基于三元组约束的神经网络降维方法

A Neural Network Dimensionality Reduction Method Based on Triplets Constraints

摘要: 与传统的降维和可视化方法(如t-SNE)相比，基于三元组约束的降维方法在保持数据全局结构方面表现优异。三元组约束是指三个数据点之间的约束，能够描述该三点的相对相似性。本文提出了一种基于三元组约束的降维模型(Trivis)，该模型能充分利用Siamese神经网络(SNNs)来增强高维数据降维和可视化的局部结构保持能力。与现有的基于三元组约束的降维方法相比，Trivis模型有两方面的改进：一方面，采用了一种新的目标损失函数，涉及除法运算，有助于保持数据的局部结构；另一方面，对SNNs的输入模块进行了增强，允许每个锚点关联多个三元组，从而能更好地捕捉数据中的局部结构。实验结果表明，Trivis模型在保持局部和全局结构方面能取得良好的平衡，提供了一个稳健的高维数据降维可视化解决方案。

Abstract: Compared with traditional dimensionality reduction and visualization methods (e.g., t-SNE), triplet constraint-based dimensionality reduction methods excel in maintaining the global structure of the data. A triplet constraint is a constraint between three data points that describes the relative similarity of those three points. In this paper, we propose a triplet constraint-based dimensionality reduction model (Trivis) that can make full use of Siamese Neural Networks (SNNs) to enhance the local structure preservation of high-dimensional data reduction and visualization. Compared with existing triplet-constraint-based dimensionality reduction methods, the Trivis model has two improvements: on one hand, a new objective loss function involving a division operation is adopted, which helps to preserve the local structure of the data; on the other hand, enhancements are made to the input module of the SNNs, which allows multiple triplets to be associated with each anchor point, thus enabling better capture of the local structure in the data. The experimental results show that the Trivis model can strike a good balance between preserving local and global structure, providing a robust solution for downscaling visualization of high-dimensional data.