# 《数据科学的数学基础》--一本系统梳理机器学习与高维数据分析数学原理的专著

- 来源：Hacker News 热门（buzzing.cc 中文翻译）
- 作者：Anon84
- 发布时间：2026-07-17 10:33
- AIHOT 分数：31
- AIHOT 链接：https://aihot.virxact.com/items/cmrocvkek01x2bitoy5n1tpj5
- 原文链接：https://arxiv.org/abs/2607.11938

## AI 摘要

该书由Afonso S. Bandeira、Amit Singer和Thomas Strohmer撰写，系统覆盖数据科学数学基础，包括高维诅咒与祝福、SVD与PCA、线性回归与正则化、图与聚类、非线性降维、随机投影、优化、分类、深度学习数学导论、图拉普拉斯大样本极限、测度集中与高斯分析、矩阵集中不等式、压缩感知与稀疏性、低秩矩阵恢复等16个章节。

## 正文

Computer Science > Machine Learning

Title:Mathematics of Data Science

Afonso S. Bandeira

Amit Singer

Thomas Strohmer

Abstract:This book is about the mathematical foundations of data science. 1. Introduction 2. Curses, Blessings, and Surprises in High Dimensions 3. Singular Value Decomposition and Principal Component Analysis 4. Linear Regression and Regularization 5. Graphs, Networks, and Clustering 6. Nonlinear Dimension Reduction and Diffusion Maps 7. Linear Dimension Reduction via Random Projections 8. Optimization for Data Science 9. Classification 10. A Mathematical Introduction to Deep Learning 11. Large Sample Limit of Graph Laplacians 12. Community 13. Concentration of Measure and Gaussian Analysis 14. Matrix Concentration Inequalities 15. Compressive Sensing and Sparsity 16. Low-Rank Matrix Recovery

Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Information Theory (cs.IT); Probability (math.PR)

Cite as: arXiv:2607.11938 [cs.LG]

(or arXiv:2607.11938v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.11938

arXiv-issued DOI via DataCite

Submission history

From: Thomas Strohmer [

Sat, 11 Jul 2026 08:31:44 UTC (15,747 KB)

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