一种基于稀疏嵌入分析的降维方法

An Embedding Dimension Reduction Algorithm Based on Sparse Analysis

近几年局部流形学习算法研究得到了广泛的关注,如局部线性嵌入以及局部切空间排列算法等.这些算法都是基于局部可线性化的假设而提出的,但局部是否可线性化的问题没有得到很好有效的解决,使得目前的降维算法对自然数据效果不佳.自然数据中有很多是稀疏的,对稀疏数据的降维是局部线性嵌入算法所面临的一个问题.基于对数据自然属性的考虑,利用数据的统计信息动态确定局部线性化范围,依据数据的分布提出一种排列的稀疏局部线性嵌入算法(Sparse local linear embedding algorithm,SLLEA).在数据集稀疏的情况下,该算法能够很好地把握数据的局部和整体信息.将该算法应用于手工流形及图像检索等试验中,验证了该算法的有效性.

In recent years, local manifold learning algorithms have been widely concerned, such as local linear embedding and local tangent space alignment algorithm. These algorithms are mostly based on the hypothesis of local linearization. However, the problem of whether local linearization can be realized has not been effectively solved, which makes the dimensionality reduction algorithms have poor results on natural data. In natural data, many of them are sparse, so it is important to deal with the dimension reduction for sparse data. Under the consideration of natural attributes with statistical information, an alignment of sparse local linear embedding algorithm （SLLEA） is proposed in this paper. In the algorithm, local linear range is determined dynamically according to the probability distribution of the data. For sparse data sets, the algorithm can effectively obtain local and global information. Experiments on handwork manifold and image retrieval test verify the effectiveness of the algorithm.