Re: Linear disciminant analysis, dimensionality of data in each class< no: classes

On May 22, 3:13 pm, veena <veena.singampa...@xxxxxxxxx> wrote:
Hii
I have 44 classes. Each class is 14 dimensional, i.e. has 14
variables. I am just getting to know LDA. When I computed the LDA
transform, inv(Sw)* Sb, I got 14 eigen vectors.  The purpose of doing
so is to transform my feature space such that the seperation between
classes is maximised. Is it right to apply LDA in this scenario? How
can 14 eigen vectors describe the seperability between 44 classes.

The question should be "How do you expect 14 variables
to describe the sepa(sic)rability between 44 classes?".
The eigenstructure just finds ordered orthogonal directions
in which the ratio of the variance of residual
between-class-distance to the variance of residual
within-class-distance is maximized after the variations
in previous directions are removed.

You can answer your own question by looking at 2-D scatter
plots in the eigenvector coordinate system. The size of
the eigenvalues quantify, to some degree, the effectiveness
of projecting the data into the direction of the corresponding
eigenvector. You are then left to your own devices to
determine all of the thresholds. It can be done. However, it
is tedious enough to consider other approaches. Moreover.
the LDA optimization objective function is not error rate.

For example, you could just look at a simple linear
regression with binary dependent variables of
the form

Y(44,N)) = B(44,15)*[ ones(1,N); X(14,N)]

in the original coordinate system or

Y(44,N)) = B(44,M+1)*[ ones(1,N); Z(M,N)]

in a reduced M-dimensional eigenspace.

When that result is not satisfactory, I
use a Neural Network to take advantage of
nonlinear separability information.

There are a plethora of other options.
However, over the years I have found that
the Linear and Neural-Net models are
sufficient fo most purposes.

Hope this helps.

Greg


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