Categorical Data Sets Research Articles

Applying GMDH algorithm to extract rules from examples

This article reports a new approach to rule extraction method by using Group Method of Data Handling (GMDH) Algorithm in Data Mining area. The advantages of this method are (1) it accepts both categorical and continuous data at the same time, and (2) rules can be extracted easily from the generated model.We applied GMDH Algorithm to categorical data set of US congress voting records to extract rules. The correction rate of GMDH rules was 97.3% -- higher than Tsukimoto's method of rule extraction from Back-propagation neural network (81.0%). It was also higher than 97.0% of C4.5.

Matrix2png: a utility for visualizing matrix data.

We describe a simple software tool, 'matrix2png', for creating color images of matrix data. Originally designed with the display of microarray data sets in mind, it is a general tool that can be used to make simple visualizations of matrices for use in figures, web pages, slide presentations and the like. It can also be used to generate images 'on the fly' in web applications. Both continuous-valued and discrete-valued (categorical) data sets can be displayed. Many options are available to the user, including the colors used, the display of row and column labels, and scale bars. In this note we describe some of matrix2png's features and describe some places it has been useful in the authors' work. A simple web interface is available, and Unix binaries are available from http://microarray.cpmc.columbia.edu/matrix2png. Source code is available on request.

Fast ordering of large categorical datasets for visualization

An important issue in visualizing categorical data is how to order categorical values -- non-numeric values that do not have a natural ordering, which makes it difficult to map them to visual coordinates. The focus of this paper is on constructing categorical orderings efficiently without compromising their visual quality. In order to avoid the inherent intractability of previous discrete formulations, we consider a continuous relaxation of the problem solvable exactly using the spectral method. The latter is based on computing certain algebraic information about the similarity matrix of the dataset. However, even computing the similarity matrix itself is prohibitive for large datasets. In order to achieve greater efficiency, we propose a new multi-level scheme based on an approximate representation of the matrix. We show that it sufficient to compute only a small portion of the matrix of size linear in the number of objects, as opposed to quadratic, to guarantee a small probability of approximation error. Thus an effective ordering can be constructed without actually having to compute {\it most} pairwise similarities of values. Experiments have been conducted to qualitatively verify the effectiveness of resulting visualizations.

Exact credal treatment of missing data

This paper proposes an exact, no-assumptions approach to dealing with incomplete sets of multivariate categorical data. An incomplete data set is regarded as a finite collection of complete data sets, and a joint distribution is obtained from each of them, at a descriptive level. The tools to simultaneously treat all the possible joint distributions compatible with an incomplete set of data are given. In particular, a linear description of the set of distributions is formulated, and it is shown that the computation of bounds on the expectation of real-valued functions under such distributions is both possible and efficient, by means of linear programming. Specific algorithms are also developed whose complexity grows linearly in the number of observations. An analysis is then carried out to estimate population probabilities from incomplete multinomial samples. The descriptive tool extends in a straightforward way to the inferential problem by exploiting Walley's imprecise Dirichlet model.

Data Visualization through Graph Drawing

In this paper the problem of visualizing categorical multivariate data sets is considered. By representing the data as the adjacency matrix of an appropriately defined bipartite graph, the problem is transformed to one of graph drawing. A general graph drawing framework is introduced, the corresponding mathematical problem defined and an algorithmic approach for solving the necessary optimization problem discussed. The new approach is illustrated through several examples.

Using log-linear models to analyse categorical data

This paper provides a brief introduction to log-linear modelling that is designed to be accessible to readers with a cursory knowledge of elementary statistics. Log-linear models belong to the family of general linear models and they are generally regarded as the method of choice for analysing the associations between variables in large sets of categorical data. The primary objective of using log-linear modelling procedures is usually to identify the simplest model that fits the data adequately, although in some instances more than one model may be acceptable. The main drawback of using log-linear models is that the procedures require very large data sets. A case study illustrates that, even with a relatively large sample, problems may arise if the data are unevenly distributed.

K-MEANS-TYPE ALGORITHMS ON DISTRIBUTED MEMORY COMPUTER

Partitioning a set of objects into homogeneous clusters is a fundamental operation in data mining. The k-means-type algorithm is best suited for implementing this operation because of its efficiency in clustering large numerical and categorical data sets. An efficient parallel k-means-type algorithm for clustering data sets on a distributed share-nothing parallel system is considered. It has a simple communication scheme which performs only one round of information exchange in every iteration. We show that the speedup of our algorithm is asymptotically linear when the number of objects is sufficiently large. We implement the parallel k-means-type algorithm on an IBM SP2 parallel machine. The performance studies show that the algorithm has nice parallelism in experiments.

Data signatures and visualization of scientific data sets

Today, as data sets used in computations grow in size and complexity, the technologies developed over the years to deal with scientific data sets have become less efficient and effective. Many frequently used operations, such as eigenvector computation, could quickly exhaust our desktop workstations once the data size reaches certain limits. On the other hand, the high-dimensional data sets we collect every day don't relieve the problem. Many conventional metric designs that build on quantitative or categorical data sets cannot be applied directly to heterogeneous data sets with multiple data types. While building new machines with more resources might conquer the data size problems, the complexity of today's computations requires a new breed of projection techniques to support analysis of the data and verification of the results. We introduce the concept of a data signature, which captures the essence of a scientific data set in a compact format, and use it to conduct analysis as if using the original. A time-dependent climate simulation data set demonstrates our approach and presents the results.

A fuzzy k-modes algorithm for clustering categorical data

This correspondence describes extensions to the fuzzy k-means algorithm for clustering categorical data. By using a simple matching dissimilarity measure for categorical objects and modes instead of means for clusters, a new approach is developed, which allows the use of the k-means paradigm to efficiently cluster large categorical data sets. A fuzzy k-modes algorithm is presented and the effectiveness of the algorithm is demonstrated with experimental results.

Modeling of global change phenomena with GIS using the global change data base. II: Prototype synthesis of the AVHRR-based vegetation index from terrestrial data

Part I of this article reviewed an approach to modeling in scientific geographic information systems (GIS) by digitally synthesizing environmental parameters or phenomena as functions of other data. This interactive approach to global environmental modeling complements the approach of dynamic process models while enabling the scientist to rigorously assess the character of data used as boundary conditions in other models on widely available personal computers and workstations. Part II presents a case history using existing GISs to recreate the AVHRR-based vegetation index using data derived from in situ study on the Earth's surface. The example explores the relationship between the global vegetation index and ecosystems, soils, and precipitation, and defects in our present ability to describe these features. The degree of success of the model shows that GIS and the global change data base can be effective modeling tools, especially when functions are added to enhance the modeling capabilities of GIS. One function, INDEX, developed for this case history, is a simple utility that models a single data set as a function of another data set. A second function THEMCOIN, takes two input categorical data sets, such as vegetation and soils maps, and computes the mean and standard deviation of a third input data set of numerical values, such as elevation, precipitation, or vegetation index computed from AVHRR data. THEMCOIN outputs a table of these empirical relationships. It also optionally models the numerical data set based on correlations with the categorical data sets. Both of these functions facilitate environmental modeling in GIS. The models begin to approximate vegetation index as a function of ecosystem, precipitation, and soils. Statistical output from the models extends our understanding of relationships between environmental parameters.

Factors affecting the fruiting of bilberries: an analysis of categorical data set

The present study is an application of categorical data analysis in ecological research. The approach is based on logistic regression following an exploratory graphical analysis. The material was collected in an extensive forest inventory in which a set of observations was made by eye in a stratified random sample of 262 mature upland forest stands in South Finland. The problem was to interpret the variation in the fertility of the tillers of bilberry (Vaccinium myrtillus). In the field, the fertility was recorded as a three-class ordinal variable. The information available for the interpretation included the visually estimated density of the tree crowns, the soil fertility class determined using Cajander's forest site types and the percent cover of V. myrtillus.

Exponential family non‐linear models for categorical data with errors of observation

AbstractWe present a general framework for treating categorical data with errors of observation. We show how both latent class models and models for doubly sampled data can be treated as exponential family nonlinear models. These are extended generalized linear models with the link function substituted by an observationwise defined non‐linear function of the model parameters. The models are formulated in terms of structural probabilities and conditional error probabilities, thus allowing natural constraints when modelling errors of observation. We use an iteratively reweighted least squares procedure for obtaining maximum likelihood estimates. This is faster than the traditionally used EM algorithm and the computations can be made in GLIM.1 As examples we analyse three sets of categorical data with errors of observation which have been analysed before by Ashford and Sowden,2 Goodman3 and Chen,4 respectively.

Log-linear models, screening and regional industrial surveys

Upton G. J. G. (1981) Log-linear models, screening and regional industrial surveys, Reg. Studies 15, 33–45. This paper uses hierarchical log-linear models to analyse a set of cross-classified categorical data obtained from a recent regional industrial survey of Northern Ireland. The data constitute a complete 27 table. Selection of an appropriate model is facilitated by use of the screening technique advocated by Brown (1976). In the analysis a clear distinction is drawn between factors and responses, and attention is concentrated on locating the factor-response interactions of likely significance. The paper is intended as a companion to that of Wrigley (1980) who performs a logit analysis of the same data.

Clinical Pure Types as a Fuzzy Partition

Abstract This paper discusses the applicability of the ideas of fuzzy sets and grades of membership to problems encountered in the quantification of clinical (i.e., diagnostic and prognostic) judgment. The methods of constrained maximum likelihood are used to derive consensus estimates of grades of membership given a set of categorical data and an a priori set of specified pure types. A numerical example is given.