流形距离与压缩感知核稀疏投影的局部线性嵌入算法

流形学习算法的目的是发现嵌入在高维数据空间中的低维表示,现有的流形学习算法对邻域参数k和噪声比较敏感。针对此问题,文中提出一种流形距离与压缩感知核稀疏投影的局部线性嵌入算法,其核心思想是集成局部线性嵌入算法对高维流形结构数据的降维有效性与压缩感知核稀疏投影的强鉴别性,以实现高效有降噪流形学习。首先,在选择各样本点的近邻域时,采用流形距离代替欧氏距离度量数据间相似度的方法,创建能够正确反映流形内部结构的邻域图,解决以欧氏距离作为相似性度量时对邻域参数的敏感。其次,利用压缩感知核稀疏投影作为从高维观测空间到低维嵌入空间的映射,增强算法的鉴别性。最后,利用Matlab工具对实验数据集进行仿真,进一步验证所提算法的有效性。

Locally Linear Embedding Algorithms Based on Manifold Distance and Compressive Sensing Kernel Sparse Representation Projections

The purpose of manifold learning algorithms discovers the low dimensional representation that embedded in high dimensional data space. The existing manifold learning algorithms are sensitive to the neighborhood parameter k and noise. To solve this problems,a local linear embedding algorithm based on manifold distance and compressed sensing nuclear sparse projection is proposed in this paper. The new method realizes efficient noise reduction learning mainly based on integrating the topology preserving property of the manifold learning method(LLE)and some prominent properties of compressed sensing nuclear sparse projection such as strong identification. Firstly,when selecting the nearest neighbors for each sample point,the paper uses manifold distance to replace the Euclidean distance to measure similarity between data. A neighborhood diagram be created that can accurately reflect the internal structure of manifolds. And the sensitivity to neighborhood parameter be solved that the Euclidean distance is measured as the similarity measure. Secondly,the identification of the algorithm is enhanced that using the compressed sensing nuclear sparse projection as a mapping from high dimensional observation space to low dimensional embedding space. Finally,the validity of the proposed algorithm is verified that using the Matlab to simulate the experimental data sets.