scholarly journals Discretization of Fractional Operators: Analysis by Means of Advanced Computational Techniques

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2429
Author(s):  
Jose Tenreiro Machado ◽  
Alexandra M. Galhano ◽  
Carla S. Cordeiro
Keyword(s):  
Multidimensional Scaling ◽  
Hierarchical Clustering ◽  
Computational Techniques ◽  
Graphical Representations ◽  
Fractional Operator ◽  
Fractional Operators ◽  
Clustering Methods ◽  
Generalized Mean ◽  
Cosine Distance ◽  
Fractional Orders

This paper studies the discretization of fractional operators by means of advanced clustering methods. The Grünwald–Letnikov fractional operator is approximated by series generated by the Euler, Tustin and generalized mean. The series for different fractional orders form the objects to be assessed. For this purpose, the several distances associated with the hierarchical clustering and multidimensional scaling computational techniques are tested. The Arc-cosine distance and the 3-dim multidimensional scaling produce good results. The visualization of the graphical representations allows a better understanding of the properties embedded in each type of approximation of the fractional operators.

scholarly journals Head-to-head comparison of clustering methods for heterogeneous data: a simulation-driven benchmark

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Gregoire Preud’homme ◽  
Kevin Duarte ◽  
Kevin Dalleau ◽  
Claire Lacomblez ◽  
Emmanuel Bresso ◽  
...  
Keyword(s):  
Hierarchical Clustering ◽  
Latent Class ◽  
Latent Class Model ◽  
Real Life ◽  
Heterogeneous Data ◽  
Mixed Data ◽  
Categorical Variables ◽  
Clustering Methods ◽  
Model Based ◽  
Partitioning Around Medoids

AbstractThe choice of the most appropriate unsupervised machine-learning method for “heterogeneous” or “mixed” data, i.e. with both continuous and categorical variables, can be challenging. Our aim was to examine the performance of various clustering strategies for mixed data using both simulated and real-life data. We conducted a benchmark analysis of “ready-to-use” tools in R comparing 4 model-based (Kamila algorithm, Latent Class Analysis, Latent Class Model [LCM] and Clustering by Mixture Modeling) and 5 distance/dissimilarity-based (Gower distance or Unsupervised Extra Trees dissimilarity followed by hierarchical clustering or Partitioning Around Medoids, K-prototypes) clustering methods. Clustering performances were assessed by Adjusted Rand Index (ARI) on 1000 generated virtual populations consisting of mixed variables using 7 scenarios with varying population sizes, number of clusters, number of continuous and categorical variables, proportions of relevant (non-noisy) variables and degree of variable relevance (low, mild, high). Clustering methods were then applied on the EPHESUS randomized clinical trial data (a heart failure trial evaluating the effect of eplerenone) allowing to illustrate the differences between different clustering techniques. The simulations revealed the dominance of K-prototypes, Kamila and LCM models over all other methods. Overall, methods using dissimilarity matrices in classical algorithms such as Partitioning Around Medoids and Hierarchical Clustering had a lower ARI compared to model-based methods in all scenarios. When applying clustering methods to a real-life clinical dataset, LCM showed promising results with regard to differences in (1) clinical profiles across clusters, (2) prognostic performance (highest C-index) and (3) identification of patient subgroups with substantial treatment benefit. The present findings suggest key differences in clustering performance between the tested algorithms (limited to tools readily available in R). In most of the tested scenarios, model-based methods (in particular the Kamila and LCM packages) and K-prototypes typically performed best in the setting of heterogeneous data.

An efficient numerical simulation and mathematical modeling for the prevention of tuberculosis

2021 ◽  
Author(s):  
Zain Ul Abadin Zafar ◽  
Samina Younas ◽  
Sumera Zaib ◽  
Cemil Tunç
Keyword(s):  
Fixed Point Theory ◽  
Dynamical Behavior ◽  
Point Theory ◽  
Model Parameters ◽  
Fractional Operator ◽  
Significant Preference ◽  
Relevant Model ◽  
Clinical Associations ◽  
Predictor Corrector ◽  
Fractional Orders

The main purpose of this research is to use a fractional-mathematical model including Atangana–Baleanu derivatives to explore the clinical associations and dynamical behavior of the tuberculosis. Herein, we used a lately introduced fractional operator having Mittag-Leffler kernel. The existence and inimitability problems to the relevant model were examined through the fixed-point theory. To verify the significance of the arbitrary fractional-order derivative, numerical outcomes were explored from the biological and mathematical viewpoints using the values of model parameters. The graphical simulations show the comparison of the predictor–corrector method (PCM) and Caputo method (CM) for different fractional orders and the results indicated the significant preference of PCM over CM.

scholarly journals Machine-learning identification of asteroid groups

2019 ◽  
Vol 488 (1) ◽  
pp. 1377-1386 ◽  
Author(s):  
V Carruba ◽  
S Aljbaae ◽  
A Lucchini
Keyword(s):  
Machine Learning ◽  
Hierarchical Clustering ◽  
Clustering Algorithms ◽  
Family Members ◽  
Parent Body ◽  
Clustering Methods ◽  
New Family ◽  
Hierarchical Clustering Methods ◽  
Rotational Failure ◽  
Asteroid Families

ABSTRACT Asteroid families are groups of asteroids that share a common origin. They can be the outcome of a collision or be the result of the rotational failure of a parent body or its satellites. Collisional asteroid families have been identified for several decades using hierarchical clustering methods (HCMs) in proper elements domains. In this method, the distance of an asteroid from a reference body is computed, and, if it is less than a critical value, the asteroid is added to the family list. The process is then repeated with the new object as a reference, until no new family members are found. Recently, new machine-learning clustering algorithms have been introduced for the purpose of cluster classification. Here, we apply supervised-learning hierarchical clustering algorithms for the purpose of asteroid families identification. The accuracy, precision, and recall values of results obtained with the new method, when compared with classical HCM, show that this approach is able to found family members with an accuracy above 89.5 per cent, and that all asteroid previously identified as family members by traditional methods are consistently retrieved. Values of the areas under the curve coefficients below Receiver Operating Characteristic curves are also optimal, with values consistently above 85 per cent. Overall, we identify 6 new families and 13 new clumps in regions where the method can be applied that appear to be consistent and homogeneous in terms of physical and taxonomic properties. Machine-learning clustering algorithms can, therefore, be very efficient and fast tools for the problem of asteroid family identification.

Efficient Document Clustering for Web Search Result

2018 ◽  
Vol 7 (3.3) ◽  
pp. 90
Author(s):  
Sumathi Rani Manukonda ◽  
Asst.Prof Kmit ◽  
Narayanguda . ◽  
Hyderabad . ◽  
Nomula Divya ◽  
...  
Keyword(s):  
Hierarchical Clustering ◽  
Web Search ◽  
Traditional Approach ◽  
Document Clustering ◽  
Nearest Neighbors ◽  
Clustering Methods ◽  
Search Query ◽  
Semantic Approach ◽  
Search Result ◽  
Distinct Method

Clustering the document in data mining is one of the traditional approach in which the same documents that are more relevant are grouped together. Document clustering take part in achieving accuracy that retrieve information for systems that identifies the nearest neighbors of the document. Day to day the massive quantity of data is being generated and it is clustered. According to particular sequence to improve the cluster qualityeven though different clustering methods have been introduced, still many challenges exist for the improvement of document clustering. For web search purposea document in group is efficiently arranged for the result retrieval.The users accordingly search query in an organized way. Hierarchical clustering is attained by document clustering.To the greatest algorithms for groupingdo not concentrate on the semantic approach, hence resulting to the unsatisfactory output clustering. The involuntary approach of organizing documents of web like Google, Yahoo is often considered as a reference. A distinct method to identify the existing group of similar things in the previously organized documents and retrieves effective document classifier for new documents. In this paper the main concentration is on hierarchical clustering and k-means algorithms, hence prove that k-means and its variant are efficient than hierarchical clustering along with this by implementing greedy fast k-means algorithm (GFA) for cluster document in efficient way is considered.  

scholarly journals Using hierarchical clustering to explore patterns of deprivation among English local authorities

2019 ◽  
Vol 42 (4) ◽  
pp. 772-777
Author(s):  
Steven L Senior
Keyword(s):  
Hierarchical Clustering ◽  
Demographic Characteristics ◽  
Homogeneous Group ◽  
Statistical Testing ◽  
Clustering Methods ◽  
Local Authorities ◽  
Multiple Deprivation ◽  
Hierarchical Clustering Methods ◽  
Different Levels ◽  
Indices Of Multiple Deprivation

Abstract Background The English Indices of Multiple Deprivation (IMD) is widely used as a measure of deprivation. However, similarly ranked areas can differ substantially in the underlying domains of deprivation. These domains contain a richer set of data that might be useful for classifying local authorities. Clustering methods offer a set of techniques to identify groups of areas with similar patterns of deprivation. Methods Hierarchical agglomerative (i.e. bottom-up) clustering methods were applied to domain scores for 152 upper tier local authorities. Advances in statistical testing allow clusters to be identified that are unlikely to have arisen from random partitioning of a homogeneous group. The resulting clusters are described in terms of their subdomain scores and basic geographic and demographic characteristics. Results Five statistically significant clusters of local authorities were identified. These clusters only partially reflect different levels of overall deprivation. In particular, two clusters share similar overall IMD scores but have contrasting patterns of deprivation. Conclusion Hierarchical clustering methods identify five distinct clusters that do not correspond closely to quintiles of deprivation. This approach may help to distinguish between places that face similar underlying challenges, and places that appear similar in terms of overall deprivation scores, but that face different challenges.

scholarly journals Kernel Treelets

2019 ◽  
Vol 11 (03n04) ◽  
pp. 1950006
Author(s):  
Hedi Xia ◽  
Hector D. Ceniceros
Keyword(s):  
Hierarchical Clustering ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Feature Space ◽  
Coefficient Matrix ◽  
Data Sets ◽  
Clustering Methods ◽  
Orthonormal Bases ◽  
Data Points ◽  
General Data

A new method for hierarchical clustering of data points is presented. It combines treelets, a particular multiresolution decomposition of data, with a mapping on a reproducing kernel Hilbert space. The proposed approach, called kernel treelets (KT), uses this mapping to go from a hierarchical clustering over attributes (the natural output of treelets) to a hierarchical clustering over data. KT effectively substitutes the correlation coefficient matrix used in treelets with a symmetric and positive semi-definite matrix efficiently constructed from a symmetric and positive semi-definite kernel function. Unlike most clustering methods, which require data sets to be numeric, KT can be applied to more general data and yields a multiresolution sequence of orthonormal bases on the data directly in feature space. The effectiveness and potential of KT in clustering analysis are illustrated with some examples.

Site Relationships at Quebrada Tarapaca, Chile: A Comparison of Clustering and Scaling Techniques

1974 ◽  
Vol 39 (1) ◽  
pp. 51-74 ◽  
Author(s):  
R. G. Matson ◽  
D. L. True
Keyword(s):  
Multidimensional Scaling ◽  
Frequency Analysis ◽  
Relative Frequency ◽  
Northern Chile ◽  
Clustering Methods ◽  
Comparison Of The Results

AbstractThis study is a comparison of the results of a variety of clustering methods and 2 multidimensional scaling techniques on data from sites in northern Chile. While differences do occur, the similarities among the results are strong in spite of differing inputs. In general, results of relative frequency analysis appear to be superior to those of presence/absence, and the techniques used seem to be viable additions to existing archaeological tools.

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