Generalized Exponential Bidirectional Fuzzy Associative Memory with Fuzzy Cardinality-Based Similarity Measures Applied to Face Recognition

SOUZA, A.C.; VALLE, M.E.

doi:10.5540/tema.2018.019.02.0221

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Articles • TEMA (São Carlos) 19 (2) • May-Aug 2018 • https://doi.org/10.5540/tema.2018.019.02.0221 copy

Generalized Exponential Bidirectional Fuzzy Associative Memory with Fuzzy Cardinality-Based Similarity Measures Applied to Face Recognition

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Associative memories are biologically inspired models designed for the storage and recall by association. Such models aim to store a finite set of associations, called the fundamental memory set. The generalized exponential bidirectional fuzzy associative memory (GEB-FAM) is a heteroassociative memory model designed for the storage and recall of fuzzy sets. A similarity measure, that is, a function that indicates how much two fuzzy sets are equal, is at the core of a GEB-FAM model. In this paper, we present a detailed study on the use of cardinality-based similarity measures in the definition of a GEB-FAM. Moreover, we evaluate the performance of the GEB-FAMs defined using such measures in a face recognition problem.

Keywords:
Associative memory; fuzzy set theory; similarity measure; face recognition

S	Expression	S	Expression
R ₁	$\frac{# (A \cap B)}{\max {# A, # B}}$	R ₁₀	$\frac{\min {# (A \ B), # (B \ A)}}{\max {# (A \ B), # (B \ A)}}$
R ₂	$\frac{# {(A Δ B)}^{c}}{\max {# {(A \ B)}^{c}, # {(B \ A)}^{c}}}$	R ₁₁	$\frac{\min {# A, # B}}{\max {# A, # B}}$
R ₃	$\frac{# (A \cap B)}{\min {# A, # B}}$	R ₁₂	$\frac{\min {# {(A \ B)}^{c}, # {(B \ A)}^{c}}}{\max {# {(A \ B)}^{c}, # {(B \ A)}^{c}}}$
R ₄	$\frac{# {(A Δ B)}^{c}}{\min {# {(A \ B)}^{c}, # {(B \ A)}^{c}}}$	R ₁₃	$\frac{\min {# (A \ B), # (B \ A)}}{# (A Δ B)}$
R ₅	$\frac{# (A \cap B)}{# (A \cup B)}$	R ₁₄	$\frac{\min {# A, # B}}{# (A \cup B)}$
R ₆	$\frac{# {(A Δ B)}^{c}}{n}$	R ₁₅	$\frac{\min {# {(A \ B)}^{c}, # {(B \ A)}^{c}}}{n}$
R ₇	$\frac{\max {# (A \ B), # (B \ A)}}{# (A Δ B)}$	S ₁₇	$\frac{# (A \cap B)}{\max {# {(A \ B)}^{c}, # {(B \ A)}^{c}}}$
R ₈	$\frac{\max {# A, # B}}{# (A \cup B)}$	S ₁₈	$\frac{# (A \cap B)}{n}$
R ₉	$\frac{\max {# {(A \ B)}^{c}, # {(B \ A)}^{c}}}{n}$	S ₁₉	$\frac{\min {# A, # B}}{n}$

	LRC	CRC	SRC	CESR	RSC	SSEC	NMR
a)	90.2	83.3	95.6	93.5	90.6	75.0	94.6
b)	30.4	54.6	54.8	34.8	39.8	23.1	70.4
	SNL₂R2	SNL₁R1	DNL₂R2	DNL₁R1
a)	95.7	96.1	95.8	96.7
b)	70.2	71.2	70.4	72.3

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[1] *Corresponding author: Aline C. Souza - E-mail: s.alinedesouza@gmail.com