Abstract
This chapter is an adapted version of the preprint article “Quantum machine learning models are kernel methods” by Maria Schuld [1].
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Notes
- 1.
The term feature vectors derives from the fact that they are elements of a vector space, not that they are vectors in the sense of the space \(\mathbb {C}^N\) or \(\mathbb {R}^N\).
- 2.
See also www.stats.ox.ac.uk/~sejdinov/teaching/atml14/Theory_2014.pdf for a great overview.
- 3.
Note that this is also true when using the trained model for predictions, where we need to compute the distance between a new input to any training input in feature space as shown in Eq. (6.51). However, in maximum margin classifiers, or support vector machines in the stricter sense, most \(\alpha _m\) coefficients are zero, and only the distances to a few “support vectors” are needed.
- 4.
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Schuld, M., Petruccione, F. (2021). Quantum Models as Kernel Methods. In: Machine Learning with Quantum Computers. Quantum Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-83098-4_6
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