On the Structure of the Quadratic Subspace in Discriminant Analysis Articles
- JOURNAL OF MULTIVARIATE ANALYSIS Journal
- May 2010
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The concept of quadratic subspace is introduced as a helpful tool for dimension reduction in quadratic discriminant analysis (QDA). It is argued that an adequate representation of the quadratic subspace may
lead to better methods for both data representation and classification.
Several theoretical results describe the structure of the quadratic
subspace, that is shown to contain some of the subspaces previously
proposed in the literature for finding differences between the class
means and covariances. A suitable assumption of orthogonality between
location and dispersion subspaces allows us to derive a convenient
reduced version of the full QDA rule. The behavior of these ideas in
practice is illustrated with three real data examples.