In class independent LDA the within-class scatter is first computed which gives us a measure of how the points in each data set is distributed about their means. The between-class scatter is then computed taking the distances, from the global mean, of each data set into account. This in turn maximizes the between-class scatter for each set proportionately with respect to the other data sets. The transform is then determined by deriving the eigen vectors from the resulting ratio of the between-class scatter to the within-class scatter. Points from the current space are mapped to the new feature space my multiplying it with the transpose of the transform. - The within-class scatter is computed which defines the scatter
of samples around their respective means Our goal is to minimize
the within-class scatter in order for the points in each data set
to be as close together as possible.
- The between-class scatter is computed which defines scatter of expected
vectors around global mean. Our goal is to maximize the between-class
scatter so that each data set is a far a possible from each other.
Where is the overall mean.
- The transform is defined by the eigen vectors and eigen values
of the covariance. The eigen vectors describe the coordinate
system of the new feature space and the eigen values describe the
variance of the data set in the new feature space.
- Here is a brief example of how the class independent LDA scheme works:
First select the**Two Gaussian**data set from the**Patterns**menu. Following that select the**Class Independent LDA**option under the**Algorithms**menu. Initialize this algorithm by selecting**Initialize**from the**Go**menu.In order to compute the line of discrimination select the**Next**option under the**Go**menu. This will display the first step of the process, data sets in both the input plot (top left) and the output plot (bottom left) of the applet. Also, the process description box indicates which step you are currently on and the algorithm that is currently being used to compute the line of discrimination.
- The second step of the process computes the mean of the each
data set. The mean of each data sets is displayed on the output plot
as black dots near the corresponding data sets. The value of the mean
for each data set, which corresponds to the current scale, is
displayed on the process description box. The covariance and
transformation matrices used to compute the line of discrimination for
the data set are also displayed in the process description box.
- The third step of the process displays the line of
discrimination of the given data sets as determined by the class
independent LDA algorithm. Also, the classification error for each
data set along with the total classification error is displayed on the
process description box.
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