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Accuracy measure
The accuracy of a classifier can be measured in any set: training,
evaluation, and test. Let
be any one of these sets and
be the
number of samples in
. The accuracy
is measured by taking
into account that the classes may have different sizes in
. If
there are two classes, for example, with very different sizes and a
classifier always assigns the label of the largest class, its accuracy
will fall drastically due to the high error rate on the smallest
class.
Let
,
, be the number of samples in
from each class
. We define
and ![$\displaystyle e_{i,2}=\frac{FN(i)}{\left\vert N(i)\right\vert}, i=1,\ldots,c$](img11.png) |
(1) |
where
and
are the false positives and false negatives,
respectively. That is,
is the number of samples from other
classes that were classified as being from the class
in
,
and
is the number of samples from the class
that were
incorrectly classified as being from other classes in
. The
errors
and
are used to define
![$\displaystyle E(i)=e_{i,1}+e_{i,2},$](img16.png) |
(2) |
where
is the partial sum error of class
. Finally, the
accuracy
of the classification is written as
![$\displaystyle Acc=\frac{2c-\sum_{i=1}^{c}E(i)}{2c}=1-\frac{\sum_{i=1}^{c}E(i)}{2c}.$](img18.png) |
(3) |
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Joao Paulo Papa
2009-09-30