Ordered Attribute Diagram

MGR: An information theory based hierarchical divisive clustering algorithm for categorical data

Partition-and-merge based fuzzy genetic clustering algorithm for categorical data

A cluster ensemble method for clustering categorical data

k-ANMI: A mutual information based clustering algorithm for categorical data

The theory introduced, presented and developed in this paper, is concerned with Rough Concept Analysis. This theory is a synthesis of the theory of Rough Sets pioneered by Zdzislaw Pawlak [10] with the theory of Formal Concept Analysis pioneered by Rudolf Wille [11]. The central notion in this paper of a rough formal concept combines in a natural fashion the two notions of rough set and formal concept — to use a slogan: “rough set + formal concept = rough formal concept”. This paper is an extension of the paper [5] presented at the international workshop on Rough Sets and Knowledge Discovery (RSKD'93). A related paper [8] using distributed constraints provides a synthesis of the two important data modeling techniques: conceptual scaling of Formal Concept Analysis, and Entity-Relationship database modeling. A follow-up paper [9] will extend rough concept analysis from formal contexts to distributed constraints.

Clustering categorical data poses two challenges defining an inherently meaningful similarity measure, and effectively dealing with clusters which are often embedded in different subspaces. In this paper, we propose a novel divisive hierarchical clustering algorithm for categorical data, named DHCC. We view the task of clustering categorical data from an optimization perspective, and propose effective procedures to initialize and refine the splitting of clusters. The initialization of the splitting is based on multiple correspondence analysis (MCA). We also devise a strategy for deciding when to terminate the splitting process. The proposed algorithm has five merits. First, due to its hierarchical nature, our algorithm yields a dendrogram representing nested groupings of patterns and similarity levels at different granularities. Second, it is parameter-free, fully automatic and, in particular, requires no assumption regarding the number of clusters. Third, it is independent of the order in which the data is processed. Fourth, it is scalable to large data sets. And finally, our algorithm is capable of seamlessly discovering clusters embedded in subspaces, thanks to its use of a novel data representation and Chi-square dissimilarity measures. Experiments on both synthetic and real data demonstrate the superior performance of our algorithm.

This paper introduces a self-organizing map dedicated to clustering, analysis and visualization of categorical data. Usually, when dealing with categorical data, topological maps use an encoding stage: categorical data are changed into numerical vectors and traditional numerical algorithms (SOM) are run. In the present paper, we propose a novel probabilistic formalism of Kohonen map dedicated to categorical data where neurons are represented by probability tables. We do not need to use any coding to encode variables. We evaluate the effectiveness of our model in four examples using real data. Our experiments show that our model provides a good quality of results when dealing with categorical data.

Formal concept analysis (FCA) is an effective formal tool for data analysis. However, when FCA is applied to documents knowledge discovery, there are many situations in which uncertainty information also occurs. This paper proposed an approach to fuzzy many-valued context analysis by using formal descriptions instead of scaling. Within this approach, we extended the many-valued context by using the theory of fuzzy set. It certainly does not provide a better analysis than scaling, but it allows to do document knowledge discovery with the theory of FCA and to reduce the complexity of fuzzy concept lattice by using the conjunction and disjunction of confidence thresholds of different attributes.

This paper focuses on solving the problem of clustering for categorical data with missing values. Specifically, we design a new framework that can impute missing values and assign objects into appropriate clusters. For the imputation step, we use a decision tree-based method to fill in missing values. For the clustering step, we use a kernel density estimation approach to define cluster centers and an information theoretic-based dissimilarity measure to quantify the differences between objects. Then, we propose a center-based algorithm for clustering categorical data with missing values, namely k-CCM. An experimental evaluation was performed on real-life datasets with missing values to compare the performance of the proposed algorithm with other popular clustering algorithms in terms of clustering quality. Generally, the experimental result shows that the proposed algorithm has a comparative performance when compared to other algorithms for all datasets.

In order to solve the problems that how to mine and express classification knowledge and rules in compatibility of prescription, this paper introduces a new theory of formal concept analysis (FCA), and realizes the compatibility of prescription knowledge mining. Meanwhile, the prescription drugs of reverting yin disease treatment in Treatise on febrile diseases are selected to apply the FCA theory to mine the compatibility of prescription. The result shows that complete knowledge which is related to prescription can be obtained from the attribute partial order chart, therefore it has been proved that the theory of FCA provides a new method to discovery the new knowledge of prescription of TCP.

The paper examines Formal Concept Analysis (FCA) and Rough Set Theory (RST) against the background of the theory of finite approximations of continuous topological spaces. We define the operators of FCA and RST by means of the specialisation order on elements of a topological space X which induces a finite approximation of X. On this basis we prove that FCA and RST together provide a semantics for tense logic S4.t. Moreover, the paper demonstrates that a topological space X cannot be distinguished from its finite approximation by means of the basic temporal language. It means that from the perspective of topology S4.t is a better account of approximate reasoning then unimodal logics, which have been typically employed.

Pattern extraction is one of the major topics in Knowledge Discovery. Out of numerous data mining techniques we propose to use a new approach: Formal Concept Analysis (FCA) together with Graph Databases with the implementation Neo4j. FCA is a prominent field of applied mathematics using maximal clusters of object-attribute relationships to discover and represent knowledge structures. The use of FCA gained much importance in many research domains in recent years. Despite the similarity of the graph representation between FCA and Neo4j, the structure and relations among the elements are represented differently and can offer a different perspective on the analysis. This paper gives more insight into how patterns can be extracted from medical data and interpreted by means of FCA and Neo4j in order to help medical staff improve the accuracy of diagnoses. We examine the factors related to patients' symptoms and diagnostics and then compare the results with the ones provided by a medical care center. We apply knowledge discovery techniques and conceptual landscapes paradigm in order to obtain an in-depth and high qualitative knowledge representation of medical data. By making use of the effectiveness and the graphical representation of conceptual hierarchies we extract valuable knowledge from medical data sets through which we solve the knowledge discovery, processing and representation task in Electronic Health Record systems.

Clustering is an important data mining technique that groups similar data records. In this research, the problem of clustering categorical (or transactional) data is studied. An algorithm for clustering transactional data, called F-Tree (frequent tree), is proposed, and a new similarity measure function, called PWO (probability of the weights of overlapped items), is introduced. Then, a framework to detect the best similarity value for different datasets is developed. Based on the items' frequencies in transactions, the F-Tree algorithm first generates small but highly pure clusters. It then merges similar clusters using the PWO similarity measure function, which depends on the probability of weights of overlapped items. One advantage of PWO is that it outputs the percentage of similarity between items; this is a clearer and more accurate measure of similarity than other similarity measures. Our experimental evaluation on real categorical datasets such as (Mushrooms, KrVskp, Congressional Voting, Soybean-Large, Soybean-Small, Hepatitis, Zoo, Lenses, and Adult-Stretch) shows that: Firstly, F-Tree is effective in finding rare or interesting clusters, and produces clusters with higher purity than LargeItem, WCD and CLOPE. Secondly, PWO is more effective in measuring the similarity between categorical data than LargeItem and CLOPE. Thirdly, clustering using the similarity measure PWO with pre-defined number of clusters results in separate classes with a good purity of average 80% coverage of real classes. Fourthly, the overlap estimator perfectly estimates the value of the overlap threshold using a small sample of dataset of around 5%. Finally, it is seen that the process of merging pure and small clusters increases the purity of resulted clusters as well as reduces time of clustering better than the process of generating clusters directly from the dataset then refining clusters. Based on the items' frequencies in transactions, The F-Tree algorithm first generates small but highly pure clusters. It then merges similar clusters using the PWO similarity measure function, which depends on the probability of weights of overlapped items. One advantage of PWO is that it outputs the percentage of similarity between items; this is a clearer and more accurate measure of similarity than other similarity measures. Our experimental evaluation on real categorical datasets such as "Mushrooms, KrVskp, Congressional Voting, Soybean-Large, Soybean-Small, Hepatitis, Zoo, Lenses, and Adult-Stretch" shows that: Firstly, F-Tree is effective in finding rare or interesting clusters, and produces clusters with higher purity than LargeItem, WCD and CLOPE. Secondly, PWO is more effective in measuring the similarity between categorical data than LargeItem and CLOPE. Thirdly, Clustering using the similarity measure PWO with pre-defined number of clusters results in separate classes with a good purity of average 80% coverage of real classes. Fourthly, the overlap estimator perfectly estimates the value of the overlap threshold using a small sample of dataset of around 5 percent. Finally, It is seen that the process of merging pure and small clusters increases the purity of resulted clusters as well as reduces time of clustering better than the process of generating clusters directly from the dataset then refining clusters.

Clustering is a widely used technique in data mining application for discovering patterns in underlying data. Most traditional clustering algorithms are limited in handling datasets that contain categorical attributes. Howerver, datasets with categorical types of attributes are common in real life data mining problem. For these data sets, no inherent distance measure, like the Euclidean distance, would work to compute the distance between two catgorical objects. In this article, we have described differential evolution, genetic algorithm and simulated annealing based fuzzy clustering. The performance of the proposed algorithms have been compared with that of different well known categorical data clustering algorithms and demonstrated for a variety of artificial and real life categorical data sets. Statistical significance test has been performed to establish the superiority of the proposed algorithms.

Recent advances in information system development suggest the use of ontology as a main knowledge management tool. Ontology contains concepts, a hierarchy, arbitrary relations between concepts, and possibly other axioms. However, there are some defects between several kinds of existing ontology construction methods in many aspects. After analyzing and comparing, this paper makes up these defects by applying formal concept analysis and association rule theory to construct concept hierarchies of ontology. This paper puts forward formal concept analysis and association rules applied in ontology learning based on non-structured of source data. The experimental results have shown our suggested ontology-based information system will increase precision and performance.