Fuzzy Clustering Methods for Categorical Multivariate Data Based on q-Divergence

In an optical flow field, the background and moving objects present different vector groups with different directions, velocities and region areas. The idea optical flow field is not easy to obtain for some kinds of reasons; in practical field, the motion vectors present confusion and uncertainty to some extent. The fuzzy clustering provides an effective way to process unclear classification. It maps every vector into every group, and the ascription presents a degree a vector belongs to a group. However, conventional fuzzy clustering method needs to determine the group number, namely the moving objects number in the view field. Before all samples are processed and the group number is fixed during iteration. The unsuitable number easily results in inaccurate segmentation. In view of this problem, an enhanced detection algorithm using fuzzy clustering with elastic grouping logic is proposed. To be called elastic grouping logic, it means that in the process of optical flow field detection, according to the ascription the vector to each group, together with the vector's location, direction and magnitude, the group number, namely the moving object number, is selfadaptively generated, and further to achieve the moving objects segmentation with precision. A stability model of motion vectors for an object group and the group's partition is also established. The experimental results illustrate the proposed algorithm is able to satisfy the need of multi-objects detection and locate the moving objects successfully.

Hard and fuzzy clustering algorithms are part of the partition-based clustering family. They are widely used in real-world applications to cluster numerical and categorical data. While in hard clustering an object is assigned to a cluster with certainty, in fuzzy clustering an object can be assigned to different clusters given a membership degree. For both types of method an entropy can be incorporated into the objective function, mostly to avoid solutions raising too much uncertainties. In this paper, we present an extension of a fuzzy clustering method for categorical data using fuzzy centroids. The new algorithm, referred to as Categorical Fuzzy Entropy (CFE), integrates an entropy term in the objective function. This allows a better fuzzification of the cluster prototypes. Experiments on ten real-world data sets and statistical comparisons show that the new method can efficiently handle categorical data.

Partition-and-merge based fuzzy genetic clustering algorithm for categorical data

In view of the considerable applications of data clustering techniques in various fields, such as engineering, artificial intelligence, machine learning, clinical medicine, biology, ecology, disease diagnosis, and business marketing, many data clustering algorithms and methods have been developed to deal with complicated data. These techniques include supervised learning methods and unsupervised learning methods such as density-based clustering, K-means clustering, and K-nearest neighbor clustering. This book reviews recently developed data clustering techniques and algorithms and discusses the development of data clustering, including measures of similarity or dissimilarity for data clustering, data clustering algorithms, assessment of clustering algorithms, and data clustering methods recently developed for insurance, psychology, pattern recognition, and survey data.

A new online clustering method based on not only reinforcement and competitive learning but also pursuit algorithm (Pursuit Reinforcement Competitive Learning: PRCL) as well as learning automata is proposed for reaching a relatively stable clustering solution in comparatively short time duration. UCI repository data which are widely used for evaluation of clustering performance in usual is used for a comparative study among the existing conventional online clustering methods of Reinforcement Guided Competitive Learning: RGCL, Sustained RGCL: SRGCL, Vector Quantization, and the proposed PRCL. The results show that the clustering accuracy of the proposed method is superior to the conventional methods. More importantly, it is found that the proposed PRCL is much faster than the conventional methods. The proposed method is then applied to the evacuation simulation study. It is found that the proposed method is much faster than the conventional method of vector quatization to find the most appropriate evacuation route. Due to the fact that the proposed PRCL method allows finding the most appropriate evacuation route, collisions among peoples who have to evacuate for the proposed method is much less than that of vector quatization.

Abstract. Accurate boundary layer structure and height are critical in the analysis of the features of air pollutants and local circulation. Although surface-based remote sensing instruments provide a high temporal resolution of the boundary layer structure, there are numerous uncertainties in terms of the accurate determination of the atmospheric boundary layer heights (ABLHs). In this study, an algorithm for an integrated system for ABLH estimation (ISABLE) was developed and applied to the vertical profile data obtained using a ceilometer and a microwave radiometer in Seoul city, Korea. A maximum of 19 ABLHs were estimated via the conventional time-variance, gradient, wavelet, and clustering methods using the backscatter coefficient from the ceilometer. Meanwhile, several stable boundary layer heights were extracted through near-surface inversion and environmental lapse rate methods using the potential temperature from the microwave radiometer. The ISABLE algorithm can find an optimal ABLH from post-processing, such as k-means clustering and density-based spatial clustering of applications with noise (DBSCAN) techniques. It was found that the ABLH determined using ISABLE exhibited more significant correlation coefficients and smaller mean bias and root mean square error between the radiosonde-derived ABLHs than those obtained using the most conventional methods. Clear skies exhibited higher daytime ABLH than cloudy skies, and the daily maximum ABLH was recorded in summer because of the more intense radiation. The ABLHs estimated by ISABLE are expected to contribute to the parameterization of vertical diffusion in the atmospheric boundary layer.

In this paper, a clustering algorithm for relational data based on q-divergence between memberships and variables that control cluster sizes is proposed. A conventional method for vectorial data is first presented for interpretation as the regularization of another conventional method with q-divergence. With this interpretation, a clustering algorithm for relational data, based on q-divergence, is then derived from an optimization problem built by regularizing the conventional method with q-divergence. A theoretical discussion reveals the property of the proposed method. Numerical results are presented that substantiate this property and show that the proposed method outperforms two conventional methods in terms of accuracy.

Recently, the differential transcriptional responses of Mycobacterium tuberculosis to drug and growth-inhibitory conditions were monitored to generate a data set of 436 microarray profiles. These profiles were valuably used for grouping drugs, identifying drug targets and detecting related pathways, based on various conventional methods; such as Pearson correlation, hierarchical clustering, and statistical tests. These conventional clustering methods used the high dimensionality of gene space to reveal drug groups basing on the similarity of expression levels of all genes. In this study, we applied the factor analysis with these conventional methods for drug clustering, drug target detection and pathway detection. The latent variables or factors of gene expression levels in loading space from factor analysis allowed the hierarchical clustering to discover true drug groups. The t-test method was applied to identify drug targets which most significantly associated with each drug cluster. Then, gene ontology was used to detect pathway associations for each group of drug targets.

Fuzzy clustering is an invaluable data mining technique that allows each data point to belong to more than one cluster with some degree of membership. It is widely employed in exploratory data mining to discover overlapping communities in social networks, find structure in spectral data, and capture user interests in recommendation systems. Nowadays, the variety and volume of data are increasing at a tremendous rate. Data is power; the massive data, along with an effective technique, can unravel valuable information. The existing fuzzy clustering algorithms do not perform well on massive heterogeneous datasets. Processing an enormous amount of data is beyond the capacity of a single processor. The need of the hour is to develop fuzzy clustering techniques that can work on a distributed framework for Big Data processing and can handle heterogeneous data. In this research, we evaluate the performance of the recently proposed algorithm for the Fuzzy clustering of mixed-mode data FCMD-MD (D’Urso and Massari in Inf Sci 505:513–534, 2019) with different real-world datasets. We develop a distributed FCMD-MD, a fuzzy clustering algorithm for mixed-mode data in Apache SPARK. The experimental results show that the algorithm is scalable, performs well in a distributed environment, and clusters enormous heterogeneous data with high accuracy. We also compared the performance of distributed FCMD-MD and the distributed k-medoid algorithm.

Spatial clustering has been identified as an important technique in data mining owing to its various applications. In the conventional spatial clustering methods, data points are clustered mainly according to their geographic attributes. In real applications, however, the obtained data points consist of not only geographic attributes but also non-geographic ones. In general, geographic attributes indicate the data locations and non-geographic attributes show the characteristics of data points. It is thus infeasible, by using conventional spatial clustering methods, to partition the geographic space such that similar data points are grouped together. In this paper, we propose an effective and efficient algorithm, named incremental clustering toward the Bound INformation of Geography and Optimization spaces, abbreviated as BINGO, to solve the problem. The proposed BINGO algorithm combines the information in both geographic and non-geographic attributes by constructing a summary structure and possesses incremental clustering capability by appropriately adjusting this structure. Furthermore, most parameters in algorithm BINGO are determined automatically so that it is easy to be applied to applications without resorting to extra knowledge. Experiments on synthetic are performed to validate the effectiveness and the efficiency of algorithm BINGO.

Clustering method, which groups thousands of genes by their similarities of expression levels, has been used for identifying unknown functions of genes. Fuzzy clustering method that is one category of clustering assigns one sample to multiple groups according to their membership degrees. It is more appropriate than hard clustering algorithms for analyzing gene expression profiles since single gene might involve multiple genetic functions. However, general clustering methods have problems that they are sensitive to initialization and can be trapped into local optima. To solve the problems, we propose an evolutionary fuzzy clustering algorithm with knowledge-based evaluation. It uses a genetic algorithm for clustering and prior knowledge of data for evaluation. Yeast cell-cycle dataset has been used for experiments to show the usefulness of the proposed method.KeywordsFuzzy ClusterMembership DegreeCluster PartitionAnalyze Gene Expression ProfileFuzzy Cluster MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Classifying genes into clusters depending on their expression profiles is one of the most important analysis techniques for microarray data. Because temporal gene expression profiles are indicative of the dynamic functional properties of genes, the application of clustering analysis to time-course data allows the more precise division of genes into functional classes. Conventional clustering methods treat the sampling data at each time point as data obtained under different experimental conditions without considering the continuity of time-course data between time periods t and t+1. Here, we propose a method designated mathematical model-based clustering (MMBC). The proposed method, designated MMBC, was applied to artificial data and time-course data obtained using Saccharomyces cerevisiae. Our method is able to divide data into clusters more accurately and coherently than conventional clustering methods. Furthermore, MMBC is more tolerant to noise than conventional clustering methods. Software is available upon request. taizo@brs.kyushu-u.ac.jp.

The Fuzzy C-Means (FCM) algorithm is commonly used for clustering. The weighting exponent c and the clustering number m are the important parameters in FCM algorithm. Conventional fuzzy clustering method must use both of the two prespecified parameters, so in this paper we analyses the original algorithm and studies on the optimal selection methods of the c and m by introducing the fuzzy decision theory and the validity index basing on the geometric structure of the dataset. Experiment results with the IRIS dataset show that this algorithm can obtain the optimal weighting exponent m and the optimal clustering number c. Moreover, the fact that the best value scope of m achieved in practical applications indicates that the method is effective.

Background: The occurrence of fire and explosion accidents in the process industries is accompanied by the gradual release of large amounts of energy. The DOW Index is one of the methods of evaluating fire and explosion in the process industries. The present study used the fuzzy logic method to improve the results of the fire and explosion risk analysis method and reduce their uncertainty (error in achieving the correct result). Methods: In the present cross-sectional study, having analyzed the gas separation process, the DOW index was applied to study high-risk equipment. Then, to optimize the behavior of the parameters affecting the DOW index, each weight parameter was assigned to between 0 and 1, and the membership functions of each degree of risk were determined based on the fuzzy rules classification system. The five selected linguistic variables based on membership functions were used to assess the risk level. Results: Considering butane, the level of fire and explosion risk was 231.3, which was less risky than the fuzzy logic result of 248.6. Methane risk was calculated according to the fire and explosion index of 262.1 while using fuzzy logic that was 265.6. The lowest risk difference was observed between the two methods for ethane (258.9 conventional method and 259.1 fuzzy method results). The risk level calculated by DOW for propane was 243.6, and the risk level was 255.1 while using fuzzy logic. Conclusion: Although both methods yielded a high degree of risk, fuzzy logic results indicated higher numerical values comparing to the conventional DOW method. Compared to the conventional DOW method, fuzzy logic results are closer to reality with higher confidence levels.

BackgroundOpen gingival embrasures form complex aesthetic and functional problems. This clinical trial assessed the bioclear matrix using injection molding technique against conventional celluloid matrix technique in management of black triangle.MethodsA total of 26 participants were randomly divided into two groups (13 participants each) according to the technique used. In group (A) celluloid conventional matrix method was used, while in group (B) bioclear matrix with injection molding technique was used. The different outcomes (Esthetic evaluation, marginal integrity and patient satisfaction) were evaluated following the FDI criteria by two blinded examiners. The evaluation was done at (T0) (immediate after restoration); (T6) after 6 months; and (T12) after 12 months. Statistical analysis was done as categorical and ordinal data were presented as frequency and percentage values. Categorical data were compared using fisher’s exact test. Intergroup comparisons for ordinal data were analyzed utilizing the Mann–Whitney U test, while intragroup comparisons were analyzed using Friedman’s test followed by the Nemenyi post hoc test. The significance level was set at p ≤ 0.05 within all tests.ResultsRegarding radiographic marginal integrity and marginal adaptation, the bioclear matrix group revealed superior results when compared to celluloid matrix group with a significant difference between both groups at all intervals (p < 0.05); however no significant difference was detected at different intervals. While for proximal anatomical form and esthetic anatomical form, as well as phonetics and food impaction, all cases in both groups were successful with no statistical significant difference between groups. For the periodontal response, there was no significant difference between groups. However, there was a significant difference between scores measured at different intervals, with T0 being significantly different from other intervals (p < 0.001). Marginal staining revealed that there was no significant difference between groups. While, a significant difference between scores measured at different intervals.ConclusionsThe restorative management of the black triangle with both protocols was able to deliver superior aesthetic and good marginal adaptation; suitable biological properties; with adequate survival time. Both techniques were almost equally successful, however they are depending on the operator skills.Trial registrationThe clinical trial was registered in the (www.clinicaltrials.gov/) database in 23/07/2020; with the unique identification number NCT04482790.