Laplacian-based Cluster-Contractive t-SNE for High-Dimensional Data Visualization

Author:

Sun Yan1ORCID,Han Yi1ORCID,Fan Jicong2ORCID

Affiliation:

1. The Chinese University of Hong Kong, Shenzhen, China

2. The Chinese University of Hong Kong, Shenzhen and Shenzhen Research Institute of Big Data, China

Abstract

Dimensionality reduction techniques aim at representing high-dimensional data in low-dimensional spaces to extract hidden and useful information or facilitate visual understanding and interpretation of the data. However, few of them take into consideration the potential cluster information contained implicitly in the high-dimensional data. In this article, we propose Lap tSNE, a new graph-layout nonlinear dimensionality reduction method based on t-SNE, one of the best techniques for visualizing high-dimensional data as 2D scatter plots. Specifically, Lap tSNE leverages the eigenvalue information of the graph Laplacian to shrink the potential clusters in the low-dimensional embedding when learning to preserve the local and global structure from high-dimensional space to low-dimensional space. It is nontrivial to solve the proposed model because the eigenvalues of normalized symmetric Laplacian are functions of the decision variable. We provide a majorization-minimization algorithm with convergence guarantee to solve the optimization problem of Lap tSNE and show how to calculate the gradient analytically, which may be of broad interest when considering optimization with Laplacian-composited objective. We evaluate our method by a formal comparison with state-of-the-art methods on seven benchmark datasets, both visually and via established quantitative measurements. The results demonstrate the superiority of our method over baselines such as t-SNE and UMAP. We also provide out-of-sample extension, large-scale extension, and mini-batch extension for our Lap tSNE to facilitate dimensionality reduction in various scenarios.

Funder

National Natural Science Foundation of China

Shenzhen Fundamental Research

Shenzhen Research Institute of Big Data

The Chinese University of Hong Kong, Shenzhen

Publisher

Association for Computing Machinery (ACM)

Subject

General Computer Science

Reference54 articles.

1. Sanjeev Arora, Wei Hu, and Pravesh K. Kothari. 2018. An analysis of the t-SNE algorithm for data visualization. In Proceedings of the 31st Conference On Learning Theory.Sébastien Bubeck, Vianney Perchet, and Philippe Rigollet (Eds.), PMLR, 1455–1462. Retrieved from https://proceedings.mlr.press/v75/arora18a.html

2. Christopher T. H. Baker. 1977. The Numerical Treatment of Integral Equations. Oxford University Press.

3. Laplacian Eigenmaps for Dimensionality Reduction and Data Representation

4. Classification And Regression Trees

5. Lars Buitinck Gilles Louppe and Mathieu Blondel. 2013. API design for machine learning software: experiences from the scikit-learn project. In ECML/PKDD 2013 Workshop: Languages for Data Mining and Machine Learning .

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3