Mathematical Foundations for Data Analysis
📖 Overview
I read this book after learning the basics of machine learning. It really strengthened my understanding of the mathematical concepts that underpin data analysis techniques. The book covers a wide range of topics, including probability, linear algebra, distance metrics, regression, clustering, and classification. Each chapter builds on the previous ones, providing a comprehensive foundation for anyone interested in data science. And this book solves many questions that I haven’t figure out before like the meaning of Support Vector Machine, Principal Component Analysis, and Singular Value Decomposition. I highly recommend this book to anyone looking to deepen their understanding of the mathematical principles behind data analysis or machine learning.
📅 Learning Journey
Chapter 1 Probability Review
- 2025.10.22 1.1 Sample Space
- 2025.10.22 1.2 Conditional Probability and Independence
- 2025.10.25 1.3 Density Functions
- 2025.10.25 1.4 Expected Value
- 2025.10.25 1.5 Variance
- 2025.10.25 1.6 Joint, Marginal, and Conditional Distributions
- 2025.10.25 1.7 Bayes’ Rule
- 2025.10.25 1.8 Bayesian Inference
Chapter 2 Convergence and Sampling
- 2025.10.28 2.1 Sampling and Estimation
- 2025.10.28 2.2 Probably Approximately Correct (PAC)
- 2025.10.28 2.3 Concentration of Measure
- 2025.10.28 2.4 Importance Sampling
Chapter 3 Linear Algebra Review
- 2025.10.31 3.1 Vectors and Matrices
- 2025.10.31 3.2 Addition and Multiplication
- 2025.10.31 3.3 Norms
- 2025.10.31 3.4 Linear Independence
- 2025.10.31 3.5 Rank
- 2025.10.31 3.6 Square Matrices and Properties
- 2025.10.31 3.7 Orthogonality
Chapter 4 Distance and Nearest Neighbors
- 2025.11.6 4.1 Metrics
- 2025.11.6 4.2 Lp Distances and their Relatives
- 2025.11.6 4.3 Distances for Sets and Strings
- 2025.11.6 4.4 Modeling Text with Distances
- 2025.11.7 4.5 Similarities
- 2025.11.7 4.6 Locality Sensitive Hashing
Chapter 5 Linear Regression
- 2025.11.19 5.1 Simple Linear Regression
- 2025.11.19 5.2 Linear Regression with Multiple Explanatory Variables
- 2025.11.19 5.3 Polynomial Regression
- 2025.11.19 5.4 Cross-Validation
- 2025.11.20 5.5 Regularized Regression
Chapter 6 Gradient Descent
- 2025.11.24 6.1 Functions
- 2025.11.24 6.2 Gradients
- 2025.11.24 6.3 Gradient Descent
- 2025.11.24 6.4 Fitting a Model to Data
Chapter 7 Dimensionality Reduction
- 2025.12.1 7.1 Data Matrices
- 2025.12.1 7.2 Singular Value Decomposition
- 2025.12.1 7.3 Eigenvalues and Eigenvectors
- 2025.12.1 7.4 The Power Method
- 2025.12.1 7.5 Principal Component Analysis
- 2025.12.9 7.6 Multidimensional Scaling
- 2025.12.9 7.7 Linear Discriminant Analysis
- 2025.12.9 7.8 Distance Metric Learning
- 2025.12.9 7.9 Matrix Completion
- 2025.12.9 7.10 Random Projections
Chapter 8 Clustering
- 2025.12.23 8.1 Voronoi Diagrams
- 2025.12.23 8.2 Gonzalez’s Algorithm for k-Center Clustering
- 2025.12.23 8.3 Lloyd’s Algorithm for k-Means Clustering
- 2025.12.23 8.4 Mixture of Gaussians
- 2025.12.23 8.5 Hierarchical Clustering
- 2025.12.23 8.6 Density-Based Clustering and Outliers
- 2025.12.23 8.7 Mean Shift Clustering
Chapter 9 Classification
- 2026.1.17 9.1 Linear Classifiers
- 2026.1.17 9.2 Perceptron Algorithm
- 2026.1.17 9.3 Support Vector Machines and Kernels
- 2026.1.17 9.4 Learnability and VC dimension
- 2026.1.17 9.5 kNN Classifiers
- 2026.1.17 9.6 Decision Trees
- 2026.1.17 9.7 Neural Networks
Chapter 10 Graph Structured Data
- 2026.1.18 10.1 Markov Chains
- 2026.1.18 10.2 PageRank
- 2026.1.18 10.3 Spectral Clustering on Graphs
- 2026.1.18 10.4 Communities in Graphs
Chapter 11 Big Data and Sketching
- 2026.1.19 11.1 The Streaming Model
- 2026.1.19 11.2 Frequent Items
- 2026.1.19 11.3 Matrix Sketching