Towards Solving Dimension Reduction Problems for Multi-Dimensional Data

In this paper, the authors present continuous research on data analysis based on their previous work on the shrinking approach. Shrinking is a novel data preprocessing technique which optimizes the inner structure of data. In this paper, the authors propose the shrinking-based dimension reduction approach which tends to solve the dimension reduction problem from a new perspective. In this paper data are moved along the direction of the density gradient, thus making the clusters denser. Dimension reduction process is performed based on the difference of the data distribution projected on each dimension before and after the data-shrinking process.