Combining Biometric Fractal Pattern and Particle Swarm Optimization-Based Classifier for Fingerprint Recognition

Table 1

Related data of the PSO-based classifier and traditional classifier.

	Method
Task	Proposed PSO-based classifier	Traditional classifier
Training data	30	30
Activation function	(2.7)	Gaussian function:
	$\xi =5,$	$H_k=\exp \hspace{0.17em}\hspace{0.17em}\left[-\frac{\text{ED}{(k)}^2}{2{\sigma }_k^2}\right]$
	$k=1,2,3,\dots ,K,$	$k=\mathrm{1,2},3,\dots ,K,$
	${\sigma }_1={\sigma }_2=\cdots ={\sigma }_K=\sigma .$	${\sigma }_1={\sigma }_2=\cdots ={\sigma }_K=\sigma .$
Parameter assignment	$\omega \in [\mathrm{0,1}]$	$\sigma (t=0)$ = 0.4$~$1.0
	${\text{rand}}_1\in [\mathrm{0,1}]$	$\eta (t=0)\mathrm{\hspace{0.17em}\hspace{0.17em}}=1.0$
	${\text{rand}}_2\in [\mathrm{0,1}]$	$\eta (t\to \infty )=0.1$
	$a_1=2.5,b_1=0.5$	$\eta$ = 0.1$~$1.0
	$c_1$ = 2.5$~$0.5
	$a_2=0.5,b_2=2.5$
	$c_2$ = 0.5$~$2.5
	$t_{\max \hspace{0.17em}}=100$
Parameter estimation	PSO algorithm with TVAC	Least mean square (LMS) Algorithm
Convergent condition	The number of iterations achieve the maximum allowable number $t_{\max \hspace{0.17em}}=100$	MSEF is less than the prespecified value 10^-3
Training iteration	Figure 5	Figure 5
Optimal parameter	0.0129	0.0131$~$0.0302
Training time (sec)	2.5790	2.4210

Note: Time-Varying Learning Rate: $\eta (t)={\eta }_0\exp \hspace{0.17em}\hspace{0.17em}(-t/\tau )$.