Fuzzy Transform for Analyzing Massive Datasets

2020 ◽  
pp. 193-211
Author(s):  
Ferdinando Di Martino ◽  
Salvatore Sessa
Keyword(s):  
Fuzzy Transform ◽  
Massive Datasets

scholarly journals Attribute dependency data analysis for massive datasets by fuzzy transforms

2021 ◽  
Author(s):  
Ferdinando Di Martino ◽  
Salvatore Sessa
Keyword(s):  
Data Analysis ◽  
Regression Function ◽  
Previous Method ◽  
Support Vector ◽  
Fuzzy Transform ◽  
Large Dataset ◽  
Massive Datasets ◽  
Statistical Institute ◽  
Italian Regions ◽  
Comparable Performance

AbstractWe present a numerical attribute dependency method for massive datasets based on the concepts of direct and inverse fuzzy transform. In a previous work, we used these concepts for numerical attribute dependency in data analysis: Therein, the multi-dimensional inverse fuzzy transform was useful for approximating a regression function. Here we give an extension of this method in massive datasets because the previous method could not be applied due to the high memory size. Our method is proved on a large dataset formed from 402,678 census sections of the Italian regions provided by the Italian National Statistical Institute (ISTAT) in 2011. The results of comparative tests with the well-known methods of regression, called support vector regression and multilayer perceptron, show that the proposed algorithm has comparable performance with those obtained using these two methods. Moreover, the number of parameters requested in our method is minor with respect to those of the cited in the above two algorithms.

Mining of Massive Datasets

2020 ◽  
Author(s):  
Jure Leskovec ◽  
Anand Rajaraman ◽  
Jeffrey David Ullman
Keyword(s):  
Massive Datasets

scholarly journals Stochastic Local Interaction Model: An Alternative to Kriging for Massive Datasets

2021 ◽  
Author(s):  
Dionissios T. Hristopulos ◽  
Andrew Pavlides ◽  
Vasiliki D. Agou ◽  
Panagiota Gkafa
Keyword(s):  
Interaction Model ◽  
Local Interaction ◽  
Massive Datasets

scholarly journals Sparse HJ Biplot: A New Methodology via Elastic Net

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1298
Author(s):  
Mitzi Cubilla-Montilla ◽  
Ana Belén Nieto-Librero ◽  
M. Purificación Galindo-Villardón ◽  
Carlos A. Torres-Cubilla
Keyword(s):  
Multivariate Analysis ◽  
Elastic Net ◽  
Massive Datasets ◽  
New Techniques ◽  
Modern Approach ◽  
R Language ◽  
Reduced Dimensions ◽  
Analysis Technique ◽  
Practical Support ◽  
Novel Algorithm

The HJ biplot is a multivariate analysis technique that allows us to represent both individuals and variables in a space of reduced dimensions. To adapt this approach to massive datasets, it is necessary to implement new techniques that are capable of reducing the dimensionality of the data and improving interpretation. Because of this, we propose a modern approach to obtaining the HJ biplot called the elastic net HJ biplot, which applies the elastic net penalty to improve the interpretation of the results. It is a novel algorithm in the sense that it is the first attempt within the biplot family in which regularisation methods are used to obtain modified loadings to optimise the results. As a complement to the proposed method, and to give practical support to it, a package has been developed in the R language called SparseBiplots. This package fills a gap that exists in the context of the HJ biplot through penalized techniques since in addition to the elastic net, it also includes the ridge and lasso to obtain the HJ biplot. To complete the study, a practical comparison is made with the standard HJ biplot and the disjoint biplot, and some results common to these methods are analysed.

scholarly journals A Summary of F-Transform Techniques in Data Analysis

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1771
Author(s):  
Ferdinando Di Martino ◽  
Irina Perfilieva ◽  
Salvatore Sessa
Keyword(s):  
Data Analysis ◽  
Analysis Data ◽  
High Dimensional ◽  
Sufficient Data ◽  
Fuzzy Transform ◽  
Transform Method ◽  
Data Density ◽  
Fuzzy Partitions ◽  
Definition Of ◽  
Performance Results

Fuzzy transform is a technique applied to approximate a function of one or more variables applied by researchers in various image and data analysis. In this work we present a summary of a fuzzy transform method proposed in recent years in different data mining disciplines, such as the detection of relationships between features and the extraction of association rules, time series analysis, data classification. After having given the definition of the concept of Fuzzy Transform in one or more dimensions in which the constraint of sufficient data density with respect to fuzzy partitions is also explored, the data analysis approaches recently proposed in the literature based on the use of the Fuzzy Transform are analyzed. In particular, the strategies adopted in these approaches for managing the constraint of sufficient data density and the performance results obtained, compared with those measured by adopting other methods in the literature, are explored. The last section is dedicated to final considerations and future scenarios for using the Fuzzy Transform for the analysis of massive and high-dimensional data.

scholarly journals Multi-dimensional fuzzy transform and projection

2017 ◽  
Vol 307 ◽  
pp. 83-98 ◽  
Author(s):  
Jean-François Crouzet
Keyword(s):  
Fuzzy Transform

Introduction to the Special Section on Massive Datasets

1999 ◽  
Vol 8 (3) ◽  
pp. 544-544 ◽  
Author(s):  
Andreas Buja ◽  
Sallie Keller-McNulty
Keyword(s):  
Special Section ◽  
Massive Datasets

Tests and variables selection on regression analysis for massive datasets

2007 ◽  
Vol 63 (3) ◽  
pp. 811-819 ◽  
Author(s):  
Tsai-Hung Fan ◽  
Kuang-Fu Cheng
Keyword(s):  
Regression Analysis ◽  
Massive Datasets ◽  
Variables Selection

scholarly journals New Approximation Methods Based on Fuzzy Transform for Solving SODEs: II

2018 ◽  
Vol 1 (3) ◽  
pp. 30 ◽  
Author(s):  
Hussein ALKasasbeh ◽  
Irina Perfilieva ◽  
Muhammad Ahmad ◽  
Zainor Yahya
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Trapezoidal Rule ◽  
Approximation Methods ◽  
System Of Differential Equations ◽  
Fuzzy Transform ◽  
Fuzzy Partition ◽  
Fuzzy Approximation ◽  
One Step ◽  
Basic Functions

In this research, three approximation methods are used in the new generalized uniform fuzzy partition to solve the system of differential equations (SODEs) based on fuzzy transform (FzT). New representations of basic functions are proposed based on the new types of a uniform fuzzy partition and a subnormal generating function. The main properties of a new uniform fuzzy partition are examined. Further, the simpler form of the fuzzy transform is given alongside some of its fundamental results. New theorems and lemmas are proved. In accordance with the three conventional numerical methods: Trapezoidal rule (one step) and Adams Moulton method (two and three step modifications), new iterative methods (NIM) based on the fuzzy transform are proposed. These new fuzzy approximation methods yield more accurate results in comparison with the above-mentioned conventional methods.

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