Detection of Malignant and Benign Breast Cancer Using the ANOVA-BOOTSTRAP-SVM

Figure 1

Time comparison of SVMs’s versions on the WBCD_

	Time
l2-SVM	0.20
LP-SVM	0.10
MILP1-NFS	0.20
MILP2-NFS	0.30
Fisher + SVM	0.20
l1-SVM	0.40
RFE-SVM	0.40
l0-SVM	0.50
MILP1-FS	0.20
MILP2-FS	0.20
ANOVA-CV-L-SVM	0.04
ANOVA-CV-RBF-SVM	0.05
ANOVA-Bootstrap-L-SVM	0.05
ANOVA-Bootstrap-RBF-SVM	0.07
ANOVA-PCA-Bootstrap-L-SVM	0.07
ANOVA-PCA-Bootstrap-RBF-SVM	0.06
Classical SVM with linear kernel C=1	0.65
Classical SVM with RBF kerne C=1	0.95
Classical SVM with linear kernel C=0.1	0.55
Classical SVM with RBF kernel C=0.1	1.02

Khairunnahar et al_’s results on WBCD (sigmoid classification function)_

	ACC	AUC	k	Error rate
Classical system	95.708	82.000	12	4.3
Proposed sigmoid	97.425	90.000	12	2.6
Classical system	95.423	97.540	31	4.6
Proposed sigmoid	96.831	99.000	31	3.2

Vrigazova’s results on the WBCD_

	ACC	AUC	k	Error rate
ANOVA-CV-RBF-SVM	97.310	99.750	3	2.7
ANOVA-Bootstrap-L-SVM*	97.270	99.131	24	2.7
ANOVA-Bootstrap-RBF-SVM	97.561	99.477	27	2.4
ANOVA-PCA-Bootstrap-L-SVM*	95.985	99.221	27	4.0
ANOVA-PCA-Bootstrap-RBF-SVM*	92.908	99.445	3	7.1
Classical SVM with linear kernel C=1	97.540	99.990	30	2.5
Classical SVM with RBF kernel C=1	97.720	99.990	30	2.3
Classical SVM with linear kernel C=0.10	97.890	99.941	30	2.1
Classical SVM with RBF kernel C=0.10	94.550	99.059	30	5.5

Performance of modified classifications on the WBCD_

	ACC	AUC	k	Error rate
LR with bootstrap	97.362	99.494	30	2.6
DT with bootstrap	92.085	92.458	30	7.9
SVM bootstrap	97.070	99.451	30	2.9
KNN bootstrap	96.159	98.082	30	3.8
ANOVA-Bootstrap-RBF-SVM C=5	98.561	99.425	27	1.4
ANOVA-Bootstrap-RBF-SVM C=7	98.201	99.412	30	1.8
ANOVA-Bootstrap-RBF-SVM C=13	98.221	99.088	21	1.8
ANOVA-Bootstrap-RBF-SVM C=14	98.276	99.648	27	1.7
ANOVA-Bootstrap-RBF-SVM C=30	98.913	99.445	24	1.1
ANOVA-Bootstrap-RBF-SVM C=32	99.627	98.808	27	0.4

Comparison of the ANOVA-BOOTSTRAP-RBF-SVM performance and the classic ANOVA-SVMs with cross validation_

Algorithm	Datset	Kernel	C	ACC	AUC	N of features	Error rate
ANOVA-BOOTSTRAP-RBF-SVM	WPBC	rbf	30	85.4	71.9	20	14.6
		rbf	5	82.3	70.3	26	17.7
		rbf	7	84.5	71.0	20	15.5
		rbf	13	83.7	71.5	26	16.3
		rbf	14	87.8	75.8	23	12.2
		rbf	32	84.6	71.9	26	15.4
	Mamographic	rbf	5	83.3	83.5	4	16.7
	Mass dataset	rbf	7	81.5	83.5	4	18.5
		rbf	13	82.4	83.7	5	17.6
		rbf	14	82.5	83.7	5	17.5
		rbf	32	84.5	83.7	5	15.5
		rbf	30	81.7	83.8	3	18.3
Classic ANOVA SVMs with tenfold cross validation	WPBC	rbf	30	78.5	71.7	26	21.5
		rbf	5	74.6	69.1	3	25.4
		rbf	7	74.9	69.1	3	25.1
		rbf	13	75.1	69.1	23	24.9
		rbf	14	75.4	69.1	30	24.6
		rbf	32	78.5	71.7	26	21.5
	Mamographic	rbf	5	78.7	85.8	3	21.3
	Mass dataset	rbf	7	79.0	85.9	3	21.0
		rbf	13	79.5	86.4	4	20.5
		rbf	14	79.6	86.3	4	20.4
		rbf	32	80.0	87.0	5	20.0
		rfb	30	80.1	86.9	5	19.9

Maldonado et al_’s results on WBCD (Mixed linear integer approach)_

	ACC	AUC	k	Error rate
l2-SVM*	97.900	97.300	31	2.1
LP-SVM*	97.200	96.500	31	2.8
l1-SVM*	97.500	97.200	31	2.5
Fisher+ SVM*	97.900	97.300	31	2.1
RFE-SVM*	97.900	97.300	23	2.1
l0-SVM*	97.900	97.300	16	2.1
MILP1*	98.100	97.700	26	1.9
MILP2*	97.900	97.300	17	2.1