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首页> 外文期刊>Knowledge and Data Engineering, IEEE Transactions on >Trace Ratio Optimization-Based Semi-Supervised Nonlinear Dimensionality Reduction for Marginal Manifold Visualization
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Trace Ratio Optimization-Based Semi-Supervised Nonlinear Dimensionality Reduction for Marginal Manifold Visualization

机译：基于迹线比率优化的半监督非线性降维实现边缘流形

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Visualizing similarity data of different objects by exhibiting more separate organizations with local and multimodal characteristics preserved is important in multivariate data analysis. Laplacian Eigenmaps (LAE) and Locally Linear Embedding (LLE) aim at preserving the embeddings of all similarity pairs in the close vicinity of the reduced output space, but they are unable to identify and separate interclass neighbors. This paper considers the semi-supervised manifold learning problems. We apply the pairwise Cannot-Link and Must-Link constraints induced by the neighborhood graph to specify the types of neighboring pairs. More flexible regulation on supervised information is provided. Two novel multimodal nonlinear techniques, which we call trace ratio (TR) criterion-based semi-supervised LAE ($({rm S}^2{rm LAE})$) and LLE ($({rm S}^2{rm LLE})$), are then proposed for marginal manifold visualization. We also present the kernelized $({rm S}^2{rm LAE})$ and $({rm S}^2{rm LLE})$. We verify the feasibility of $({rm S}^2{rm LAE})$ and $({rm S}^2{rm LLE})$ through extensive simulations over benchmark real-world MIT CBCL, CMU PIE, MNIST, and USPS data sets. Manifold visualizations show that $({rm S}^2{rm LAE})$ and $({rm S}^2{rm LLE})$ are able to deliver large margins between different clusters or classes with multimodal distributions preserved. Clustering evaluations show they can achieve comparable to or even better results than some widely used methods.
机译：通过展示保留了局部和多峰特征的更多独立组织来可视化不同对象的相似性数据在多变量数据分析中很重要。拉普拉斯特征图（LAE）和局部线性嵌入（LLE）的目的是在缩小的输出空间附近保留所有相似对的嵌入，但是它们无法识别和分离类间邻居。本文考虑了半监督流形学习问题。我们应用由邻域图引起的成对的Cannot-Link和Must-Link约束来指定相邻对的类型。提供了对受监管信息的更灵活的法规。两种新颖的多峰非线性技术，我们称为基于迹线比率（TR）准则的半监督LAE（$（{rm S} ^ 2 {rm LAE}）$）和LLE（$（{rm S} ^ 2 {rm然后提出将LLE}）$）用于边缘流形可视化。我们还介绍了内核化的$ {{rm S} ^ 2 {rm LAE}）$和$ {{rm S} ^ 2 {rm LLE}）$。我们通过对基准现实世界中的MIT CBCL，CMU PIE，MNIST进行广泛的模拟，验证了$ {{rm S} ^ 2 {rm LAE}）$和$ {{rm S} ^ 2 {rm LLE}）$$的可行性。和USPS数据集。流形可视化显示$（{rm S} ^ 2 {rm LAE}）$和$ {{rm S} ^ 2 {rm LLE}）$能够在保留了多峰分布的不同群集或类之间提供较大的利润。聚类评估表明，与某些广泛使用的方法相比，它们可以达到可比甚至更好的结果。

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