基于切空间判别的稀疏数据降维方法

Dimensionality reduction method for sparse data based on tangent space discriminant

为了有效地约简稀疏数据的维度,提出一种基于切空间判别的稀疏数据局部降维方法,其思想是扩展局部邻域,增大样本点间的重叠信息,使之在稀疏降维过程中通过充分的信息达到精确的低维嵌入;利用切空间判别的方法对扩展后局部区域的样本点进行选择保留,弃除切方向变化较大的点,使之实现更好的降维效果。实验结果表明,在人工生成的数据集上,新方法获得了较好的嵌入结果;并且在人脸识别与图像检索中得到了期望的可视化分类结果。

To effectively reduce dimension of sparse data, a local dimensionality reduction method for sparse data based on tangent space discriminant is proposed. The idea is to expand local neighborhood and overlapping of information among sample points, which exactly achieves the low-dimensional embedding with the adequate information when reducing dimensionality for sparse data. The sample points in the expanded local neighborhood are selected and retained by using the tangent space discrimi nant, which can remove the points with larger change in the tangent direction and achieve better dimension reduction results. The experimental results show that the new method derives a better embedding result on the artificially generated data sets. In addition, the desired visual classification results are obtained on face recognition and image retrieval.