f-entropies, probability of error, and feature selection

Moshe Ben-Bassat

doi:10.1016/S0019-9958(78)90587-9

f-entropies, probability of error, and feature selection

Moshe Ben-Bassat^*

^*Corresponding author for this work

University of Southern California

Research output: Contribution to journal › Article › peer-review

55 Scopus citations

Abstract

The f{hook}-entropy family of information measures: u(P₁,..., p_m) = Σf(p_k), f{hook} concave (e.g., Shannon (1948)Bell Syst. Tech. J. 27, 379-423, 623-656; Suadratic; Daroczy (1970)Inform. Contr. 16, 36-51; etc.), is considered. Characterization of the tightest upper and lower bounds on f{hook}-entropies by means of the probability of error, is presented. These bounds are used to derive the dual bounds, i.e., the tightest lower and upper bounds on the probability of error by means of f{hook}-entropies. Concerning the use of f{hook}-entropies as a tool for feature selection, it is proved that none of the members of this family induce over an arbitrary set of features the same preference order as does the probability of error rule.

Original language	English
Pages (from-to)	227-242
Number of pages	16
Journal	Information and control
Volume	39
Issue number	3
DOIs	https://doi.org/10.1016/S0019-9958(78)90587-9
State	Published - Dec 1978
Externally published	Yes

Funding

Funders	Funder number
Health Resources and Services Administration
U.S. Public Health Service	RO1HS01474

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10.1016/S0019-9958(78)90587-9

Cite this

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title = "f-entropies, probability of error, and feature selection",

abstract = "The f{hook}-entropy family of information measures: u(P1,..., pm) = Σf(pk), f{hook} concave (e.g., Shannon (1948)Bell Syst. Tech. J. 27, 379-423, 623-656; Suadratic; Daroczy (1970)Inform. Contr. 16, 36-51; etc.), is considered. Characterization of the tightest upper and lower bounds on f{hook}-entropies by means of the probability of error, is presented. These bounds are used to derive the dual bounds, i.e., the tightest lower and upper bounds on the probability of error by means of f{hook}-entropies. Concerning the use of f{hook}-entropies as a tool for feature selection, it is proved that none of the members of this family induce over an arbitrary set of features the same preference order as does the probability of error rule.",

author = "Moshe Ben-Bassat",

note = "Funding Information: * This study was supported by United States Public Health Service Research Grant RO1HS01474 from the Health Resources Administration.",

year = "1978",

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PY - 1978/12

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N2 - The f{hook}-entropy family of information measures: u(P1,..., pm) = Σf(pk), f{hook} concave (e.g., Shannon (1948)Bell Syst. Tech. J. 27, 379-423, 623-656; Suadratic; Daroczy (1970)Inform. Contr. 16, 36-51; etc.), is considered. Characterization of the tightest upper and lower bounds on f{hook}-entropies by means of the probability of error, is presented. These bounds are used to derive the dual bounds, i.e., the tightest lower and upper bounds on the probability of error by means of f{hook}-entropies. Concerning the use of f{hook}-entropies as a tool for feature selection, it is proved that none of the members of this family induce over an arbitrary set of features the same preference order as does the probability of error rule.

AB - The f{hook}-entropy family of information measures: u(P1,..., pm) = Σf(pk), f{hook} concave (e.g., Shannon (1948)Bell Syst. Tech. J. 27, 379-423, 623-656; Suadratic; Daroczy (1970)Inform. Contr. 16, 36-51; etc.), is considered. Characterization of the tightest upper and lower bounds on f{hook}-entropies by means of the probability of error, is presented. These bounds are used to derive the dual bounds, i.e., the tightest lower and upper bounds on the probability of error by means of f{hook}-entropies. Concerning the use of f{hook}-entropies as a tool for feature selection, it is proved that none of the members of this family induce over an arbitrary set of features the same preference order as does the probability of error rule.

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f-entropies, probability of error, and feature selection

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