论文标题
使用牛顿重力和爱因斯坦的一般相对论降低重力维度
Gravitational Dimensionality Reduction Using Newtonian Gravity and Einstein's General Relativity
论文作者
论文摘要
由于在物理学中使用机器学习的有效性，文献中已广泛受到关注。但是，在机器学习中应用物理学的概念尚未得到太多的认识。这项工作是物理和机器学习的混合体，在机器学习中使用了物理学的概念。我们提出了有监督的重力降低（GDR）算法，其中每个类的数据点相互移动以减少阶级方差和更好的类别分离。对于每个数据点，其他点都被认为是重力颗粒，例如恒星，其中该点被重力吸引到了其类别的点。首先，使用主组件分析将数据点投影到时空歧管上。我们提出了两个GDR的变体 - 一个具有牛顿重力，一个具有爱因斯坦的总体相对论。前者在点之间的直线上使用牛顿重力，但后者沿时空歧管的大地测量学移动数据点。对于具有相对性重力的GDR，我们同时使用Schwarzschild和Minkowski度量张量来涵盖一般相对论和特殊相对论。我们的模拟显示了GDR在歧视阶层中的有效性。
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.
