MACHINE LEARNING TECHNIQUES - LASA

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To better understand the effect that n has on the optimization observe first that if ν ≥ 1 then the
second and third conditions in (5.75) are redundant and hence all values of n greater than 1 will
have the same effect on the optimization. One should then work solely with values ranging
between 0≤ν
≤ 1.
Interestingly, a number of properties can be derived:
(*)
• n is an upper bound on the fraction of error (i.e. the proportion of datapoints with ξ > 0),
• n is a lower bound on the fraction of support vectors.
These two properties are illustrated in Figure 5-16.
In summary, n-SVR is advantageous over e-SVM in that it allows one to automatically adjust the
sensitivity of the algorithm through the automatic computation of e. To some extent, this is
equivalent to fitting a model of the noise on the data (assuming a uniform noise model). This is
illustrated in Figure 5-15.
Figure 5-15: Effect of the automatic adaptation of e using n-SVR. (Top) Data with no noise. (Bottom) Same
dataset with a white noise. In both plots, n-SVR was fitted with C=100, n=0.05, and a Gaussian kernel with
kernel width=0.021.
© A.G.Billard 2004 – Last Update March 2011