基于随机矩阵变换的快速PCA算法

主成分分析PCA（PrincipleComponentAnalysis）是一种重要的分析方法，广泛应用于图像检索、机器学习、模式识别等领域。随着近年来数据维数越来越大，算法的稳定性、时间复杂度和内存使用成了PCA进一步应用所必须要解决的问题。为此提出一种快速算法，该算法利用随机矩阵构造卷数据降维矩阵，在保持点与点之间“核距离”不变的情况下，将待分解矩阵变换成一个低维矩阵。在没有偏差的情况下，将对原始大矩阵的分解变成对这个低维矩阵的分解，大幅降低了时间复杂度，减少了对内存的使用，同时增加了算法的稳定性，从而在根本上解决了上述3个问题。

A new fast principal component analysis based on random matrix

Principal Component Analysis （PCA） is an important method of analysis, widely used in image retrieval, machine learning, pattern recognition and other fields. With the recent growing number of data dimensions, stability, time complexity and memory usage of the algorithm have become problems of further application of the PCA that must be solved. Therefore, the authors present a fast algorithm that uses the random matrix to make wrapped dimensionality reduction data matrix in order to keep ＂nucle- ar distance＂ between points unchanged. The original matrix needed to be decomposed has been transformed into a low-dimensional matrix in the case of no deviation. Therefore we significantly reduce the time complexity and memory usage while increasing the stability of the algorithm, fundamentally solve the above three problems.