intrinsic dimensions meaning in Chinese
固有维数
Examples
- In section 4 . 2 we analyze its main idea and algorithm in detail , two relevant theorems included ; section 4 . 3 provides plenty instances so to explain its nonlinear dimension reduction ability , section 4 . 4 propose a combined method that integrates the advantage of various methods . in section 4 . 5 we analyze some significant problems in lle , including the locality of manifold representation , the choice of the neighborhood , the intrinsic dimension estimation and the parametric representation of mapping . in section 4 . 6 we design an algorithm for estimating the intrinsic dimension in the base of locally linear approximation and discuss the choice of its parameters
第四章是本文的重点内容，研究一种全新的非线性降维方法? ?局部线性嵌入方法，对它的思想和算法进行了详细的分析，给出算法两个相关定理的证明；第三节对比主成分分析，通过实例说明局部线性嵌入方法的非线性降维特征；第四节在此基础上提出了旨在结合两者优势的组合降维方法；第五节提出了局部线性嵌入方法中存在的若干关键性问题，包括流形的局部性、邻点的选择、本征维数的估计和降维映射的表示，第六节基于局部线性近似的思想提出了一种本征维数的估计方法，设计了实用算法，结合实例对算法中参数的选取进行了讨论；最后一节提出了一种基于局部线性重构的图形分类和识别方法，将其应用于手写体数字的图像分类识别实验，实验得到的分类准确率达96 . 67 。 - In the first and second section of chapter 1 we introduce the model of dimension reduction problem , put forward the concepts of dimension - reduction function and embedding function , and make a classification for the dimension reduction problem ; in section 1 . 3 we discuss " the curse of dimension " and the sparsity of high - dimensional space ; in section 1 . 4 we discuss " intrinsic dimension " and its estimation based on the model of dimension reduction
第一章首先提出了降维的模型和定义，讨论了相关的问题；第三节讨论“维数祸根”现象和高维空间的稀疏性，通过实例分析其对高维空间的数据分布特性具体影响；第四节讨论了本征维数及其估计的基本问题。 - In last section we propose a new method for image classification and recognition , and the result of experiment shows that the method is effective with classification accuracy of 96 . 67 % . the main creative points in this paper are : propose the concepts of dimension - reduction function and embedding function , define the projection index in term of linear operator and prove two relevant theorems ; design a method to estimate the intrinsic dimension ; put forward an classification algorithm based on lle
本文的主要创新点在于：提出了降维映射和嵌入映射的概念；给出了投影指标的严格定义，证明了两个相关定理；提出了一种用于估计本征维数的方法并设计了实用算法；提出了一种基于局部线性重构思想的分类和识别方法。