Page 211 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

200 FEATURE EXTRACTION AND SELECTION

included in the selected sets, it cannot be removed, even if at a higher
level in the tree, when more features are added, this feature would be less
useful.
The SFS adds one feature at a time to the current set. An improvement
is to add more than one, say l, features at a time. Suppose that at a given
stage of the selection process we have a set F j (n) consisting of n features.
Then, the next step is to expand this set with l features taken from the
remaining N n measurements. For that we have (N n)!=
((N n l)! l!) combinations which all must be checked to see which
one is most profitable. This strategy is called the generalized sequential
forward selection (GSFS(l)).
Both the SFS and the GSFS(l) lack a backtracking mechanism. Once a
feature has been added, it cannot be undone. Therefore, a further
improvement is to add l features at a time, and after that to dispose of
some of the features from the set obtained so far. Hence, starting with a
set of F j (n) features we select the combination of l remaining measure-
ments that when added to F j (n) yields the best performance. From this
expanded set, say F i (n þ l), we select a subset of r features and remove
it from F i (n þ l) to obtain a set, say F k (n þ l r). The subset of r features
is selected such that F k (n þ l r) has the best performance. This strategy
is called ‘Plus l – take away r selection’.

Example 6.2 Character classification for license plate recognition
In traffic management, automated license plate recognition is useful
for a number of tasks, e.g. speed checking and automated toll collec-
tion. The functions in a system for license plate recognition include
image acquisition, vehicle detection, license plate localization, etc.
Once the license plate has been localized in the image, it is partitioned
such that each part of the image – a bitmap – holds exactly one
character. The classes include all alphanumerical values. Therefore,
the number of classes is 36. Figure 6.6(a) provides some examples of
bitmaps obtained in this way.
The size of the bitmaps ranges from 15 6upto30 15. In order
to fix the number of pixels, and also to normalize the position, scale
and contrasts of the character within the bitmap, all characters are
normalized to 15 11.
Using the raw image data as measurements, the number of mea-
surements per object is 15 11 ¼ 165. A labelled training set con-
sisting of about 70 000 samples, i.e. about 2000 samples/class, is
available. Comparing the number of measurements against the num-
ber of samples/class we conclude that overfitting is likely to occur.