On improving ROCK-based clustering for categorical data

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.

We develop new algorithmic methods with provable guarantees for feature selection in regard to categorical data clustering. While feature selection is one of the most common approaches to reduce dimensionality in practice, most of the known feature selection methods are heuristics. We study the following mathematical model. We assume that there are some inadvertent (or undesirable) features of the input data that unnecessarily increase the cost of clustering. Consequently, we want to select a subset of the original features from the data such that there is a small-cost clustering on the selected features. More precisely, for given integers ℓ (the number of irrelevant features) and k (the number of clusters), budget B , and a set of n categorical data points (represented by m -dimensional vectors whose elements belong to a finite set of values Σ), we want to select m -ℓ relevant features such that the cost of any optimal k -clustering on these features does not exceed B . Here the cost of a cluster is the sum of Hamming distances (ℓ 0 -distances) between the selected features of the elements of the cluster and its center. The clustering cost is the total sum of the costs of the clusters. We use the framework of parameterized complexity to identify how the complexity of the problem depends on parameters k , B , and |Σ|. Our main result is an algorithm that solves the Feature Selection problem in time f ( k, B , |Σ|)⋅ m g ( k , |Σ|) ⋅ n 2 for some functions f and g . In other words, the problem is fixed-parameter tractable parameterized by B when |Σ| and k are constants. Our algorithm for Feature Selection is based on a solution to a more general problem, Constrained Clustering with Outliers. In this problem, we want to delete a certain number of outliers such that the remaining points could be clustered around centers satisfying specific constraints. One interesting fact about Constrained Clustering with Outliers is that besides Feature Selection, it encompasses many other fundamental problems regarding categorical data such as Robust Clustering and Binary and Boolean Low-rank Matrix Approximation with Outliers. Thus, as a byproduct of our theorem, we obtain algorithms for all these problems. We also complement our algorithmic findings with complexity lower bounds.

A cluster ensemble method for clustering categorical data

Quite often in medical studies multiple discrete indicators are used to measure some characters that are defined only conceptually and are difficult to measure directly. Studies of this type exhibit categorical responses of dependent nature. Analysis of such categorical data appears to be extremely difficult (intractable) particularly in the presence of risk (causal) factors. In the present article, our purpose is to develop a latent mixture regression model for analysing such multivariate categorical data. Such a mixture model accommodates correlated and overdispersed data through the incorporation of random effects. Unfortunately, a full likelihood analysis is often hampered by the need for numerical integration. Two different procedures have been considered here. Both involve intensive computations. Numerical investigation has been carried out on the basis of a survey data covering 220 individuals from medical colleges in and around Calcutta (India). The purpose of the study is to compare tooth cleaning efficiency of brushes manufactured by different companies.

This primary study uses of ICT in higher education, university teacher prospective analysis of categorical data using r programming tries to explore the satisfaction of ICT uses in higher education of university teacher on Prithvi Narayan campus Pokhara. The primary data were collected from February to March 2020. Although there was a large research gap in many researchers to analyze accurately if the variable is in categorical type. This research tries to meet the gap between the selection of appropriate tools for a categorical questionnaire survey of 32 university teachers. The satisfaction of teachers’ concepts regarding the use of ICT to enhance student educational quality had expressed on different Likert scale could be summarized with the count, 93 percent of university teacher was satisfied for ICT use in classroom teaching. The chi-square value p equal to 0.08 signifies there was not rejection evidence of avoiding the null hypothesis. The different bar plots with a colorful image and their percentage and count could easily plot using r programming.

Three-way space structure and clustering of categorical data

The models of symmetry and quasi-symmetry may have use in the analysis of categorical data in square tables where the row and column classifications are the same. Under the model of symmetry, the probability that an observation falls in, say, the (i,j) cell of a square table is the same as the probability that it falls in the (j,i) cell. The model of symmetry requires that the expected marginal total for any one row of the table be the same as the expected marginal total for the corresponding column. The model of quasi-symmetry, which is a generalization of the model of symmetry, does not require this equality of expected row and column totals. In this paper, we illustrate the use of the models of symmetry and quasi-symmetry in the analysis of categorical data that summarize pairs of sounds in infants' and toddlers' early utterances. In the past, the complexity of infants' early vocalizations has been difficult to measure because of a lack of methods to quantify prelinguistic phonetic variables. We use the models of symmetry and quasi-symmetry as a first attempt to quantify the complexity of infants' early speech. We hope that the discovery of models appropriate for quantification of language development in normal children will have later use in identification of children at risk for communicative disorders.

Model-based clustering methods for continuous data are well established and commonly used in a wide range of applications. However, model-based clustering methods for categorical data are less standard. Latent class analysis is a commonly used method for model-based clustering of binary data and/or categorical data, but due to an assumed local independence structure there may not be a correspondence between the estimated latent classes and groups in the population of interest. The mixture of latent trait analyzers model extends latent class analysis by assuming a model for the categorical response variables that depends on both a categorical latent class and a continuous latent trait variable; the discrete latent class accommodates group structure and the continuous latent trait accommodates dependence within these groups. Fitting the mixture of latent trait analyzers model is potentially difficult because the likelihood function involves an integral that cannot be evaluated analytically. We develop a variational approach for fitting the mixture of latent trait models and this provides an efficient model fitting strategy. The mixture of latent trait analyzers model is demonstrated on the analysis of data from the National Long Term Care Survey (NLTCS) and voting in the U.S. Congress. The model is shown to yield intuitive clustering results and it gives a much better fit than either latent class analysis or latent trait analysis alone.

In the recent years, the Web has been rapidly deepened with the prevalence of databases online. On this deep Web, many are structured by providing structured query interfaces and results. Organizing such structured into a domain hierarchy is one of the critical steps toward the integration of heterogeneous Web sources. We observe that, for structured Web sources, query schemas ie, attributes in query interfaces) are discriminative representatives of the and thus can be exploited for source characterization. In particular, by viewing query schemas as a type of categorical data, we abstract the problem of source organization into the clustering of categorical data. Our approach hypothesizes that homogeneous sources are characterized by the same hidden generative models for their schemas. To find clusters governed by such statistical distributions, we propose a new objective function, model-differentiation, which employs principled hypothesis testing to maximize statistical heterogeneity among clusters. Our evaluation over hundreds of real indicates that (1) the schema-based clustering accurately organizes by object domains eg, Books, Movies), and (2) on clustering Web query schemas, the model-differentiation function outperforms existing ones, such as likelihood, entropy, and context linkages, with the hierarchical agglomerative clustering algorithm.

In many real world data analysis tasks, it is expected to get much more useful knowledge by utilizing multiple databases stored in different organizations, such as cooperation groups, state organs and allied countries. However, in many such organizations, they often hesitate to publish their databases because of privacy and security issues although they believe the advantages of collaborative analysis. To utilize such multiple databases without fear of information leaks, a privacy preserving procedure was introduced to fuzzy clustering for categorical multivariate data (FCCM). This method deals with vertically partitioned databases, and several experimental results demonstrated that the method can contribute to revealing global intrinsic co-cluster structure rather than individual site-wise analysis. In this paper, site-wise confidence is introduced to the method to weaken harmful effects of insignificant sites for estimating stable intrinsic co-cluster structures. Site-wise confidence is measured with a degree of coincidence between site-wise object memberships and the global ones. Several experimental results show that site-wise confidence is useful for estimating reliable co-cluster structures.

The roots of the modern log-linear model approach to the analysis of cross-classified data in the form of multi-dimensional contingency tables can found in the work of S. N. Roy and his students in the 1950s at the University of North Carolina. These papers set the stage for two major sets of developments in the analysis of categorical data in the 1960s and 1970s. I describe some of these contributions, where they intersected and where they diverged in focus, and some subsequent advances, including the role of latent variables alternatives, mixed membership models, and methods for very large sparse categorical data arrays.

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

Knowledge discovery is the process of extracting useful and understandable patterns in data. A knowledge discovery process involves different learning methods in the data mining step or different model visualization methods in the post-processing phase. Among them, categorical data clustering has attracted much attention recently. While many algorithms for clustering categorical data have been proposed, some have low clustering accuracy while others have high computational complexity. In this paper, a visualization method of structured partial ordered attribute diagram for clustering categorical data is proposed based on the formal concept analysis theory. The structured partial ordered attribute diagram is constructed based on covering operations. Knowledge can be extracted from the hierarchies and clusters in a structured partial ordered attribute diagram. The method is applied to a famous formal context in formal concept analysis and a categorical dataset in UCI Machine Learning Repository. The results show that the structured partial ordered attribute diagram provides a new way for visual knowledge mining.

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.

The k-modes clustering algorithm is undoubtedly one of the most widely used partitional algorithms for categorical data. Unfortunately, due to its gradient descent nature, this algorithm is highly sensitive to the initialization of clustering. Categorical initialization methods have been proposed to address this problem. In this paper, we present an overview of initialization methods of clustering for numerical data and categorical data respectively with an emphasis on their computational efficiency. We then propose a new initialization method for categorical data, which can obtain the good initial cluster centers using the new distance base on the RD, and explore the methods of density and grid. Finally, proposed method has been tested on diagnosis dataset, a real world data set from UCI Machine Learning Repository, and been analyzed the experimental results, which illustrates that the proposed method is effective and efficient for initializing categorical data.