Relative Transformation for Machine Learning

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.