Fuzzy PCA Orthogonal

The major novelty of this algorithm is in the way the other fuzzy principal components are computed. The original data set is projected onto the hyperplane orthogonal to the first fuzzy principal component, that is, determined by all the other principal components, as determined by the Fuzzy First Component PCA algorithm. Practically, this may be done by computing the scores 

This produces a data set in a Euclidean space of dimension p—, where p is the 

Now we need only a final transformation to revert these eigenvectors and eigenvalues to the original space. We use relations similar to those used for computing the initial projection, but in reverse. The FuzzyOrthogonal-PCA Algorithm is the following  

Call DetermineFuzzyMembershipIcx) with the value of a computed above, and determine the optimal value of the fuzzy membership degrees. 

Using the fuzzy membership degrees determined above, compute the fuzzy covariance matrix C. 

---