scholarly journals Mixture-based Clustering for the Ordered Stereotype Model

2021 ◽  
Author(s):  
◽  
Daniel Fernández Martínez
Keyword(s):  
Count Data ◽  
Ordinal Data ◽  
Finite Mixture Models ◽  
Probability Model ◽  
Model Fitting ◽  
Real Data ◽  
Information Criteria ◽  
Categorical Variables ◽  
Clustering Methods ◽  
Data Set

<p>Many of the methods which deal with the reduction of dimensionality in matrices of data are based on mathematical techniques. In general, it is not possible to use statistical inferences or select the appropriateness of a model via information criteria with these techniques because there is no underlying probability model. Furthermore, the use of ordinal data is very common (e.g. Likert or Braun-Blanquet scale) and the clustering methods in common use treat ordered categorical variables as nominal or continuous rather than as true ordinal data. Recently a group of likelihood-based finite mixture models for binary or count data has been developed (Pledger and Arnold, 2014). This thesis extends this idea and establishes novel likelihood-based multivariate methods for data reduction of a matrix containing ordinal data. This new approach applies fuzzy clustering via finite mixtures to the ordered stereotype model (Fernández et al., 2014a). Fuzzy allocation of rows and columns to corresponding clusters is achieved by performing the EM algorithm, and also Bayesian model fitting is obtained by performing a reversible jump MCMC sampler. Their performances for one-dimensional clustering are compared. Simulation studies and three real data sets are used to illustrate the application of these approaches and also to present novel data visualisation tools for depicting the fuzziness of the clustering results for ordinal data. Additionally, a simulation study is set up to empirically establish a relationship between our likelihood-based methodology and the performance of eleven information criteria in common use. Finally, clustering comparisons between count data and categorising the data as ordinal over a same data set are performed and results are analysed and presented.</p>

scholarly journals Mixture-based Clustering for the Ordered Stereotype Model

2021 ◽  
Author(s):  
◽  
Daniel Fernández Martínez
Keyword(s):  
Count Data ◽  
Ordinal Data ◽  
Finite Mixture Models ◽  
Probability Model ◽  
Model Fitting ◽  
Real Data ◽  
Information Criteria ◽  
Categorical Variables ◽  
Clustering Methods ◽  
Data Set

<p>Many of the methods which deal with the reduction of dimensionality in matrices of data are based on mathematical techniques. In general, it is not possible to use statistical inferences or select the appropriateness of a model via information criteria with these techniques because there is no underlying probability model. Furthermore, the use of ordinal data is very common (e.g. Likert or Braun-Blanquet scale) and the clustering methods in common use treat ordered categorical variables as nominal or continuous rather than as true ordinal data. Recently a group of likelihood-based finite mixture models for binary or count data has been developed (Pledger and Arnold, 2014). This thesis extends this idea and establishes novel likelihood-based multivariate methods for data reduction of a matrix containing ordinal data. This new approach applies fuzzy clustering via finite mixtures to the ordered stereotype model (Fernández et al., 2014a). Fuzzy allocation of rows and columns to corresponding clusters is achieved by performing the EM algorithm, and also Bayesian model fitting is obtained by performing a reversible jump MCMC sampler. Their performances for one-dimensional clustering are compared. Simulation studies and three real data sets are used to illustrate the application of these approaches and also to present novel data visualisation tools for depicting the fuzziness of the clustering results for ordinal data. Additionally, a simulation study is set up to empirically establish a relationship between our likelihood-based methodology and the performance of eleven information criteria in common use. Finally, clustering comparisons between count data and categorising the data as ordinal over a same data set are performed and results are analysed and presented.</p>

scholarly journals Mixture of Lindley and Lognormal Distributions: Properties, Estimation, and Application

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
A. S. Al-Moisheer
Keyword(s):  
Finite Mixture Models ◽  
Mixture Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Heterogeneous Data ◽  
Information Criteria ◽  
Flexible Tool ◽  
Data Set ◽  
Lognormal Distributions ◽  
Kolmogorov Smirnov

Finite mixture models provide a flexible tool for handling heterogeneous data. This paper introduces a new mixture model which is the mixture of Lindley and lognormal distributions (MLLND). First, the model is formulated, and some of its statistical properties are studied. Next, maximum likelihood estimation of the parameters of the model is considered, and the performance of the estimators of the parameters of the proposed models is evaluated via simulation. Also, the flexibility of the proposed mixture distribution is demonstrated by showing its superiority to fit a well-known real data set of 128 bladder cancer patients compared to several mixture and nonmixture distributions. The Kolmogorov Smirnov test and some information criteria are used to compare the fitted models to the real dataset. Finally, the results are verified using several graphical methods.

A Growth Model for Multilevel Ordinal Data

2005 ◽  
Vol 30 (4) ◽  
pp. 369-396 ◽  
Author(s):  
Eisuke Segawa
Keyword(s):  
Latent Variable ◽  
Ordinal Data ◽  
Linear Models ◽  
Growth Models ◽  
Simulated Data ◽  
Real Data ◽  
Analytic Structure ◽  
Data Sets ◽  
Data Set ◽  
Time Points

Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can analyze not only data with item- and time-level missing observations, but also data with time points freely specified over subjects. Furthermore, features useful for longitudinal analyses, “autoregressive error degree one” structure for the trait residuals and estimated time-scores, were included. The approach is Bayesian with Markov Chain and Monte Carlo, and the model is implemented in WinBUGS. They are illustrated with two simulated data sets and one real data set with planned missing items within a scale.

Clustering Based on a Novel Density Estimation Method

2013 ◽  
Vol 748 ◽  
pp. 590-594
Author(s):  
Li Liao ◽  
Yong Gang Lu ◽  
Xu Rong Chen
Keyword(s):  
Density Estimation ◽  
Nearest Neighbor ◽  
Mean Shift ◽  
Estimation Method ◽  
Synthetic Data ◽  
Real Data ◽  
Data Sets ◽  
Clustering Methods ◽  
K Nearest Neighbor ◽  
Data Set

We propose a novel density estimation method using both the k-nearest neighbor (KNN) graph and the potential field of the data points to capture the local and global data distribution information respectively. The clustering is performed based on the computed density values. A forest of trees is built using each data point as the tree node. And the clusters are formed according to the trees in the forest. The new clustering method is evaluated by comparing with three popular clustering methods, K-means++, Mean Shift and DBSCAN. Experiments on two synthetic data sets and one real data set show that our approach can effectively improve the clustering results.

scholarly journals Statistical methods of fracture characterization using acoustic borehole televiewer log interpretation

2021 ◽  
Author(s):  
C Massiot ◽  
John Townend ◽  
A Nicol ◽  
DD McNamara
Keyword(s):  
Probability Distributions ◽  
Likelihood Estimation ◽  
Information Criterion ◽  
Geothermal Field ◽  
Information Criteria ◽  
Clustering Methods ◽  
Agglomerative Clustering ◽  
Data Set ◽  
Data Points ◽  
Borehole Televiewer

©2017. American Geophysical Union. All Rights Reserved. Acoustic borehole televiewer (BHTV) logs provide measurements of fracture attributes (orientations, thickness, and spacing) at depth. Orientation, censoring, and truncation sampling biases similar to those described for one-dimensional outcrop scanlines, and other logging or drilling artifacts specific to BHTV logs, can affect the interpretation of fracture attributes from BHTV logs. K-means, fuzzy K-means, and agglomerative clustering methods provide transparent means of separating fracture groups on the basis of their orientation. Fracture spacing is calculated for each of these fracture sets. Maximum likelihood estimation using truncated distributions permits the fitting of several probability distributions to the fracture attribute data sets within truncation limits, which can then be extrapolated over the entire range where they naturally occur. Akaike Information Criterion (AIC) and Schwartz Bayesian Criterion (SBC) statistical information criteria rank the distributions by how well they fit the data. We demonstrate these attribute analysis methods with a data set derived from three BHTV logs acquired from the high-temperature Rotokawa geothermal field, New Zealand. Varying BHTV log quality reduces the number of input data points, but careful selection of the quality levels where fractures are deemed fully sampled increases the reliability of the analysis. Spacing data analysis comprising up to 300 data points and spanning three orders of magnitude can be approximated similarly well (similar AIC rankings) with several distributions. Several clustering configurations and probability distributions can often characterize the data at similar levels of statistical criteria. Thus, several scenarios should be considered when using BHTV log data to constrain numerical fracture models.

scholarly journals Statistical methods of fracture characterization using acoustic borehole televiewer log interpretation

2021 ◽  
Author(s):  
C Massiot ◽  
John Townend ◽  
A Nicol ◽  
DD McNamara
Keyword(s):  
Probability Distributions ◽  
Likelihood Estimation ◽  
Information Criterion ◽  
Geothermal Field ◽  
Information Criteria ◽  
Clustering Methods ◽  
Agglomerative Clustering ◽  
Data Set ◽  
Data Points ◽  
Borehole Televiewer

©2017. American Geophysical Union. All Rights Reserved. Acoustic borehole televiewer (BHTV) logs provide measurements of fracture attributes (orientations, thickness, and spacing) at depth. Orientation, censoring, and truncation sampling biases similar to those described for one-dimensional outcrop scanlines, and other logging or drilling artifacts specific to BHTV logs, can affect the interpretation of fracture attributes from BHTV logs. K-means, fuzzy K-means, and agglomerative clustering methods provide transparent means of separating fracture groups on the basis of their orientation. Fracture spacing is calculated for each of these fracture sets. Maximum likelihood estimation using truncated distributions permits the fitting of several probability distributions to the fracture attribute data sets within truncation limits, which can then be extrapolated over the entire range where they naturally occur. Akaike Information Criterion (AIC) and Schwartz Bayesian Criterion (SBC) statistical information criteria rank the distributions by how well they fit the data. We demonstrate these attribute analysis methods with a data set derived from three BHTV logs acquired from the high-temperature Rotokawa geothermal field, New Zealand. Varying BHTV log quality reduces the number of input data points, but careful selection of the quality levels where fractures are deemed fully sampled increases the reliability of the analysis. Spacing data analysis comprising up to 300 data points and spanning three orders of magnitude can be approximated similarly well (similar AIC rankings) with several distributions. Several clustering configurations and probability distributions can often characterize the data at similar levels of statistical criteria. Thus, several scenarios should be considered when using BHTV log data to constrain numerical fracture models.

scholarly journals Vehicle Dimensions Based Passenger Car Classification using Fuzzy and Non-Fuzzy Clustering Methods

2021 ◽  
pp. 036119812110107
Author(s):  
Naghmeh Niroomand ◽  
Christian Bach ◽  
Miriam Elser
Keyword(s):  
Fuzzy Clustering ◽  
Clustering Algorithm ◽  
Real Data ◽  
Superior Performance ◽  
Clustering Methods ◽  
Data Set ◽  
Passenger Car ◽  
Continuous Growth ◽  
Taxation Policy ◽  
Fuzzy Clustering Algorithm

There has been globally continuous growth in passenger car sizes and types over the past few decades. To assess the development of vehicular specifications in this context and to evaluate changes in powertrain technologies depending on surrounding frame conditions, such as charging stations and vehicle taxation policy, we need a detailed understanding of the vehicle fleet composition. This paper aims therefore to introduce a novel mathematical approach to segment passenger vehicles based on dimensions features using a means fuzzy clustering algorithm, Fuzzy C-means (FCM), and a non-fuzzy clustering algorithm, K-means (KM). We analyze the performance of the proposed algorithms and compare them with Swiss expert segmentation. Experiments on the real data sets demonstrate that the FCM classifier has better correlation with the expert segmentation than KM. Furthermore, the outputs from FCM with five clusters show that the proposed algorithm has a superior performance for accurate vehicle categorization because of its capacity to recognize and consolidate dimension attributes from the unsupervised data set. Its performance in categorizing vehicles was promising with an average accuracy rate of 79% and an average positive predictive value of 75%.

scholarly journals Using anticlustering to partition data sets into equivalent parts

2019 ◽  
Author(s):  
Martin Papenberg ◽  
Gunnar W. Klau
Keyword(s):  
Cross Validation ◽  
Item Difficulty ◽  
Large Data ◽  
Real Data ◽  
Psychological Research ◽  
Data Sets ◽  
Clustering Methods ◽  
Data Set ◽  
R Programming Language ◽  
R Programming

Numerous applications in psychological research require that a pool of elements is partitioned into multiple parts. While many applications seek groups that are well-separated, i.e., dissimilar from each other, others require the different groups to be as similar as possible. Examples include the assignment of students to parallel courses, assembling stimulus sets in experimental psychology, splitting achievement tests into parts of equal difficulty, and dividing a data set for cross validation. We present anticlust, an easy-to-use and free software package for solving these problems fast and in an automated manner. The package anticlust is an open source extension to the R programming language and implements the methodology of anticlustering. Anticlustering divides elements into similar parts, ensuring similarity between groups by enforcing heterogeneity within groups. Thus, anticlustering is the direct reversal of cluster analysis that aims to maximize homogeneity within groups and dissimilarity between groups. Our package anticlust implements two anticlustering criteria, reversing the clustering methods k-means and cluster editing, respectively. In a simulation study, we show that anticlustering returns excellent results and outperforms alternative approaches like random assignment and matching. In three example applications, we illustrate how to apply anticlust on real data sets. We demonstrate how to assign experimental stimuli to equivalent sets based on norming data, how to divide a large data set for cross validation, and how to split a test into parts of equal item difficulty and discrimination.

scholarly journals MDST-DBSCAN: A Density-Based Clustering Method for Multidimensional Spatiotemporal Data

2021 ◽  
Vol 10 (6) ◽  
pp. 391
Author(s):  
Changlock Choi ◽  
Seong-Yun Hong
Keyword(s):  
Large Scale ◽  
Complex Structure ◽  
Real Data ◽  
Spatiotemporal Data ◽  
Clustering Methods ◽  
Computationally Efficient ◽  
Clustering Method ◽  
Efficient Manner ◽  
Data Set ◽  
Urban Dynamics

The increasing use of mobile devices and the growing popularity of location-based ser-vices have generated massive spatiotemporal data over the last several years. While it provides new opportunities to enhance our understanding of various urban dynamics, it poses challenges at the same time due to the complex structure and large-volume characteristic of the spatiotemporal data. To facilitate the process and analysis of such spatiotemporal data, various data mining and clustering methods have been proposed, but there still needs to develop a more flexible and computationally efficient method. The purpose of this paper is to present a clustering method that can work with large-scale, multidimensional spatiotemporal data in a reliable and efficient manner. The proposed method, called MDST-DBSCAN, is applied to idealized patterns and a real data set, and the results from both examples demonstrate that it can identify clusters accurately within a reasonable amount of time. MDST-DBSCAN performs well on both spatial and spatiotemporal data, and it can be particularly useful for exploring massive spatiotemporal data, such as detailed real estate transactions data in Seoul, Korea.

scholarly journals On Modeling Concrete Compressive Strength Data Using Laplace Birnbaum-Saunders Distribution Assuming Contaminated Information

Crystals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 830
Author(s):  
Farouq Mohammad A. Alam ◽  
Mazen Nassar
Keyword(s):  
Compressive Strength ◽  
Optimization Problems ◽  
Probability Model ◽  
Simulated Data ◽  
Real Data ◽  
Reliability Function ◽  
Stress Factors ◽  
Model Parameters ◽  
Data Set ◽  
Suggested Approach

Compressive strength is a well-known measurement to evaluate the endurance of a given concrete mixture to stress factors, such as compressive loads. A suggested approach to assess compressive strength of concrete is to assume that it follows a probability model from which its reliability is calculated. In reliability analysis, a probability distribution’s reliability function is used to calculate the probability of a specimen surviving to a certain threshold without damage. To approximate the reliability of a subject of interest, one must estimate the corresponding parameters of the probability model. Researchers typically formulate an optimization problem, which is often nonlinear, based on the maximum likelihood theory to obtain estimates for the targeted parameters and then estimate the reliability. Nevertheless, there are additional nonlinear optimization problems in practice from which different estimators for the model parameters are obtained once they are solved numerically. Under normal circumstances, these estimators may perform similarly. However, some might become more robust under irregular situations, such as in the case of data contamination. In this paper, nine frequentist estimators are derived for the parameters of the Laplace Birnbaum-Saunders distribution and then applied to a simulated data set and a real data set. Afterwards, they are compared numerically via Monte Carlo comparative simulation study. The resulting estimates for the reliability based on these estimators are also assessed in the latter study.

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