MMeNR: Neighborhood rough set theory based algorithm for clustering heterogeneous data
01 Mar 2017-pp 323-328
TL;DR: The MMeR algorithm with neighbourhood relations is generalized and made a neighbourhood rough set model which it is called MMeNR (Min Mean Neighborhood Roughness), which takes care of the heterogeneous data and also the uncertainty associated with it.
Abstract: In recent times enumerable number of clustering algorithms have been developed whose main function is to make sets of objects having almost the same features. But due to the presence of categorical data values, these algorithms face a challenge in their implementation. Also some algorithms which are able to take care of categorical data are not able to process uncertainty in the values and so have stability issues. Thus handling categorical data along with uncertainty has been made necessary owing to such difficulties. So, in 2007 MMR [1] algorithm was developed which was based on basic rough set theory. MMeR [2] was proposed in 2009 which surpassed the results of MMR in taking care of categorical data. It has the capability of handling heterogeneous data but only to a limited extent because it is based on classical rough set model. In this paper, we generalize the MMeR algorithm with neighbourhood relations and make it a neighbourhood rough set model which we call MMeNR (Min Mean Neighborhood Roughness). It takes care of the heterogeneous data and also the uncertainty associated with it. Standard data sets have been used to gauge its effectiveness over the other methods.
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01 Jan 2012
139,059 citations
"MMeNR: Neighborhood rough set theor..." refers methods in this paper
...In 2009 Tripathy et al [2] [17] [22] extended the MMR to MMeR algorithm and got a much higher clustering accuracy....
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...In comparison to MMR the MMeR algorithm had higher accuracy in doing the same process....
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...Keywords- Neighborhood; MMeNR; Clustering; Uncertainty; MMR; MMeR; I. INTRODUCTION Making sets of data which are analogous to each other is the prime notion of clustering....
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...Parmar proposed in [1] the MMR or Min-Min-Roughness algorithm....
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...So, in 2007 MMR [1] algorithm was developed which was based on basic rough set theory....
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49,597 citations
TL;DR: In this article, the authors present an overview of the basic concepts of multivariate analysis, including matrix algebra and random vectors, as well as a strategy for analyzing multivariate models.
Abstract: (NOTE: Each chapter begins with an Introduction, and concludes with Exercises and References.) I. GETTING STARTED. 1. Aspects of Multivariate Analysis. Applications of Multivariate Techniques. The Organization of Data. Data Displays and Pictorial Representations. Distance. Final Comments. 2. Matrix Algebra and Random Vectors. Some Basics of Matrix and Vector Algebra. Positive Definite Matrices. A Square-Root Matrix. Random Vectors and Matrices. Mean Vectors and Covariance Matrices. Matrix Inequalities and Maximization. Supplement 2A Vectors and Matrices: Basic Concepts. 3. Sample Geometry and Random Sampling. The Geometry of the Sample. Random Samples and the Expected Values of the Sample Mean and Covariance Matrix. Generalized Variance. Sample Mean, Covariance, and Correlation as Matrix Operations. Sample Values of Linear Combinations of Variables. 4. The Multivariate Normal Distribution. The Multivariate Normal Density and Its Properties. Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation. The Sampling Distribution of 'X and S. Large-Sample Behavior of 'X and S. Assessing the Assumption of Normality. Detecting Outliners and Data Cleaning. Transformations to Near Normality. II. INFERENCES ABOUT MULTIVARIATE MEANS AND LINEAR MODELS. 5. Inferences About a Mean Vector. The Plausibility of ...m0 as a Value for a Normal Population Mean. Hotelling's T 2 and Likelihood Ratio Tests. Confidence Regions and Simultaneous Comparisons of Component Means. Large Sample Inferences about a Population Mean Vector. Multivariate Quality Control Charts. Inferences about Mean Vectors When Some Observations Are Missing. Difficulties Due To Time Dependence in Multivariate Observations. Supplement 5A Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids. 6. Comparisons of Several Multivariate Means. Paired Comparisons and a Repeated Measures Design. Comparing Mean Vectors from Two Populations. Comparison of Several Multivariate Population Means (One-Way MANOVA). Simultaneous Confidence Intervals for Treatment Effects. Two-Way Multivariate Analysis of Variance. Profile Analysis. Repealed Measures, Designs, and Growth Curves. Perspectives and a Strategy for Analyzing Multivariate Models. 7. Multivariate Linear Regression Models. The Classical Linear Regression Model. Least Squares Estimation. Inferences About the Regression Model. Inferences from the Estimated Regression Function. Model Checking and Other Aspects of Regression. Multivariate Multiple Regression. The Concept of Linear Regression. Comparing the Two Formulations of the Regression Model. Multiple Regression Models with Time Dependant Errors. Supplement 7A The Distribution of the Likelihood Ratio for the Multivariate Regression Model. III. ANALYSIS OF A COVARIANCE STRUCTURE. 8. Principal Components. Population Principal Components. Summarizing Sample Variation by Principal Components. Graphing the Principal Components. Large-Sample Inferences. Monitoring Quality with Principal Components. Supplement 8A The Geometry of the Sample Principal Component Approximation. 9. Factor Analysis and Inference for Structured Covariance Matrices. The Orthogonal Factor Model. Methods of Estimation. Factor Rotation. Factor Scores. Perspectives and a Strategy for Factor Analysis. Structural Equation Models. Supplement 9A Some Computational Details for Maximum Likelihood Estimation. 10. Canonical Correlation Analysis Canonical Variates and Canonical Correlations. Interpreting the Population Canonical Variables. The Sample Canonical Variates and Sample Canonical Correlations. Additional Sample Descriptive Measures. Large Sample Inferences. IV. CLASSIFICATION AND GROUPING TECHNIQUES. 11. Discrimination and Classification. Separation and Classification for Two Populations. Classifications with Two Multivariate Normal Populations. Evaluating Classification Functions. Fisher's Discriminant Function...nSeparation of Populations. Classification with Several Populations. Fisher's Method for Discriminating among Several Populations. Final Comments. 12. Clustering, Distance Methods and Ordination. Similarity Measures. Hierarchical Clustering Methods. Nonhierarchical Clustering Methods. Multidimensional Scaling. Correspondence Analysis. Biplots for Viewing Sample Units and Variables. Procustes Analysis: A Method for Comparing Configurations. Appendix. Standard Normal Probabilities. Student's t-Distribution Percentage Points. ...c2 Distribution Percentage Points. F-Distribution Percentage Points. F-Distribution Percentage Points (...a = .10). F-Distribution Percentage Points (...a = .05). F-Distribution Percentage Points (...a = .01). Data Index. Subject Index.
10,148 citations
Journal Article•
4,506 citations
TL;DR: Two algorithms which extend the k-means algorithm to categorical domains and domains with mixed numeric and categorical values are presented and are shown to be efficient when clustering large data sets, which is critical to data mining applications.
Abstract: The k-means algorithm is well known for its efficiency in clustering large data sets. However, working only on numeric values prohibits it from being used to cluster real world data containing categorical values. In this paper we present two algorithms which extend the k-means algorithm to categorical domains and domains with mixed numeric and categorical values. The k-modes algorithm uses a simple matching dissimilarity measure to deal with categorical objects, replaces the means of clusters with modes, and uses a frequency-based method to update modes in the clustering process to minimise the clustering cost function. With these extensions the k-modes algorithm enables the clustering of categorical data in a fashion similar to k-means. The k-prototypes algorithm, through the definition of a combined dissimilarity measure, further integrates the k-means and k-modes algorithms to allow for clustering objects described by mixed numeric and categorical attributes. We use the well known soybean disease and credit approval data sets to demonstrate the clustering performance of the two algorithms. Our experiments on two real world data sets with half a million objects each show that the two algorithms are efficient when clustering large data sets, which is critical to data mining applications.
2,289 citations
"MMeNR: Neighborhood rough set theor..." refers methods in this paper
...Clustering is used to make small subsets which can be easily managed, analysed and taken care of by segmenting large hybrid data sets [3]....
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