基于局部结构学习的非线性属性选择算法

针对大多数高维数据之间不仅有相似性，而且还有非线性关系等特点，提出一种基于局部结构学习的非线性属性选择算法。该算法首先通过核函数把数据映射到高维空间，在高维空间中表示出数据属性之间的非线性关系；然后在低维空间中通过局部结构学习来充分挖掘属性之间的相似性，同时通过低秩约束来排除噪声的干扰；最后通过稀疏正则化因子来进行属性选择。其通过核函数映射来找出数据属性之间的非线性关系，运用局部结构学习来找出数据属性之间的相似性，是一种嵌入了局部结构学习的非线性属性选择算法。实验结果表明，该算法相比其他的对比算法，有更好的效果。

Nonlinear feature selection algorithm via local structure learning

Due to that most high-dimensional data not only has the similarities, but also has nonlinear relationships. This paper proposed a nonlinear feature selection algorithm based on local structure learning. Firstly, the algorithm mapped the data to high-dimensional space through kernel functions, and expressed the nonlinear relationship between data features in high-dimensional space. Then, it exploited the similarity between the features in the low-dimensional space through local structural learning. At the same time, it eliminated the interference of noise by the low-rank constraint. Finally, it selected features by sparse regularization factors. It found the non-linear relationships between data features by the kernel function, and found the similarities between the data attributes as the local structure learning. The algorithm was a nonlinear feature selection algorithm embedded with local structure learning. Experimental results show that the algorithm has better results than other comparison algorithms.