Semisupervised Tangent Space Discriminant Analysis

Zhou Yang; Sun Shiliang

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Semisupervised Tangent Space Discriminant Analysis

机译：半监督切线空间判别分析

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摘要

A novel semisupervised dimensionality reduction method named Semisupervised Tangent Space Discriminant Analysis (STSD) is presented, where we assume that data can be well characterized by a linear function on the underlying manifold. For this purpose, a new regularizer using tangent spaces is developed, which not only can capture the local manifold structure from both labeled and unlabeled data, but also has the complementarity with the Laplacian regularizer. Furthermore, STSD has an analytic form of the global optimal solution which can be computed by solving a generalized eigenvalue problem. To perform nonlinear dimensionality reduction and process structured data, a kernel extension of our method is also presented. Experimental results on multiple real-world data sets demonstrate the effectiveness of the proposed method.

机译：提出了一种新的半监督降维方法，称为半监督正切空间判别分析（STSD），我们假设数据可以通过底层流形上的线性函数很好地表征。为此，开发了一种使用切线空间的新正则化器，它不仅可以从标记和未标记的数据中捕获局部流形结构，而且与拉普拉斯正则化器具有互补性。此外，STSD具有可以通过解决广义特征值问题来计算的全局最优解的解析形式。为了进行非线性降维和处理结构化数据，还提出了我们方法的内核扩展。在多个实际数据集上的实验结果证明了该方法的有效性。

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《Mathematical Problems in Engineering》 |2015年第17期|706180.1-706180.10|共10页
作者
Zhou Yang; Sun Shiliang;
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E China Normal Univ, Dept Comp Sci & Technol, Shanghai Key Lab Multidimens Informat Proc, Shanghai 200241, Peoples R China.;

E China Normal Univ, Dept Comp Sci & Technol, Shanghai Key Lab Multidimens Informat Proc, Shanghai 200241, Peoples R China.;

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1. Semisupervised Tangent Space Discriminant Analysis [J] . YangZhou, ShiliangSun Mathematical Problems in Engineering: Theory, Methods and Applications . 2015,第2期

机译：半监督切线空间判别分析
2. Semisupervised Tangent Space Discriminant Analysis [J] . YangZhou, ShiliangSun Mathematical Problems in Engineering: Theory, Methods and Applications . 2015,第1期

机译：半监督切线空间判别分析
3. Local Tangent Space Discriminant Analysis [J] . Zhou Yang, Sun Shiliang Neural processing letters . 2016,第3期

机译：局部切线空间判别分析
4. A Riemannian Framework for Linear and Quadratic Discriminant Analysis on the Tangent Space of Shapes [C] . Susovan Pal, Roger P. Woods, Suchit Panjiyar, IEEE Conference on Computer Vision and Pattern Recognition Workshops . 2017

机译：形状切线空间的线性和二次判别分析的黎曼框架
5. A COMPARISON OF SIX MODELS FOR PREDICTING CORPORATE BANKRUPTCY: MULTIPLE LINEAR REGRESSION ANALYSIS, MULTIPLE LINEAR DISCRIMINANT ANALYSIS, STEPWISE REGRESSION ANALYSIS, STEPWISE DISCRIMINANT ANALYSIS, MULTIPLE LINEAR REGRESSION ANALYSIS WITH RIDGE REGRESSION, AND MULTIPLE LINEAR DISCRIMINANT ANALYSIS WITH BIASED MINIMUM CHI-SQUARE RULE [D] . MAPP, JOHNNIE ALBERT. 1981

机译：六种预测公司破产的模型的比较：多个线性回归分析，多个线性判别分析，逐步回归分析，逐步判别分析，多个带岭点回归的线性回归分析，以及多个线性离散
6. A Riemannian Framework for Linear and Quadratic Discriminant Analysis on the Tangent Space of Shapes [O] . Susovan Pal, Roger P. Woods, Suchit Panjiyar, -1

机译：形状切线空间的线性和二次判别分析的黎曼框架
7. Semisupervised Tangent Space Discriminant Analysis [O] . Yang Zhou, Shiliang Sun 2015

机译：半质化切线空间判别分析
8. Simplified Nonlinear Analysis of Large Space-Trusses and Space-Frames, Using Explicitly Derived Tangent Stiffnesses and Accounting for Local Buckling [R] . Kondoh, K., Tanaka, K., Atluri, S. N. 1985

机译：大空间桁架和空间框架的简化非线性分析，使用显式导出的切线刚度和局部屈曲的计算

Semisupervised Tangent Space Discriminant Analysis

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