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Data Description Through Information Granules: A Multiview Perspective

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Abstract

In light of the remarkable diversity of data, arises an interesting and challenging problem of their description and concise interpretation. In a nutshell, in the proposed description pursued in this study, we consider a framework of information granules. The study develops a general scheme composed of two functional phases: (i) clustering data and features forming segments of original data and delivering a meaningful partition of data, and (ii) development of information granules. In both phases, we discuss a suite of performance indexes quantifying the quality of segments of data and the resulting information granules. Along this line, discussed are collections of information granules and their mutual relationships. A series of publicly available data sets is used in the experiments—their granular signature is quantified, and the quality of these findings is analyzed.

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Acknowledgements

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia, under Grant No. (KEP-5-135-39). The authors, therefore, acknowledge with thanks DSR technical and financial support.

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Authors and Affiliations

  1. Department of Electrical & Computer Engineering, University of Alberta, Edmonton, AB, T6R 2V4, Canada

    Witold Pedrycz

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Witold Pedrycz

  3. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Abdullah Balamash, Witold Pedrycz, Rami Al-Hmouz & Ali Morfeq

  4. Center of Excellence in Intelligent Engineering Systems (CEIES), King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Abdullah Balamash

Authors
  1. Abdullah Balamash
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  2. Witold Pedrycz
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  3. Rami Al-Hmouz
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  4. Ali Morfeq
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Corresponding author

Correspondence to Abdullah Balamash.

Appendix A

Appendix A

Used symbols

Symbol

Description

Di

Data cluster i

Fj

Feature cluster j

r

Number of feature clusters

c

Number of data clusters

Q

FCM objective variable

xk

Data point k

zj

Feature j

N

Total number of data points

n

Total number of features

vi

Data cluster i prototype

m

Fuzzification coefficient

uik

The membership value of a data point xk to the data cluster i

gij

The membership value of a feature zj to the feature cluster i

Vij

Reconstruction error produced for (Di, Fj)

\(\left\| \cdot \right\|_{{F_{j} }}\)

Distance completed for features forming Fj

ρij

The probability class j exists in information granule i

vij

Data cluster i prototype computed by averaging cluster data points just for features forming Fj

h

Entropy

Ci

Vagueness of the ith information granule

σiy

The variance of the output values of data cluster i

\(\bar{y}_{i}\)

The average of the output values of data cluster i

Ri

 

Nij

Number of data points in information granule Gij ≡ (Di, Fj)

cov

Coverage

sp

Specify

\(\hat{y}\)

Predicted y value

\(\rho\)

Predicted class

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Balamash, A., Pedrycz, W., Al-Hmouz, R. et al. Data Description Through Information Granules: A Multiview Perspective. Int. J. Fuzzy Syst. 22, 1731–1747 (2020). https://doi.org/10.1007/s40815-020-00903-z

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  • DOI: https://doi.org/10.1007/s40815-020-00903-z

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