Abstract: . . .  R at a low value, then in minimizing the second term of (1). B. Hyperplane Classification Our training data is formed by l points N i x l i ... 1 = and N is the number of considered parameters. At each i x we associate an 1 = i y Let's suppose that ( ) i i y x , , l i .. 1 = , are linearly separable in N by an hyperplane defined by: 0 , = + b x w with N w , b . Finding this hyperplane is equivalent to maximize the margin. The margin is the minimal distance between the surface of decision and training observations, otherwise, it is the distance to the nearest point i x . Fig. 2. Hyperplane classification We can easily show that the margin is equal to: w 2 It leads to the following optimization problem under constraint: Optimal hyperplane Page 3 3 of 4 [ ] ( ) = = + l i y x f b x w y cs w i i i i ,..., 1 , . . .
. . .  73.06 73.51 SE variance 8.18 7.35 7.63 7.55 For each function, we also calculate the number of experiences (NB_76) where SP and SE reached 76%. The result is reported in table II. T ABLE II Number of experiences for SP and SE 76% linear polynomial RBF ERBF NB_76 6 9 13 15 Fig. 7. SP (solid line) and SE (dotted line) variation according to C. According to the preceding study, it is clear that the ERBF function fits well our case. Then, we study the evolution of SP and SE in function of C (fig.7). We choose C=990 giving SP mean of 75% and SE mean of 73%. Once these parameters are fixed, the performances obtained are : a specificity of 90% and a sensitivity of 84.7%. With the same training base, a discriminant analysis or a neural network leads to SP=65% and SE=70% [5]. VI. CONCLUSION In this paper, SVM is applied to detect patients prone to to atrial fibrillation . The classification results are promising: 90% of specificity and 84.7% of sensitivity that represents an increase of more 20% compared to two other classic methods : discriminant analysis and neural network. R EFERENCES [1] W.B. Kanel, R.D. Abbott, D.D.Savage, P.M. McNamara, Epidemiologic features of chronic atrial fibrillation : the Framingham study, N.Engl.J.Med 306, pp1018-1022, 1982. . . .
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