一种多局部线性模式保持的降维算法

A DIMENSION REDUCTION ALGORITHM FOR MULTI LOCAL LINEAR PATTERN PRESERVING

为了更准确地捕捉数据的局部非线性结构,提出一种基于多局部线性模式保持的降维算法。该文通过局部区域线性重构相应的数据点,利用方向导数代替一阶泰勒展开式中的梯度,降低逼近误差;利用多重线性模式表征数据点,从而更精确地描述数据的局部非线性几何特征;进一步通过最小化嵌入数据空间中的多局部线性重构误差得到嵌入结果。在4个合成数据集和6个真实数据集上实验,结果表明提出方法能够准确捕捉数据的多个非线性结构。

In order to capture the local nonlinear structure of data more accurately,an unsupervised dimension reduction algorithm based on multiple local linear pattern preserving is proposed.The corresponding data points were reconstructed linearly in the local region,and the directional derivative was used to replace the gradient in the first-order Taylor expansion to reduce the approximation error.The multi-linear patterns were used to represent the data points,so as to describe the local nonlinear geometric features of the data more accurately.Furthermore,the embedding result was obtained by minimizing the multi local linear reconstruction error in the embedded data space.The experimental results on 4 synthetic datasets and 6 real datasets show that the proposed method can accurately capture the nonlinear structure.