拉普拉斯特征映射新增样本点问题及正则化降维研究

发布时间：2018-06-28 21:57

本文选题：数据降维 + 拉普拉斯特征映射　；参考：《暨南大学》2017年硕士论文

【摘要】：首先,针对拉普拉斯特征映射的新增样本点延拓问题,提出一种基于邻域信息的新增样本点延拓方法:假设新增样本点与邻域保持线性关系,使用稀疏编码方法求解线性系数,再由这些系数在低维空间重构得到新增样本点的低维表示。实验结果表明,与基于全局信息的稀疏编码重构方法相比,基于邻域信息的稀疏编码重构算法使用更少的时间取得更高的分类准确率。此外,该方法可以推广至其他非线性降维方法的新增样本点问题。其次,针对降维问题,提出同时从类标签和高维数据结构学习低维表示的监督学习降维方法,使用两步交替迭代法求解相应的优化问题,给出了该方法有解并收敛的证明。与其他有监督的数据降维方法对比,本文的算法在实验中表现出其优越性。
[Abstract]:First, an additional sample point extension method based on neighborhood information is proposed for the new sample point extension problem of Laplasse's feature mapping. It is assumed that the new sample points keep linear relationship with the neighbourhood, and the linear coefficients are solved by the sparse coding method, and then the low dimension representation of the new sample points is obtained by these coefficients in the low dimensional space reconstruction. The experimental results show that the sparse coding reconstruction algorithm based on neighborhood information uses less time to obtain higher classification accuracy compared with the sparse coding reconstruction method based on global information. In addition, this method can be extended to the new sample point problem of other nonlinear dimensionality reduction methods. Secondly, in view of the dimensionality reduction problem, this method is proposed at the same time. The label and high dimensional data structure learn the supervised learning reduction method of low dimension representation, use the two step alternate iterative method to solve the corresponding optimization problem, and give the proof of the solution and convergence of the method. Compared with other supervised data reduction methods, the algorithm of this paper shows its superiority in the experiment.
【学位授予单位】：暨南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP181

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