Abstract: Linear transformation can not better retain the nonlinear structure of data，but the nonlinear transformation often requires lots of complex measurements.To address this，a fast and effective method of nonlinear feature extraction is proposed.This method studies the linear invariance of mutual information gradient in the kernel space，and employs a fast algorithm for mutual information and gradient ascent.In this way，the extracted features can reflect the characteristics of discriminative higher-order statistics，and effectively reduce the computational complexity.Detailed data projection and classification experiments show that the proposed approach performs well in classification performance，and is better than traditional nonlinear algorithms for the time complexity.

Key words: kernel method, nonlinear transformation, feature extraction, mutual information

摘要： 由于线性变换无法较好保留数据的非线性结构而非线性变换往往需要进行大量的复杂运算，提出一种快速、高效的非线性特征提取方法。该方法通过研究互信息梯度在核空间中的线性不变性，采用互信息二次熵快速算法及梯度上升寻优策略，在有效降低计算量的同时能够提取有判别力的非线性高阶统计量。详细的数据投影和分类实验表明该方法在分类性能和算法时间复杂度上都优于传统算法。

关键词: 核方法, 非线性变换, 特征提取, 互信息