高维数据降维中的PCA与CUR分解对比分析

PCA and CUR Decomposition Analysis in Dimensionality Reduction of High-Dimensional Data

摘要: 在大数据的时代，使高维数据降低维度有很多种方法。其中，在线性降维方法中最典型的方法是PCA和CUR分解方法，但是目前我们利用这两种方法对高维数据降维的研究成果还不够，因此，本文通过对这主成分分析和CUR分解方法的探讨和研究，分析了这两种降维方法的使用条件和实际效果，得出：与传统的主成分分析的矩阵分解方法相比较，在特征选择方面，CUR分解方法不仅具有很高的准确度，而且还具有很好的可解释性；在矩阵恢复方面，CUR矩阵分解方法具有很高的稳定性同时还具有很高的准确度，其准确度有时候能够达到90%以上，因此我认为CUR矩阵分解具有很好的应用价值，值得我们利用CUR矩阵分解法去对高维数据进行降维。

Abstract: In the era of big data, there are many ways to reduce the dimension of high-dimensional data. Among them, the linear dimension reduction method is the most typical method in PCA and CUR decomposition method, but at present, using the two methods on the research achievements of high-dimensional data dimension reduction is not enough. Therefore, through the discussion and research of the principal component analysis and CUR decomposition method, this paper analyzes the use conditions and practical effects of the two methods. It is concluded that: with the traditional principal component analysis method of the matrix decomposition, in terms of feature selection, CUR decomposition method not only has high accuracy, but also has good interpretability. In terms of matrix recovery, CUR matrix decomposition method has high stability and accuracy, and its accuracy can sometimes reach more than 90%. Therefore, I think CUR matrix decomposition has good application value, and it is worth using CUR matrix decomposition method to reduce the dimension of high-dimensional data.