1 August 2002 Embedding of feature space for pattern recognition using quantum computing
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In order to deal with a general pattern recognition problem by quantum computing, this paper proposes an embedding method that corresponds a feature vector of n-dimensional space Vn to a vector of the surface of Riemann sphere in the n+1 dimensional space Vn+1, keeping the topology among feature vectors. Because the radius of this Riemann sphere is one, the feature vectors are mapped into normalized vectors. This paper shows that multiple linear discriminant functions can be defined to separate two arbitrary clusters that are mapped onto the Riemann sphere in the space Vn+1. This paper also shows that we can define a unitary transformation that computes the signs of values of those multiple linear discriminant functions, in parallel by quantum computing.
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Tetsuo Hattori, Osamu Matoba, Bahram Javidi, "Embedding of feature space for pattern recognition using quantum computing", Proc. SPIE 4732, Photonic and Quantum Technologies for Aerospace Applications IV, (1 August 2002); doi: 10.1117/12.477426; https://doi.org/10.1117/12.477426

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