Database Reference
In-Depth Information
the class for the literal. If the literal is false, then the weight of the class
for the literal is subtracted from the weight of the class.
The first literal in the table
“true percentage(E, x, 1 4, 4, 36, 95)”
has
associated for each class the weights
54. This means
that if the literal is true (false), it is likely that the class is (not) the second
one. This literal is not useful for discriminating between the first and the
third class.
−
0
.
55, 3.43 and
−
0
.
4. Variable Length Series
Due to the method used to select the literals that forms the base classi-
fiers, the learning system that we have introduced in the preceding sections
requires series of equal length. Consequently, to apply it to series of differ-
ent lengths, it is necessary to preprocess the data, normalizing the length
of the series.
There are several methods, more or less complex, that allow normalizing
the length of a set of series. These methods, which preprocess the data set,
can be adequate for some domains. However, the use of these methods is
not a general solution, because they destroy a piece of information that may
be useful for the classification: the own length of the series. Therefore, it is
important that the learning method can deal with variable length series. Of
course, it can still be used with preprocessed data sets of uniform length.
To learn from series of variable length, we have opted for a slight mod-
ification of the learning algorithm, that allow a literal to inhibit — or
abstain — when there are not enough data for its evaluation. This modifi-
cation also requires some change on the boosting method. With the basic
boosting method, for binary problems, the base classifiers return +1 or
−
1. Nevertheless, there are variants that use confidence-rated predictions
[Schapire and Singer (1998)]. In this case, the base learner returns a real
value: the sign indicates the classification and the absolute value the confi-
dence in this prediction. A special case consists in the use of three values:
−
1, 0 and +1. The value 0 indicates that that base classifier abstains. The
value of
α
is again selected as
2
ln
W
+
=
1
α
.
W
−
Until now, a literal could be true or false, because all the series had the
same length. If the series are of different lengths, there will be literals with
intervals that are after the end of the shortest series. For these cases, the
result of the evaluation of the literal could be an abstention, a 0, but due
