This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.

本书介绍了数据科学的数学和算法基础，包括机器学习、高维几何和大型网络的分析。主题包括高维数据的反直觉性质、重要的线性代数技术，如奇异值分解、随机漫步和马尔科夫链的理论、机器学习的基础和重要算法、聚类的算法和分析、大型网络的概率模型、包括主题建模和非负矩阵分解的表示学习、小波和压缩感应。重要的概率技术被开发出来，包括大数法则、尾部不等式、随机投影的分析、机器学习中的泛化保证，以及用于分析大型随机图中相变的矩方法。此外，还讨论了重要的结构性和复杂性措施，如矩阵规范和VC-维度。本书适用于数据算法设计和分析的本科和研究生课程。