Abstract
- This paper introduces a variant of the prototype-based generalized learning vector quantization algorithm (GLVQ) for classification learning, which is inspired by quantum computing. Starting from the motivation of kernelized GLVQ, the nonlinear transformation of real data and prototypes into quantum bit vectors allows to formulate a GLVQ variant in a (n-dimensional) quantum bit vector space Hn. A key feature for this approach is that Hn is an Hilbert space with particular inner product properties, which finally restrict the prototype adaptation to be unitary transformations. The resulting approach is denoted as Qu-GLVQ. We provide the mathematical framework and give exemplary numerical results.