LASSO算法在高维数据分析模型中应用和实现
摘要本课题以高维数据的分析建模为研究背景，重点对LASSO (Least Absolute Shrinkage and Selection Operator)算法的实现和应用展开研究。本课题首先探讨了高维数据分析采用的正则化方法，深入理解了LASSO方法的变量选择和系数估计。本课题选取了一种针对LASSO问题的快速迭代收缩阈值算法(Fast Iterative Shrinkage Thresholding Algorithm, FISTA)作为研究对象，使用MATLAB平台对算法进行了实现，对高维数据模型的拟合结果做出了相应的测试分析，并和正交匹配追踪(Orthogonal Matching Pursuits, OMP)算法的拟合结果进行对比。实验数据表明，FISTA算法无论在简单性和收敛速度上都相对OMP算法占有优势。82576
毕业论文关键词 高维数据 LASSO 正则化 变量选择 FISTA
毕业设计说明书外文摘要
Title Implementation and Application of LASSO Algorithm in High-dimensional Data Modelling
Abstract This project conducts a research on high-dimensional data analysis and modeling, with particular emphasis on the implementation and application of LASSO (Least Absolute Shrinkage and Selection Operator) algorithm。 This thesis starts with several regularization methods that are developed for high-dimensional data analysis, for the purpose of acquiring an in-depth understanding of variable selection and coefficients estimate in LASSO problem。 This project selects FISTA (Fast Iterative Shrinkage Thresholding Algorithm) as the research subject, and implements this algorithm using MATLAB programming。 This paper further performs a verification and analysis procedure based on the fitting results by FISTA method, and compares the results with the results by another regularization method, OMP (Orthogonal Matching Pursuits)。 Experimental results demonstrate that FISTA outperforms OMP in both simplicity and convergence rate。 This research task indicates that FISTA can achieve its convergence rate that was proved theoretically, and therefore can be used in solving the problem of large-scale data modeling。
Keywords high-dimensional data LASSO regularization variable selection FISTA
目 次
1 绪论 1
1。1 研究背景和意义 1
1。2 高维数据分析模型及正则化的研究现状 1
1。3 本文研究工作 2
1。4 本文的内容安排 2
2 高维数据分析的理论基础 4
2。1 高维数据分析模型及实际应用 4
2。2 高维数据分析的正则化方法 6
2。3 LASSO方法 7
2。4 高维数据分析模型的效果评价 9
2。5 本章小结 9
3 实验核心算法FISTA及具体实现 10
3。1 LASSO方程 10
3。2 ISTA及适用范围 10
3。3 FISTA介绍及其优势 12
3。4 FISTA基本操作和实现 13
3。5 本章小结 19
4 实验过程 20
4。1 实验环境和工具 20
4。2 实验数据