Dimension Reduction Based on Sampling

Zhuping Li, Donghua Yang, Mengmeng Li, Haifeng Guo, Tiansheng Ye, Hongzhi Wang

Abstract: Dimension reduction provides a powerful means of reducing the number of random variables under consideration. However, there were many similar tuples in large datasets, and before reducing the dimension of the dataset, we removed some similar tuples to retain the main information of the dataset while accelerating the dimension reduction. Accordingly, we propose a dimension reduction technique based on biased sampling, a new procedure that incorporates features of both dimensional reduction and biased sampling to obtain a computationally efficient means of reducing the number of random variables under consideration. In this paper, we choose Principal Components Analysis(PCA) as the main dimensional reduction algorithm to study, and we show how this approach works.