SLIDE 10 10
Information Technologies Institute Centre for Research and Technology Hellas
KSDA+LSVM
- Partition a training set = [, … , ] ∈ ℝ× in sub-classes, where , contains
the samples of the th subclass of class
- Use a vector-valued function ⋅ : ℝ → ℝ, = () as a kernel (map data
from the input space to a higher-dimensional space): T = , = ,
- AGSDA seeks the coefficient matrix ∈ ℝ× solving = (1):
– = ΦTΦ, with ∈ ℝ× being the Gram matrix. ∈ ℝ× ( ≪ ) is a diagonal matrix with the eigenvalues of the generalized eigenvalue problem in (1) on its main diagonal – ∈ ℝ× is the between subclass factor matrix
- Each element A, corresponds to samples ∈ , and ∈ , where:
– , , are the estimated priors of th class and (, )th subclass – , is the number of samples of (, )th subclass
- The problem above can be solved by:
– Identifying the eigenpairs ( ∈ ℝ×, ∈ ℝ×) of , – Solving = for