面向机器学习的相对变换

Relative Transformation for Machine Learning

机器学习常常面临数据稀疏和数据噪音问题.根据认知的相对性规律提出了相对变换方法,证明了相对变换是非线性的放大变换,可提高数据之间的可区分性.同时在一定条件下相对变换还能抑制噪音,并使稀疏的数据变得相对密集.通过相对变换将数据的原始空间变换到相对空间后,在相对空间中度量数据的相似性或距离更加符合人们的直觉,从而提高机器学习的性能.理论分析和实践验证了所提方法的普适性和有效性.

Recently developed machine learning approaches such as manifold learning and the support vector machine learning work well on the clean data sets even if these data sets are highly folded, twisted, or curved. However, they are much sensitive to noises or outliers contained in the data set, as these noises or outliers easily distort the real topological structure of the underlying data manifold. To solve the problem, the relative transformation on the original data space is proposed by modeling the cognitive relative laws. It is proved that the relative transformation is a kind of nonlinear enlarging transformation so that it makes the transformed data more distinguishable. Meanwhile, the relative transformation can weaken the influence of noise on data and make data relative denser. To measure the similarity and distance between data points in relative space is more consistent with the intuition of people, which can be then applied to improve the machine learning approach. The relative transformation is simple, general and easy to implement. It also has clear physical meaning and does not add any parameter. The theoretical analysis and conducted experiments validate the proposed approach.