TY - GEN
T1 - Similarity-Based Correlation Functions for Binary Data
AU - Batyrshin, Ildar Z.
AU - Ramirez-Mejia, Ivan
AU - Batyrshin, Ilnur I.
AU - Solovyev, Valery
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - The purpose of this study is to survey the correlation and association coefficients introduced previously on the set of binary n-tuples and to determine coefficients satisfying the properties of correlation functions. These functions were recently introduced on the sets with involutive operation as functions generalizing classical correlation coefficients: Pearson’s product-moment correlation, Spearmen’s and Kendall’ rank correlation coefficients, Yule’s Q and Hamann’s association coefficients, etc. It is shown that several, but not all, known correlation and association coefficients defined on the set of binary n-tuples, satisfy the properties of correlation functions. For these association coefficients, there were established similarity measures on the set of binary data that can be used for the generation of these association coefficients. A new parametric family of correlation functions for binary data is proposed. As a particular case, it contains Hamann’s association coefficient.
AB - The purpose of this study is to survey the correlation and association coefficients introduced previously on the set of binary n-tuples and to determine coefficients satisfying the properties of correlation functions. These functions were recently introduced on the sets with involutive operation as functions generalizing classical correlation coefficients: Pearson’s product-moment correlation, Spearmen’s and Kendall’ rank correlation coefficients, Yule’s Q and Hamann’s association coefficients, etc. It is shown that several, but not all, known correlation and association coefficients defined on the set of binary n-tuples, satisfy the properties of correlation functions. For these association coefficients, there were established similarity measures on the set of binary data that can be used for the generation of these association coefficients. A new parametric family of correlation functions for binary data is proposed. As a particular case, it contains Hamann’s association coefficient.
KW - Association coefficient
KW - Binary data
KW - Correlation coefficient
KW - Correlation function
KW - Negation of Binary n-Tuples
KW - Similarity measure
UR - http://www.scopus.com/inward/record.url?scp=85092909575&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-60887-3_20
DO - 10.1007/978-3-030-60887-3_20
M3 - Contribución a la conferencia
AN - SCOPUS:85092909575
SN - 9783030608866
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 224
EP - 233
BT - Advances in Computational Intelligence - 19th Mexican International Conference on Artificial Intelligence, MICAI 2020, Proceedings
A2 - Martínez-Villaseñor, Lourdes
A2 - Ponce, Hiram
A2 - Herrera-Alcántara, Oscar
A2 - Castro-Espinoza, Félix A.
PB - Springer Science and Business Media Deutschland GmbH
T2 - 19th Mexican International Conference on Artificial Intelligence, MICAI 2020
Y2 - 12 October 2020 through 17 October 2020
ER -