L2-norm multiple kernel learning and its application to biomedical data fusion

Yu, Shi; Falck, Tillmann; Daemen, Anneleen; Tranchevent, Leon-Charles; Suykens, Johan AK; De Moor, Bart; Moreau, Yves

doi:10.1186/1471-2105-11-309

BMC Bioinformatics

Table 7 Results of experiment 3: classification of patients in rectal cancer clinical decision using microarray and proteomics data sets

From: L₂-norm multiple kernel learning and its application to biomedical data fusion

	LSSVM L_∞					SVM L_∞
	14 p	15 p	16 p	17 p	18 p	14 p	15 p	16 p	17 p	18 p
24 g	0.0584	0.0519	0.0747	0.0812	0.0812	0.1331	0.1331	0.1331	0.1331	0.1364
25 g	0.0390	0.0390	0.0519	0.0617	0.0649	0.1136	0.1104	0.1234	0.1201	0.1234
26 g	0.0487	0.0487	0.0812	0.0844	0.0877	0.1266	0.1136	0.1234	0.1299	0.1364
27 g	0.0617	0.0649	0.0812	0.0877	0.0942	0.1429	0.1364	0.1364	0.1331	0.1461
28 g	0.0552	0.0487	0.0617	0.0747	0.0714	0.1429	0.1331	0.1331	0.1364	0.1396
	LSSVM L_∞ (0.5)					SVM L_∞ (0.5)
	14 p	15 p	16 p	17 p	18 p	14 p	15 p	16 p	17 p	18 p
24 g	0.0584	0.0519	0.0747	0.0812	0.0812	0.1266	0.1006	0.1266	0.1299	0.1331
25 g	0.0390	0.0390	0.0519	0.0617	0.0649	0.1136	0.1071	0.1234	0.1201	0.1234
26 g	0.0487	0.0487	0.0812	0.0844	0.0877	0.1136	0.1136	0.1201	0.1266	0.1331
27 g	0.0617	0.0649	0.0812	0.0877	0.0942	0.1364	0.1364	0.1364	0.1331	0.1461
28 g	0.0552	0.0487	0.0617	0.0747	0.0714	0.1299	0.1299	0.1299	0.1331	0.1364
	LSSVM L₁					SVM L₁
	14 p	15 p	16 p	17 p	18 p	14 p	15 p	16 p	17 p	18 p
24 g	0.0487	0.0487	0.0682	0.0682	0.0747	0.0747	0.0584	0.0714	0.0682	0.0747
25 g	0.0357	0.0325	0.0422	0.0455	0.0455	0.0584	0.0519	0.0649	0.0714	0.0714
26 g	0.0357	0.0357	0.0455	0.0455	0.0455	0.0584	0.0519	0.0682	0.0682	0.0682
27 g	0.0357	0.0357	0.0455	0.0487	0.0519	0.0617	0.0584	0.0714	0.0682	0.0682
28 g	0.0422	0.0325	0.0487	0.0487	0.0519	0.0584	0.0584	0.0649	0.0649	0.0682
	LSSVM L₂					SVM L₂
	14 p	15 p	16 p	17 p	18 p	14 p	15 p	16 p	17 p	18 p
24 g	0.0552	0.0487	0.0747	0.0779	0.0714	0.0909	0.0877	0.0974	0.0942	0.1006
25 g	0.0390	0.0390	0.0487	0.0552	0.0552	0.0747	0.0649	0.0812	0.0844	0.0844
26 g	0.0390	0.0455	0.0552	0.0649	0.0649	0.0747	0.0584	0.0812	0.0779	0.0779
27g	0.0422	0.0487	0.0552	0.0584	0.0649	0.0779	0.0812	0.0844	0.0812	0.0812
28 g	0.0455	0.0325	0.0487	0.0584	0.0552	0.0812	0.0714	0.0812	0.0779	0.0812

The table shows the error of AUC in patient classification using microarray and proteomics data. In LSSVM L_∞, L_∞ (0.5), and L₂, the regularization parameter λ was estimated jointly as the kernel coefficient of an identity matrix. In LSSVM L₁, λ was set to 1. In all SVM approaches, the C parameter of the box constraint was set to 1. In the table, the row and column labels represent the numbers of genes (g) and proteins (p) used to construct the kernels. The genes and proteins were ranked by feature selection techniques (see text). The AUC of LOO validation was evaluated without the bias term b (as the implicit bias approach) because its value varied by each left out sample. In this problem, considering the bias term decreased the AUC performance. The performance was compared among eight algorithms for the same number of genes and proteins, where the best values (the smallest Error of AUC) are represented in bold, the second best ones in italic. The best performance of all the feature selection results is underlined. The table presents the 25 best feature selection results of each method. The complete experimental results containing 26 different numbers of genes and 26 numbers of proteins is available at http://homes.esat.kuleuven.be/~sistawww/bioi/syu/l2lssvm.html.

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ISSN: 1471-2105

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