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In-Depth Information
consider initially a limited set of candidate features, and consider new ones
incrementally until an optimal subset is selected. The proposed algorithm
proceeds in an iterative manner: it receives at each time step either a new
example or a new feature or both, and adjusts the current set of selected
features. When a new feature is provided, the algorithm makes a decision
regarding whether to substitute an existing feature with the new one, or
maintain the current set of features, according to a value computed for
each feature relative to the current feature set. The value of each feature is
evaluated
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by the amount of class information it contributes to the features
in the selected set. The algorithm also keeps a fixed-size set of the most
recent examples, used to evaluate newly provided features. In this way, the
evaluation time of the features value, which depends only on the number
of examples and the number of features in the selected set, is constant
throughout the learning. Given a feature
f
and a set of selected features
S, the desired merit value
MV
(
f
;
S
)
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should express the additional class
information gained by adding
f
to
S
. This can be measured using mutual
information by:
MV
(
f
;
S
)=
I
(
f
;
S
;
C
)
−
I
(
S
;
C
)
,
(8.6)
where
I
stands for mutual information.
8.2.10.
Multiclass MTS for simultaneous feature selection
and classification
Here the important features are identified using the orthogonal arrays
and the signal-to-noise ratio, and are then used to construct a reduced
model measurement scale. Mahalanobis distance and Taguchi's robust
engineering.
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Mahalanobis distance is used to construct a multidimensional
measurement scale and define a reference point of the scale with a set
of observations from a reference group. Taguchi's robust engineering is
applied to determine the important features and then optimize the system.
The goal of multiclass classification problems
76,77
is to find a mapping or
function,
C
i
=
f
(
X
), that can predict the associated class label
C
(
i
)ofa
given example vector
X
. Thus, it is expected that the mapping or function
can accurately separate the data classes. MTS is different from classical
multivariate methods in the following ways.
78,79
First, the methods used in
MTS are data analytic instead of probability-based inference. This means
that MTS does not require any assumptions on the distribution of input
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