Kernel density discriminant analysis
Section of Statistical classifiers and discriminant analysis, part of Statistical learning
Kernel density discriminant analysis
| Type | Section |
| Taught in | Statistical classifiers and discriminant analysis |
| Part | Statistical learning |
Kernel discriminant analysis replaces each class density by a kernel estimate from Hierarchical clustering and kernel density estimation. This avoids choosing a finite component count, and it introduces bandwidths and still needs enough observations locally. Its difficulty grows with dimension. Six is a software limit in some implementations. The same weighted-density rule can be written in more dimensions when the sample supports the bandwidths. Choose bandwidths inside each training split, then apply the same weighted-density rule:
g^*=\arg\max_g \pi_g\widehat f_g(\mathbf{x}), \qquad \widehat f_g(\mathbf{x})=\frac{1}{n_g}\sum_{i:y_i=g}K_{H_g}(\mathbf{x}-\mathbf{x}_i),
where \pi_g is the prior probability of class g and H_g is the bandwidth matrix of class g. As with kernel density estimation, the method is practical in a few dimensions.
Used in
See also
Training data and classifier · Posterior class probability · Zero–one loss and risk · Bayes-optimal rule · Fisher’s direction · Classification problem · Bayes classifier · Error rates and optimal classifiers