Optimized Feature-Level Fusion Model For Multimodal Biometric System

R. Bharathi; M. B. Anandaraju

doi:10.2478/ijssis-2026-0002

Figures & Tables

Acquisition function used in BO. BO, Bayesian optimization.

Parallel coordinates plot of the Hyperparameters.

Convergence of hyper parameter optimization.

Optimized EER. EER, equal error rate; FPR, false positive rate; TPR, true positive rate.

Performance of optimized multimodal system. EER, equal error rate.

ROC curve in fourth iteration. FPR, false positive rate.

Statistical Parameter analysis using 5-Fold cross Validation_

Iteration	Accuracy	Macro AUC	Macro Recall	Macro F1-score	EER	NRMSE
1	0.9480	0.9133	0.8853	0.9131	0.1491	0.0897
2	0.9101	0.8946	0.8728	0.8937	0.2325	0.0864
3	0.9328	0.8845	0.9269	0.8740	0.1497	0.0879
4	0.9501	0.9644	0.9559	0.9494	0.1478	0.0983
5	0.9306	0.9161	0.9087	0.9570	0.1581	0.0941
Average	0.9343	0.9146	0.9099	0.9174	0.1674	0.0913

SMBO

Data: f,x,A,M

// Data initialiszation

Q ← Init. Samples (f,x);

// run up to N steps

for i ← |Q| to N do

// Model Training

p(y ∣ x, Q) ← FitModel(M, Q);

// Selection of best hyperparameter

x_i ← argmax_x∈X A(x,p(y ∣ x, Q));

// estimate the hyperparameters

y_i ← f(x_i);

// append new data

Q ← Q ∪ (x_i,y_i);

end

Comparison of proposed model with state of art of models

No.	Authors	Accuracy in%
1	Kumarmohanta et al.[41]	85.20
2	Soleymani et al.[42]	88.12
3	Alshardan et al. [6]	90.01
4	Proposed Model	95.01

Optimization analysis of the parameters

Iter	Eval	Objective	Objective (run time)	Best so far	Best so far est time	Box constraint	Kernel scale
1	B	0.096	13.135	0.096	0.096	0.337	0.002
2	B	0.079	1.576	0.079	0.082	871.77	0.010
3	A	0.331	91.062	0.079	0.092	431.78	0.029
4	A	0.833	2.125	0.079	0.079	0.002	26.961
5	A	0.079	3.016	0.079	0.079	0.074	0.002
6	A	0.902	0.735	0.079	0.079	0.041	998.72
7	B	0.069	12.351	0.069	0.069	0.001	0.001
8	A	0.077	2.731	0.069	0.069	0.065	0.004
9	A	0.223	46.893	0.069	0.069	152.81	0.001
10	A	0.167	0.636	0.069	0.079	0.001	0.004
11	A	0.079	5.504	0.069	0.078	964.37	0.001
12	A	0.079	2.760	0.069	0.069	984.19	0.003
13	A	0.079	2.050	0.069	0.069	7.319	0.004
14	A	0.098	20.025	0.069	0.069	0.059	0.001
15	A	0.763	1.779	0.069	0.069	0.001	0.039
16	A	0.894	242.51	0.069	0.069	8.479	984.37
17	A	0.079	2.163	0.069	0.068	0.455	0.005
18	A	0.398	0.693	0.069	0.069	0.001	0.748
19	A	0.079	7.152	0.069	0.068	90.169	0.001
20	A	0.098	6.362	0.069	0.069	0.001	0.002
21	A	0.079	2.122	0.069	0.069	984.74	0.007
22	A	0.196	55.945	0.069	0.069	863.67	0.005
23	A	0.073	5.081	0.069	0.069	0.001	0.001
24	A	0.831	195.47	0.069	0.069	965.59	8.748
25	A	0.094	1.953	0.069	0.069	0.001	0.002
26	A	0.079	4.070	0.069	0.069	840.91	0.002
27	A	0.079	7.255	0.069	0.069	0.062	0.001
28	A	0.079	2.759	0.069	0.069	0.195	0.003
29	A	0.240	0.550	0.069	0.069	0.001	0.135
30	A	0.388	149.79	0.069	0.069	920.34	0.236

Hyper parameter optimization process using Bayesian approach

BO process	Hyperparameter tuning
Total function evaluations	30
Observed objective function value	0.06875
Estimated objective function value	0.069326
Function evaluation time	12.3512
Box constraint	0.0013385
Kernel scale	0.0010021

BSFF Objective Function

Input: F, y, λ_LBP, λ_svm

Output: Statistical Parameter

// hyperparameters usage from BO

λ_LBP← Trial from BO;

λ_SVM← Trial from BO.

// run for each Trait Ear, Iris, Fingerprint

for j←1 to n do

// LBP feature extraction

F_Ej ← Get LBP (xj, λ_LBP); //Ear

FIj ← Get LBP (x_j, λ_LBP); // Iris

F_FPj ← Get LBP (x_j, λ_LBP); // Fingerprint

// concatenate the features as a Fused Feature vector

F ← {F_Ej, F_Ij, F_FPj};

// split Fused features (F) into train and test data

x_train, x_test, y_train, y_test ← Train Test Split(x, y);

// train a SVM model with BO

SVMFit (x_train, y_train, λ_SVM);

// use the trained model (M) to predict test data

y_pred ← SVM_Predict (M, x_test);

// Evaluate Statistical Parameter (SP)

SP← Get SP (y_test, y_pred);

return SP.

Optimized Feature-Level Fusion Model For Multimodal Biometric System

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