Categorical Data Sets Research Articles

SAR

Soft-set theory proposed by Molodstov is a general mathematic tool for dealing with uncertainty. Recently, several algorithms have been proposed for decision making using soft-set theory. However, these algorithms still concern on Boolean-valued information system. In this paper, Support Attribute Representative (SAR), a soft-set based technique for decision making in categorical-valued information system is proposed. The proposed technique has been tested on three datasets to select the best partitioning attribute. Furthermore, two UCI benchmark datasets are used to elaborate the performance of the proposed technique in term of executing time. On these two datasets, it is shown that SAR outperforms three rough set-based techniques TR, MMR, and MDA up to 95% and 50%, respectively. The results of this research will provide useful information for decision makers to handle categorical datasets.

A Cluster-Based Context-Tree Model for Multivariate Data Streams with Applications to Anomaly Detection

Many applications, such as telecommunication and commercial video broadcasting systems, computer and networks, and Web mining, require modeling data streams that exhibit context dependency. Context dependency refers to the fact that the statistical distribution of a new sample is heavily conditioned by a set of the most recent samples that precedes it. However, statistical models such as context trees (CTs) that capture context dependency tend to be poorly scalable. This paper proposes a solution to the scalability problem of these models by transforming a data stream into high-level aggregates of clusters instead of modeling the original data stream. Using an information-theoretical approach, we leverage existing clustering techniques for static categorical data sets to capture dynamic data streams based on the CT models. Because the proposed approach can be applied repeatedly on different levels of a clustering hierarchy, it is suitable for predicting trends and detecting anomalies at any aggregate (or detail) level required. Experimental results, including video stream modeling, network intrusion detection, and Monte Carlo simulations, show that the proposed method is efficient in capturing high-level aggregates of large-scale dynamic systems and very effective for trend prediction and anomaly detection.

CBDL: Context-based distance learning for categorical attributes

Distance learning is an important notion and has played a critical role in success of various machine learning algorithms. Any learning algorithm that requires dissimilarity/similarity measures has to assume some forms of distance functions, either explicitly or implicitly. Hence, in recent years a considerable amount of research has been devoted to distance learning. Despite great achievements in this field, a number of important issues need to be further explored for real world datasets mainly containing categorical attributes. Based on these considerations, the current research presents a Context-Based Distance Learning approach (CBDL) to advance the state of the art existing researches on distance metric learning for categorical datasets. CBDL is designed and developed based on the idea that distance between two values of a given categorical attribute can be estimated by using information inherently exists within subset of attributes called context. CBDL composes of two main components: context extraction component and distance learning component. Context extraction component is responsible for extracting the relevant subset of feature set for a given attribute, while distance learning component tries to learn distance between each pair of values based on the extracted context. To have a comprehensive analysis, we conduct wide range of experiments in both supervised and unsupervised environments in the presence of noise. Our experimental results reveal that CBDL is the method of choice distance learning approach by offering a comparable or better performance compared to the state of the art existing distance learning schemes according to studied evaluation measures. © 2011 Wiley Periodicals, Inc. © 2011 Wiley Periodicals, Inc.

A novel attribute weighting algorithm for clustering high-dimensional categorical data

Due to data sparseness and attribute redundancy in high-dimensional data, clusters of objects often exist in subspaces rather than in the entire space. To effectively address this issue, this paper presents a new optimization algorithm for clustering high-dimensional categorical data, which is an extension of the k-modes clustering algorithm. In the proposed algorithm, a novel weighting technique for categorical data is developed to calculate two weights for each attribute (or dimension) in each cluster and use the weight values to identify the subsets of important attributes that categorize different clusters. The convergence of the algorithm under an optimization framework is proved. The performance and scalability of the algorithm is evaluated experimentally on both synthetic and real data sets. The experimental studies show that the proposed algorithm is effective in clustering categorical data sets and also scalable to large data sets owning to its linear time complexity with respect to the number of data objects, attributes or clusters.

Revisiting Kappa to account for change in the accuracy assessment of land-use change models

Land-use change models are typically calibrated to reproduce known historic changes. Calibration results can then be assessed by comparing two datasets: the simulated land-use map and the actual land-use map at the same time. A common method for this is the Kappa statistic, which expresses the agreement between two categorical datasets corrected for the expected agreement. This expected agreement is based on a stochastic model of random allocation given the distribution of class sizes. However, when a model starts from an initial land-use map and makes changes to it, that stochastic model does not pose a meaningful reference level. This paper introduces K Simulation, a statistic that is identical in form to the Kappa statistic but instead applies a more appropriate stochastic model of random allocation of class transitions relative to the initial map. The new method is illustrated on a simple example and then the results of the Kappa statistic and K Simulation are compared using the results of a land-use model. It is found that only K Simulation truly tests models in their capacity to explain land-use changes over time, and unlike Kappa it does not inflate results for simulations where little change takes place over time.

A k-means type clustering algorithm for subspace clustering of mixed numeric and categorical datasets

Almost all subspace clustering algorithms proposed so far are designed for numeric datasets. In this paper, we present a k-means type clustering algorithm that finds clusters in data subspaces in mixed numeric and categorical datasets. In this method, we compute attributes contribution to different clusters. We propose a new cost function for a k-means type algorithm. One of the advantages of this algorithm is its complexity which is linear with respect to the number of the data points. This algorithm is also useful in describing the cluster formation in terms of attributes contribution to different clusters. The algorithm is tested on various synthetic and real datasets to show its effectiveness. The clustering results are explained by using attributes weights in the clusters. The clustering results are also compared with published results.

A fuzzy multi-objective particle swarm optimization for effective data clustering

Data clustering, also called unsupervised learning, is a fundamental issue in data mining that is used to understand and mine the structure of an untagged assemblage of data into separate groups based on their similarity. Recent studies have shown that clustering techniques that optimize a single objective may not provide satisfactory result because no single validity measure works well on different kinds of data sets. Moreover, the performance of clustering algorithms degrades with more and more overlaps among clusters in a data set. These facts have motivated us to develop a fuzzy multi-objective particle swarm optimization framework in an innovative fashion for data clustering, termed as FMOPSO, which is able to deliver more effective results than state-of-the-art clustering algorithms. The key challenge in designing FMOPSO framework for data clustering is how to resolve cluster assignments confusion with such points in the data set which have significant belongingness to more than one cluster. The proposed framework addresses this problem by identification of points having significant membership to multiple classes, excluding them, and re-classifying them into single class assignments. To ascertain the superiority of the proposed algorithm, statistical tests have been performed on a variety of numerical and categorical real life data sets. Our empirical study shows that the performance of the proposed framework (in both terms of efficiency and effectiveness) significantly outperforms the state-of-the-art data clustering algorithms.

Integrating Clustering and Supervised Learning for Categorical Data Analysis

The problem of fuzzy clustering of categorical data, where no natural ordering among the elements of a categorical attribute domain can be found, is an important problem in exploratory data analysis. As a result, a few clustering algorithms with focus on categorical data have been proposed. In this paper, a modified differential evolution (DE)-based fuzzy c-medoids (FCMdd) clustering of categorical data has been proposed. The algorithm combines both local as well as global information with adaptive weighting. The performance of the proposed method has been compared with those using genetic algorithm, simulated annealing, and the classical DE technique, besides the FCMdd, fuzzy k-modes, and average linkage hierarchical clustering algorithm for four artificial and four real life categorical data sets. Statistical test has been carried out to establish the statistical significance of the proposed method. To improve the result further, the clustering method is integrated with a support vector machine (SVM), a well-known technique for supervised learning. A fraction of the data points selected from different clusters based on their proximity to the respective medoids is used for training the SVM. The clustering assignments of the remaining points are thereafter determined using the trained classifier. The superiority of the integrated clustering and supervised learning approach has been demonstrated.

Hierarchical log linear analysis of admission blood parameters and clinical outcome following traumatic brain injury

Numerous statistical methods have been utilised to generate predictive models that identify clinical and biochemical parameters of prognostic value following traumatic brain injury. While these methods provide an accurate statistical description between these variables and outcome, they are difficult to interpret intuitively. Hierarchical log linear analysis can be utilised to present the complex interactions between these variables and outcome visually. We compiled a database of 327 traumatic brain injury patients, their admission blood parameters, clinical admission parameters, and 6-month Glasgow Outcome Score. Seven variables (age, injury severity, Glasgow Coma Score, glucose, albumin, haemoglobin, white cell count) that correlated with outcome in a univariate analysis and two further variables, included on the basis of biological plausibility, (abnormal clotting and magnesium) were used to derive and present a hierarchical log linear model. Seventeen (out of an original forty-five possible) inter-relationships between the chosen variables were identified as remaining in the hierarchical log linear model. This data is presented pictorially in a hierarchy demonstrating the directness of the statistical association between each of the variables and dichotomised outcome. Four variables within the hierarchical log linear model (age, raised serum glucose, low haemoglobin, Glasgow Coma Score) had a direct independent statistical relationship with outcome. The remaining five variables only had a statistical relationship with outcome via at least one other variable. Hierarchical log linear analysis allows the presentation of multivariate, categorical data sets in a pictorial and more easily interpretable fashion.

Reconstructability Analysis as a Tool for Identifying Gene-Gene Interactions in Studies of Human Diseases

There are a number of common human diseases for which the genetic component may include an epistatic interaction of multiple genes. Detecting these interactions with standard statistical tools is difficult because there may be an interaction effect, but minimal or no main effect. Reconstructability analysis (RA) uses Shannon's information theory to detect relationships between variables in categorical datasets. We applied RA to simulated data for five different models of gene-gene interaction, and find that even with heritability levels as low as 0.008, and with the inclusion of 50 non-associated genes in the dataset, we can identify the interacting gene pairs with an accuracy of > or =80%. We applied RA to a real dataset of type 2 non-insulin-dependent diabetes (NIDDM) cases and controls, and closely approximated the results of more conventional single SNP disease association studies. In addition, we replicated prior evidence for epistatic interactions between SNPs on chromosomes 2 and 15.

Multiple correspondence analysis for “tall” data sets

Correspondence Analysis (CA) is a statistical method aiming at the graphical representation of the contingencies between the rows and the columns of a categorical data set. A critical step of the CA algorithm is the Singular Value Decomposition (SVD) analysis of a coded matrix. The size of this matrix affects drastically the analysis computational cost. As the size of the matrix increases, the method becomes computationally expensive or even impossible. In this paper we propose an alternative scheme that overpasses this limitation, without affecting the results accuracy. A set of Monte Carlo simulations and real data applications showed the efficiency of the proposed approach over the standard one, especially in the case of tall data sets.

Multiobjective Genetic Algorithm-Based Fuzzy Clustering of Categorical Attributes

Recently, the problem of clustering categorical data, where no natural ordering among the elements of a categorical attribute domain can be found, has been gaining significant attention from researchers. With the growing demand for categorical data clustering, a few clustering algorithms with focus on categorical data have recently been developed. However, most of these methods attempt to optimize a single measure of the clustering goodness. Often, such a single measure may not be appropriate for different kinds of datasets. Thus, consideration of multiple, often conflicting, objectives appears to be natural for this problem. Although we have previously addressed the problem of multiobjective fuzzy clustering for continuous data, these algorithms cannot be applied for categorical data where the cluster means are not defined. Motivated by this, in this paper a multiobjective genetic algorithm-based approach for fuzzy clustering of categorical data is proposed that encodes the cluster modes and simultaneously optimizes fuzzy compactness and fuzzy separation of the clusters. Moreover, a novel method for obtaining the final clustering solution from the set of resultant Pareto-optimal solutions in proposed. This is based on majority voting among Pareto front solutions followed by <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -nn classification. The performance of the proposed fuzzy categorical data-clustering techniques has been compared with that of some other widely used algorithms, both quantitatively and qualitatively. For this purpose, various synthetic and real-life categorical datasets have been considered. Also, a statistical significance test has been conducted to establish the significant superiority of the proposed multiobjective approach.

Differentiating Categories and Dimensions: Evaluating the Robustness of Taxometric Analyses

Interest in modeling the structure of latent variables is gaining momentum, and many simulation studies suggest that taxometric analysis can validly assess the relative fit of categorical and dimensional models. The generation and parallel analysis of categorical and dimensional comparison data sets reduces the subjectivity required to interpret results by providing an objective Comparison Curve Fit Index (CCFI). This study takes advantage of developments in the generation of comparison data to examine the robustness of taxometric analyses to unfavorable data conditions. Very large comparison data sets are treated as populations from which many samples are drawn randomly, placing the method on a firmer statistical foundation and increasing its run-time efficiency. The impressive accuracy of the CCFI was consistent with prior findings and robust across novel manipulations of asymmetry, tail weight, and heterogeneous variances. Analyses, an empirical illustration using Minnesota Multiphasic Personality Inventory (MMPI) hypochondriasis data, and discussion focus on the practical implications for differentiating categories and dimensions.

A taxometric study of alcohol abuse and dependence in a general population sample: evidence of dimensional latent structure and implications for DSM-V

To explore, with the aid of taxometric analysis, whether alcohol abuse and alcohol dependence are each conceptualized most effectively as single latent dimensions or distinct latent categories. Data were taken from a nationally representative cross-sectional epidemiological survey of psychiatric and substance use disorders. General population of Australia. A subsample of all respondents who had consumed at least 12 drinks in the year prior to the survey and who had consumed at least three drinks on at least one single day (n = 4920 of a possible 10,641). DSM-IV criteria for alcohol abuse and dependence were assessed with the Composite International Diagnostic Interview, version 2.1. Two independent taxometric procedures, MAXimum EIGenvalue (MAXEIG) and mean above minus below a cut (MAMBAC), together with analysis of simulated dimensional and categorical data sets, were carried out. Findings Consistent evidence was found for a single latent dimension underlying the symptoms of alcohol dependence. Less consistent evidence of dimensionality was found for the symptoms of alcohol abuse. These findings support the growing consensus regarding the need for continuous measures of alcohol use disorders to complement the traditional categorical representations in upcoming versions of the major psychiatric classification systems.

A new fuzzy k-modes clustering algorithm for categorical data

This correspondence describes extensions to the fuzzy k-modes algorithm for clustering categorical data. We modify a simple matching dissimilarity measure for categorical objects, which allows the use of the fuzzy k-modes paradigm to obtain a cluster with strong intra-similarity, and to efficiently cluster large categorical data sets. We derive rigorously the updating formula of the fuzzy k-modes clustering algorithm with the new dissimilarity measure, and the convergence of the algorithm under the optimisation framework. Experimental results are presented to illustrate that the effectiveness of the new fuzzy k modes algorithm is better than those of the other existing k-modes algorithms.

Identification and Analysis of Co-Occurrence Networks with NetCutter

BackgroundCo-occurrence analysis is a technique often applied in text mining, comparative genomics, and promoter analysis. The methodologies and statistical models used to evaluate the significance of association between co-occurring entities are quite diverse, however.Methodology/Principal FindingsWe present a general framework for co-occurrence analysis based on a bipartite graph representation of the data, a novel co-occurrence statistic, and software performing co-occurrence analysis as well as generation and analysis of co-occurrence networks. We show that the overall stringency of co-occurrence analysis depends critically on the choice of the null-model used to evaluate the significance of co-occurrence and find that random sampling from a complete permutation set of the bipartite graph permits co-occurrence analysis with optimal stringency. We show that the Poisson-binomial distribution is the most natural co-occurrence probability distribution when vertex degrees of the bipartite graph are variable, which is usually the case. Calculation of Poisson-binomial P-values is difficult, however. Therefore, we propose a fast bi-binomial approximation for calculation of P-values and show that this statistic is superior to other measures of association such as the Jaccard coefficient and the uncertainty coefficient. Furthermore, co-occurrence analysis of more than two entities can be performed using the same statistical model, which leads to increased signal-to-noise ratios, robustness towards noise, and the identification of implicit relationships between co-occurring entities. Using NetCutter, we identify a novel protein biosynthesis related set of genes that are frequently coordinately deregulated in human cancer related gene expression studies. NetCutter is available at http://bio.ifom-ieo-campus.it/NetCutter/).ConclusionOur approach can be applied to any set of categorical data where co-occurrence analysis might reveal functional relationships such as clinical parameters associated with cancer subtypes or SNPs associated with disease phenotypes. The stringency of our approach is expected to offer an advantage in a variety of applications.

“Best K”: critical clustering structures in categorical datasets

The demand on cluster analysis for categorical data continues to grow over the last decade. A well-known problem in categorical clustering is to determine the best K number of clusters. Although several categorical clustering algorithms have been developed, surprisingly, none has satisfactorily addressed the problem of best K for categorical clustering. Since categorical data does not have an inherent distance function as the similarity measure, traditional cluster validation techniques based on geometric shapes and density distributions are not appropriate for categorical data. In this paper, we study the entropy property between the clustering results of categorical data with different K number of clusters, and propose the BKPlot method to address the three important cluster validation problems: (1) How can we determine whether there is significant clustering structure in a categorical dataset? (2) If there is significant clustering structure, what is the set of candidate “best Ks”? (3) If the dataset is large, how can we efficiently and reliably determine the best Ks?

Genetic basis of variation in tenofovir drug susceptibility in HIV-1

To develop an improved model for the genetic basis of reduced susceptibility to tenofovir in vitro. A dataset of 532 HIV-1 subtype B reverse transcriptase genotypes for which matched phenotypic susceptibility data were available was assembled, both as a continuous (transformed) dataset and a categorical dataset generated by imposing a cut-off on the basis of earlier studies of in-vivo response of 1.4-fold. Models were generated using stepwise regression, decision tree and random forest approaches on both the continuous and categorical data. Models were compared by mean squared error (continuous models), or by misclassification rates by nested crossvalidation. From the continuous dataset, stepwise linear regression, regression tree and regression forest methods yielded models with MSE of 0.46, 0.48 and 0.42 respectively. Amino acids 215, 65, 41, 67, 184 and 151 in HIV-1 reverse transcriptase were identified in all three models and amino acid 210 in two. The categorical data yielded logistic regression, classification tree and forest models with misclassification rates of 26, 24 and 23%, respectively. Amino acids 215, 65 and 67 appeared in all; 41, 184, 210 and 151 were also included in the classification forest model. The random forests approach has yielded a substantial improvement in the available models to describe the genetic basis of reduced susceptibility to tenofovir in vitro. The most important sites in these models are amino acid sites 215, 65, 41, 67, 184, 151 and 210 in HIV-1 reverse transcriptase.

A genetic fuzzy [formula omitted]-Modes algorithm for clustering categorical data

The fuzzy k-Modes algorithm introduced by Huang and Ng [Huang, Z., & Ng, M. (1999). A fuzzy k-modes algorithm for clustering categorical data. IEEE Transactions on Fuzzy Systems, 7(4), 446–452] is very effective for identifying cluster structures from categorical data sets. However, the algorithm may stop at locally optimal solutions. In order to search for appropriate fuzzy membership matrices which can minimize the fuzzy objective function, we present a hybrid genetic fuzzy k-Modes algorithm in this paper. To circumvent the expensive crossover operator in genetic algorithms (GAs), we hybridize GA with the fuzzy k-Modes algorithm and define the crossover operator as a one-step fuzzy k-Modes algorithm. Experiments on two real data sets are carried out to illustrate the performance of the proposed algorithm.

Standardization of Borehole Data to Support Vadose Zone Flow and Transport Modeling

Numerical representation of the geologic framework and its hydrologic and geochemical properties is an integral part of all vadose zone flow‐and‐transport modeling. Historically, the geologic framework has been represented by simple homogeneous and horizontally stratified hydrogeologic units. However, as computer‐processing capabilities have become more advanced, there has been more emphasis on improving spatial resolution and quantifying uncertainty in key model parameters. One of the more popular approaches has focused on geostatistical simulation of the flow‐and‐transport properties themselves, with little regard to the geologic strata and sedimentary sequences. Newer approaches are focusing more on geostatistical simulation of the sequence‐stratigraphic relations of lithofacies and the geostatistical distributions of flow‐and‐transport properties within those facies. These approaches require more rigorous quantitative treatment of geologic data than is normally supported by the mostly qualitative nature of borehole geologic information. At the USDOE Hanford Site, efforts are being made to standardize borehole geologic data so they can be used in a systematic and quantitative way to define the spatial distribution of flow‐and‐transport properties in support of vadose zone flow‐and‐transport simulations. New detailed procedures translate qualitative descriptive information into categorical data and inconsistent quantitative and semiquantitative data into common parametric data sets. A geologic data‐management system is being developed to manage and integrate these standardized categorical data sets with other existing databases to support synergistic analysis and to improve numerical representation of the hydrogeologic architecture. These standardized data sets were used to develop lithofacies‐based geostatistical representations of hydraulic conductivity beneath one of Hanford's more complex waste sites.