流形学习降维算法中一种新动态邻域选择方法

A Dynamic Neighborhood Selection Approach for Manifold Learning Dimensionality Reduction Algorithm

近年来,高维数据算法在诸如机器学习领域以及模式识别当中有着十分广泛的应用。降维算法的目的是为了揭示出在高维数据空间中样本数据的固有的组成特性,关注于寻找原始数据集特征表示中有价值的信息。相邻区域选择问题对流形学习降维算法的性能改进至关重要。因此,该文提出一种流形学习降维算法中的新动态邻域选择方法Mod-HLLE(modified Hessian locally linear embedding)。该方法针对Hessian布局线嵌入方法HLLE进行了考察,Mod-HLLE算法是针对高维数据的局部线性嵌入降维算法的改进。Mod-HLLE主要通过计算每个数据点的局部相邻区域参数的方式来完成测量距离和欧几里德距离的评测,再通过动态的相邻区域的尺寸大小来选择新的局部相邻区域。Mod-HLLE在非噪声干扰和噪声干扰情况下,对两类典型3D高维数据集进行降维测试。实验结果表明,Mod-HLLE可以获得很好的几何直观效果,在性能和稳定性方面都优于常见的降维算法,对其他高维数据降维算法的改进也具有很好的参考价值。

In recent years,high-dimensional data algorithms have been widely used in machine learning and pattern recognition.The aim of dimensionality reduction is to reveal the intrinsic composition of the distribution of samples in the initiate high-dimensional space and find the valuable information in the original data set feature representation.The neighborhood selection is quite important to improve the performance of manifold learning dimensionality reduction algorithm.Therefore,we propose a dynamic neighborhood selection approach for manifold learning dimensionality reduction algorithm call Mod-HLLE(modified Hessian locally linear embedding).It is used to investigate the Hessian layout line embedding method(HLLE).Mod-HLLE is an improvement of local linear embedding dimensionality reduction algorithm for high dimensional data.Mod-HLLE mainly evaluates the measurement distance and Euclidean distance by calculating the local adjacent area parameters of each data point,and then selects the new local adjacent area by the size of the dynamic adjacent area.Two kinds of 3D dimensionality data sets which are often unevenly distributed are adopted in noise case and without noise case.Experiment shows that Mod-HLLE can obtain ideal geometric intuitive effect,which is superior to common dimensional reduction algorithms in terms of performance and stability,and also has a good reference value for improving other high-dimensional data dimensional reduction algorithms.