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1.2 Pattern Similarity and PR Tasks 7

As can be appreciated this time-series prediction task is an example of a broader
class of tasks known in mathematics as function approximation or regression /ask.
A system providing the regression solution will usually make forecasts (black
circles in Figure 1.5) somewhat deviated from the true value (curve, idem). The
difference between the predicted value and the true value, also known as target
value, constitutes a prediction error. Our aim is a solution yielding predicted
values similar to the targets, i.e., with small errors.
As a matter of fact regression tasks can also be cast under the form of
classification tasks. We can divide the dependent variable domain (r,) into
sufficiently small intervals and interpret the regression solution as a classification
solution, where a correct classification corresponds to a predicted value falling
inside the correct interval = class. In this sense we can view the sequence of values
as a feature vector, [r, rg rc Euro-USD-rate Interest-rate-6-months]' and
again, we express the similarity in terms of a distance, now referred to the
predicted and target values (classifications). Note that a coarse regression could be:
predict whether or not r,(t) is larger than the previous value, r,,(t-I). This is
equivalent to a 2-class classification problem with the class labelling function
sgn(ro(/)- r[,(t- 1)).
Sornetinies regression tasks are also performed as part of a classification. For
instance, in the recognition of living tissue a merit factor is often used by
physicians, depending on several features such as colour, texture, light reflectance
and density of blood vessels. An automatic tissue recognition system attempts then
to regress the merit factor evaluated by the human expert, prior to establishing a
tissue classification.

June 2000

/i~rnl A Firm B Finn C 1 1 USD 1 Interest 1 ~

, share share 1 share I 1 .O5 € , 4.66% ,
rate (6~)'
r-r r,
I '-0

Figure 1.5. Share value forecast one-day ahead, r,, r~, r( are share values of three
firms. Functional approximation (black circles) of the true value of r, (solid curve),
is shown for June 16 depending on the values of the shares, euro-dollar exchange
rate and interest rate for June 15.