为在大数据环境下处理高维矩阵和应用奇异值分解提供更高效的解决方案，从而加速数据分析和处理速度，通过研究随机投影以及Krylov子空间投影理论下关于高维矩阵求解特征值特征向量(奇异值奇异向量)问题，分别总结了6种高效计算方法并对其相关应用研究进行对比分析。结果表明，在谱聚类的应用上，通过降低核心步骤SVD(Singular Value Decomposition)的复杂度，使优化后的算法与原始谱聚类算法的精度相近，但大大缩短了运行时间，在1 200维的数据下计算速度相较原算法快了 10倍以上。同时，该方法应用于图像压缩领域，能有效地提高原有算法的运行效率，在精度不变的情况下，运行效率得到了 1～5倍的提升。
Comparative Analysis and Application of Fast Calculation Methods for Singular Value Decomposition of High Dimensional Matrix
To provide more efficient solutions for handling high-dimensional matrices and applying SVD(Singular Value Decomposition)in the context of big data,with the aim of accelerating data analysis and processing,how to quickly calculate the eigenvalues and eigenvectors(singular value singular vectors)of high-dimensional matrices is studied.By studying random projection and Krylov subspace projection theory,six efficient calculation methods are summarized,making comparative analysis and related application research.Then,the six algorithms are applied,and the algorithms in related fields are improved.In the application of spectral clustering,the algorithm reduces the complexity of the core step SVD(Singular Value Decomposition),so that the optimized algorithm has similar accuracy to the original spectral clustering algorithm,but significantly shortens the running time.The calculation speed is more than 10 times faster than the original algorithm.When this work is applied in the field of image compression,it effectively improves the operation efficiency of the original algorithm.Under the condition of constant accuracy,the operation efficiency is improved by 1～5 times.
high-dimensional matricesfast singular value decomposition(SVD)spectral clusteringimage compression
万方数据
维普
