Prototype-based models like the Generalized Learning Vector Quantization (GLVQ) belong to the class of interpretable classifiers. Moreover, quantum-inspired methods get more and more into focus in machine learning due to its potential efficient computing. Further, its interesting mathematical perspectives offer new ideas for alternative learning scenarios. This paper proposes a quantum computing-inspired variant of the prototype-based GLVQ for classification learning. We start considering kernelized GLVQ with real- and complex-valued kernels and their respective feature mapping. Thereafter, we explain how quantum space ideas could be integrated into a GLVQ using quantum bit vector space in the quantum state space $${\mathcal {H}}^{n}$$
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and show the relations to kernelized GLVQ. In particular, we explain the related feature mapping of data into the quantum state space $${\mathcal {H}}^{n}$$
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. A key feature for this approach is that $${\mathcal {H}}^{n}$$
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is an Hilbert space with particular inner product properties, which finally restrict the prototype adaptations to be unitary transformations. The resulting approach is denoted as Qu-GLVQ. We provide the mathematical framework and give exemplary numerical results.
The advantage of prototype based learning vector quantizers are the intuitive and simple model adaptation as well as the easy interpretability of the prototypes as class representatives for the class distribution to be learned. Although they frequently yield competitive performance and show robust behavior nowadays powerful alternatives have increasing attraction. Particularly, deep architectures of multilayer networks achieve frequently very high accuracies and are, thanks to modern graphic processor units use for calculation, trainable in acceptable time.In this conceptual paper we show, how we can combine both network architectures to benefit from their advantages. For this purpose, we consider learning vector quantizers in terms of feedforward network architectures and explain how it can be combined effectively with multilayer or single-layer feedforward network architectures. This approach includes deep and flat architectures as well as the popular extreme learning machines. For the resulting networks, the multi-/ single-layer networks act as adaptive filters like in signal processing while the interpretability of the prototype-based learning vector quantizers is kept for the resulting filtered feature space. In this way a powerful combination of two successful architectures is obtained.
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