局部线性嵌入算法(Locally Linear Embedding LLE)是一种功能强大的数据降维方法,但它在处理稀疏数据源时的失效问题限制了其广泛应用,且至今没有一个完善的解决方案。为解决这一问题,从算法原理和执行过程两方面分析算法失效原因,把算法的两个优化过程联合优化,对算法进行改进。通过对S曲线稀疏采样模拟稀疏数据源,把改进前后的算法对样本点实验结果进行对比,验证了算法改进的有效性;同时,用改进后的算法处理人脸数据,展示了改进后算法的实用价值。改进后的算法将进一步促进局部线性嵌入在工程和研究领域的应用,极大地改善了算法的性能。
Locally Linear Embedding(LLE) algorithm is a powerful algorithm in data dimension reduction. But, its impotence in case of sparse source data greatly restricts its applicability, and there is still no satisfactory answer to this problem. To solve this problem, this paper makes a deep -into analysis of its vulnerability on both the theory side and its specific implementation, thus to improve the algorithm by uniting the two optimizing equation of the algorithm. And then, by imitating the case of sparse source data with sparse sampling of the S - curve, this paper compare the modified algorithm's performance with its original counterpart to prove the effectiveness of the modification, and then to illustrate the modified algorithm's usability through two groups of experiments on face image. The modification can further enlarge LLE algorithm's sphere of applicability and improve the algorithm greatly.