Gravitational Dimensionality Reduction Using Newtonian Gravity and Einstein’s General Relativity. (arXiv:2211.01369v1 [cs.LG])

Due to the effectiveness of using machine learning in physics, it has been
widely received increased attention in the literature. However, the notion of
applying physics in machine learning has not been given much awareness to. This
work is a hybrid of physics and machine learning where concepts of physics are
used in machine learning. We propose the supervised Gravitational
Dimensionality Reduction (GDR) algorithm where the data points of every class
are moved to each other for reduction of intra-class variances and better
separation of classes. For every data point, the other points are considered to
be gravitational particles, such as stars, where the point is attracted to the
points of its class by gravity. The data points are first projected onto a
spacetime manifold using principal component analysis. We propose two variants
of GDR — one with the Newtonian gravity and one with the Einstein’s general
relativity. The former uses Newtonian gravity in a straight line between points
but the latter moves data points along the geodesics of spacetime manifold. For
GDR with relativity gravitation, we use both Schwarzschild and Minkowski metric
tensors to cover both general relativity and special relativity. Our
simulations show the effectiveness of GDR in discrimination of classes.



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