Aditya Narayanan
Roll No.: 14125
Operations
Group - B
Discriminant Analysis may be used
for two objectives: either we want to
assess the adequacy of classification, given the group memberships of the
objects under study; or we wish to assign objects to one of a number of (known)
groups of objects. Discriminant Analysis may thus have a descriptive or a
predictive objective.
In both cases, some group
assignments must be known before carrying out the Discriminant Analysis. Such
group assignments, or labelling, may be arrived at in any way. Hence
Discriminant Analysis can be employed as a useful complement to Cluster
Analysis (in order to judge the results of the latter) or Principal Components
Analysis. Alternatively, in star-galaxy separation, for instance, using
digitised images, the analyst may define group (stars, galaxies) membership
visually for a conveniently small training set or design set.
Methods implemented in this area
are Multiple Discriminant Analysis, Fisher's Linear Discriminant Analysis, and
K-Nearest Neighbours Discriminant Analysis.
Multiple Discriminant Analysis
(MDA) is also termed
Discriminant Factor Analysis and
Canonical Discriminant Analysis. It adopts a similar perspective to PCA: the
rows of the data matrix to be examined constitute points in a multidimensional space,
as also do the group mean vectors.
Linear Discriminant Analysis
Is the 2-group case of MDA. It optimally separates two groups, using the
Mahalanobis metric or generalized distance.
It also gives the same linear separating decision surface as Bayesian
maximum likelihood discrimination in the case of equal class covariance
matrices.
K-NNs Discriminant Analysis
Non-parametric
(distribution-free) methods dispense with the need for assumptions regarding
the probability density function. They have become very popular especially in
the image processing area. The K-NNs method assigns an object of unknown
affiliation to the group to which the majority of its K nearest neighbours
belongs.
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