Foundations of Data Science

About this Book

Foundations of Data Science by Turing Award laureate John Hopcroft and leading theorists Blum and Kannan is a landmark text. It provides the rigorous mathematical and algorithmic foundations underpinning modern machine learning, AI, and big data. The book begins with high-dimensional space geometry, exploring why counter-intuitive properties emerge in multi-dimensional data. Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) are examined as essential dimensionality reduction tools. Random walks and Markov Chain Monte Carlo (MCMC) methods are mathematically derived for graph sampling and web ranking. Machine learning theory is covered through PAC learning, VC-dimension, Support Vector Machines (SVMs), and generalization bounds. It provides theoretical insights into deep neural networks, gradient descent optimization surfaces, and non-convex convergence. Clustering algorithms (k-means, spectral clustering, hierarchical clustering) are analyzed with provable error guarantees. Topic modeling, non-negative matrix factorization, and streaming algorithms for massive distributed datasets are detailed. Crucial reading for machine learning engineers, data scientists, and researchers seeking a deep theoretical bedrock.