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Unformatted text preview: ; soe =s$clns$cln
> itret =ma([2)soe*enX,]
> bieaitret,=lp2cl"e" Plot the FLDA direction, again through the mean.
> eed-,,eedc"C""D",o=(bak,rd)ly1 Labeling the lines directly on the graph makes it easier to interpret. Dis tance Metric Learning VS FDA
In many fundamental machine learning problems, the Euclidean distances between data points do not represent the desired topology that we are trying to capture. Kernel
methods address this problem by mapping the points into new spaces where Euclidean distances may be more useful. An alternative approach is to construct a Mahalanobis
distance (quadratic Gaussian metric) over the input space and use it in place of Euclidean distances. This approach can be equivalently interpreted as a linear transformation
of the original inputs,followed by Euclidean distance in the projected space. This approach has attracted a lot of recent interest.
Some of the proposed algorithms are iterative and computationally expensive. In the paper,"Distance Metric Learning VS FDA
(http://www.aaai.org/Papers/AAAI/2008/AAAI08- 095.pdf) " written by our instructor, they propose a closed- form solution to one algorithm that previously required
expensive semidefinite optimization. They provide a new problem setup in which the algorithm performs better or as well as some standard methods, but without the
computational complexity. Furthermore, they show a strong relationship between these methods and the Fisher Discriminant Analysis (FDA). They also extend the approach
by kernelizing it, allowing for non- linear transformations of the metric. Fisher's Discriminant Analysis (FDA) - October 9, 2009
The goal of FDA is to reduce the dimensionality of data in order to have separable data points in a new space. We can consider two kinds of problems:
2- class problem
multi- class problem Two-clas s problem
In the two- class problem, we have the pre- knowledge that data points belong to two classes. Intuitively speaking points of each class form a cloud around the mean of the
class, with each...
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This document was uploaded on 03/07/2014.
- Winter '13