Graphical Data Representation in Bankruptcy Analysis

W. K. Hardle, R. A. Moro, and D. Schafer

3 Company Score Evaluation

The company score is computed as:

f (x) = x^τw + b,

where w = ^П=1 α_iy_ix_i and b = 11 (x+ + x_-)^τw; x+ and x_- are the obser-
vations from the opposite classes for which constraint (1) becomes equality.
By substituting the scalar product with a kernel function we will derive a
non-linear score function:

n

f(x) =     K(xi , x)αi yi + b.

i=1

The non-parametric score function (10) does not have a compact closed
form representation. This necessitates the use of graphical tools for its visu-
alisation.

4 Variable Selection

In this section we describe the procedure and the graphical tools for selecting
the variables of the SVM model used in forecasts. We have two most im-
portant criteria of model accuracy: the accuracy ratio (AR), which will be
used here as a criterion for model selection, (Figure 6) and the percentage of
correctly classified out-of-sample observations. Higher values indicate better
model accuracy.

Fig. 6. The power curves for a perfect (green), random (red) and some real (blue)
classification models. The AR is the ratio of two areas A/B. It lies between 0 for a
random model with no predictive power and 1 for a perfect model.

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