Page 271 - Contributed Paper Session (CPS) - Volume 4

CPS2222 Abdullah M.R. et al.
identifying outliers accurately. Essentially, the recognition of outliers should
be possible by utilizing the non-sparse − tube loss function is given by

0 | − ()| ≤ 0

( ) = { | − ()| ℎ

Thus, the convex optimization problem mentioned can be rephrase as shown
below:

1
‖‖ + ∁ ∑( − )
∗
2
2
=1

− . Φ( ) − ≤

{. Φ( ) + − ≤
∗

∗
, ≥ 0, = 1,2 … ,

Therefore, the last regression function of the non-sparse − tube SVR and
the load vector could be appointed to the following condition:

() = ∑( − )( . ) +
∗

=1

= ∑( − )Φ( )
∗

=1

As exhibited by Rojo-Álvarez et al. (2003), controlling the free parameters
of SVM (C, ɛ and the part parameter h) outliers are less taken care, or it permits
the decrease in the effect of outliers in the solution. As indicated by Üstün et
al. (2005), the strength and robustness of the SVR depends primarily on the
choice of C, in light of the fact that the most astounding and values, by
∗

meaning of the Lagrange system, are equivalent to C. More absolutely, an
extremely high value of C creates in SVs with a high variance among and
∗

values, bringing signifivant loads. The most elevated Lagrange multipliers

belong to the rare data point in the training data, is considered as an outlier
as mentioned by (Jordaan and Smts 2004). The load vector increases at any
increment in estimated point C, including the presence of outliers. In this
circumstance, it is not difficult to control the effect of outliers dependent on C
and the kernel characteristics.
The characteristic of kernel functions can also become a`nother reason to
be taken into consideration. Based on Williams (2011), the SVM calculation is
sensitive to the tuning decision (the class of kernel), thus it is essential to
understand how kernel function works. The information basically follows two
kinds of kernel such as exponential radial basis function and the linear
function. Thus, two demonstrative techniques are going to be introduced for
the suitability in a wide range of data
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