Digital Signal Processing Reference
In-Depth Information
of each class,
v
umin
is its minimum and
v
umax
is the maximum value.
v
u
(
K,
X
,
W
) is given by the average of the mean intracluster distance
over the cluster number
K
, and measures the structural compactness
of each and every class.
v
o
(
K,
X
,
W
) is given by the ratio between the
cluster number
K
and the minimum distance between cluster centers,
describing intercluster separation.
X
is the matrix of the data points
and
W
is the matrix of the prototype vectors. Similarly,
v
o
(
K
)isthe
overpartitioned measure defined as the ratio between the cluster number
and the minimum distance between cluster centers that measures the
intercluster separation.
v
omin
is its minimum and
v
omax
is the maximum
value. The goal is to find the optimal cluster number with the smallest
value of
I
Kim
for a cluster number
K
=2to
K
max
.
6.8
Classifier Evaluation Techniques
The evaluation of the classification accuracy of the pattern recognition
paradigms and the comparisons among them are accomplished based on
well-known tools such as the confusion matrix, the ranking order curves,
and ROC curves.
Confusion matrix
For a classification system, it's important to determine the percentage
of correctly and incorrectly classified data.
A convenient visualization tool when analyzing results in an error-
prone classification system in general is the
confusion matrix
,which
is a two-dimensional matrix containing information about the actual
and predicted classes. The dimension of the matrix corresponds to the
number of classes. Entries on the diagonal of the matrix are the correct
classes and those off-diagonal are the misclassifications. The columns
are the actual classes and the rows are the predicted classes. The ideal
error-free classification case is a diagonal confusion matrix. Table 6.3
shows a sample confusion matrix. The confusion matrix allows us to keep
track of all possible outcomes of a classification process. In summary,
each element of the confusion matrix indicates the chances that the row
element is confused with the column element.
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