English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Supervised dimensionality reduction has emerged as an important theme in thelast decade. Despite the plethora of models and formulations, there is a lackof a simple model which aims to project the set of patterns into a spacedefined by the classes (or categories). To this end, we set up a model in whicheach class is represented as a 1D subspace of the vector space formed by thefeatures. Assuming the set of classes does not exceed the cardinality of thefeatures, the model results in multi-class supervised learning in which thefeatures of each class are projected into the class subspace. Classdiscrimination is automatically guaranteed via the imposition of orthogonalityof the 1D class sub-spaces. The resulting optimization problem - formulated asthe minimization of a sum of quadratic functions on a Stiefel manifold - whilebeing non-convex (due to the constraints), nevertheless has a structure forwhich we can identify when we have reached a global minimum. After formulatinga version with standard inner products, we extend the formulation toreproducing kernel Hilbert spaces in a straightforward manner. The optimizationapproach also extends in a similar fashion to the kernel version. Results andcomparisons with the multi-class Fisher linear (and kernel) discriminants andprincipal component analysis (linear and kernel) showcase the relative meritsof this approach to dimensionality reduction.

A Category Space Approach to Supervised Dimensionality Reduction