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Part VIII
Conclusions
195
How Far You Have Come
You made it. Well done. Take a moment and look back at how far you have come. You now
know:
What linear algebra is and why it is relevant and important to machine learning.
How to create, index, and generally manipulate data in NumPy arrays.
What a vector is and how to perform vector arithmetic and calculate vector norms.
What a matrix is and how to perform matrix arithmetic, including matrix multiplication.
A suite of types of matrices, their properties, and advanced operations involving matrices.
What a tensor is and how to perform basic tensor arithmetic.
Matrix factorization methods, including the eigendecomposition and singular-value de-
composition.
How to calculate and interpret basic statistics using the tools of linear algebra.
How to implement methods using the tools of linear algebra, such as principal component
analysis and linear least squares regression.
Don’t make light of this. You have come a long way in a short amount of time. You
have developed the important and valuable foundational skills in linear algebra. You can now
confidently:
Read the linear algebra mathematics in machine learning papers.
Implement the linear algebra descriptions of machine learning algorithms.
Describe your machine learning models using the notation and operations of linear algebra.
The sky’s the limit.
Thank You!
I want to take a moment and sincerely thank you for letting me help you start your linear
algebra journey. I hope you keep learning and have fun as you continue to master machine
learning.
Jason Brownlee
2018
196
Document Outline - Copyright
- Contents
- Preface
- I Introduction
- Welcome
- Who Is This Book For?
- About Your Outcomes
- How to Read This Book
- About the Book Structure
- About Python Code Examples
- About Further Reading
- About Getting Help
- Summary
- II Foundations
- Introduction to Linear Algebra
- Tutorial Overview
- Linear Algebra
- Numerical Linear Algebra
- Linear Algebra and Statistics
- Applications of Linear Algebra
- Further Reading
- Summary
- Linear Algebra and Machine Learning
- Reasons to NOT Learn Linear Algebra
- Learn Linear Algebra Notation
- Learn Linear Algebra Arithmetic
- Learn Linear Algebra for Statistics
- Learn Matrix Factorization
- Learn Linear Least Squares
- One More Reason
- Summary
- Examples of Linear Algebra in Machine Learning
- Overview
- Dataset and Data Files
- Images and Photographs
- One Hot Encoding
- Linear Regression
- Regularization
- Principal Component Analysis
- Singular-Value Decomposition
- Latent Semantic Analysis
- Recommender Systems
- Deep Learning
- Summary
- III NumPy
- Introduction to NumPy Arrays
- Tutorial Overview
- NumPy N-dimensional Array
- Functions to Create Arrays
- Combining Arrays
- Extensions
- Further Reading
- Summary
- Index, Slice and Reshape NumPy Arrays
- Tutorial Overview
- From List to Arrays
- Array Indexing
- Array Slicing
- Array Reshaping
- Extensions
- Further Reading
- Summary
- NumPy Array Broadcasting
- Tutorial Overview
- Limitation with Array Arithmetic
- Array Broadcasting
- Broadcasting in NumPy
- Limitations of Broadcasting
- Extensions
- Further Reading
- Summary
- IV Matrices
- Vectors and Vector Arithmetic
- Tutorial Overview
- What is a Vector
- Defining a Vector
- Vector Arithmetic
- Vector Dot Product
- Vector-Scalar Multiplication
- Extensions
- Further Reading
- Summary
- Vector Norms
- Tutorial Overview
- Vector Norm
- Vector L1 Norm
- Vector L2 Norm
- Vector Max Norm
- Extensions
- Further Reading
- Summary
- Matrices and Matrix Arithmetic
- Tutorial Overview
- What is a Matrix
- Defining a Matrix
- Matrix Arithmetic
- Matrix-Matrix Multiplication
- Matrix-Vector Multiplication
- Matrix-Scalar Multiplication
- Extensions
- Further Reading
- Summary
- Types of Matrices
- Tutorial Overview
- Square Matrix
- Symmetric Matrix
- Triangular Matrix
- Diagonal Matrix
- Identity Matrix
- Orthogonal Matrix
- Extensions
- Further Reading
- Summary
- Matrix Operations
- Tutorial Overview
- Transpose
- Inverse
- Trace
- Determinant
- Rank
- Extensions
- Further Reading
- Summary
- Sparse Matrices
- Tutorial Overview
- Sparse Matrix
- Problems with Sparsity
- Sparse Matrices in Machine Learning
- Working with Sparse Matrices
- Sparse Matrices in Python
- Extensions
- Further Reading
- Summary
- Tensors and Tensor Arithmetic
- Tutorial Overview
- What are Tensors
- Tensors in Python
- Tensor Arithmetic
- Tensor Product
- Extensions
- Further Reading
- Summary
- V Factorization
- Matrix Decompositions
- Tutorial Overview
- What is a Matrix Decomposition
- LU Decomposition
- QR Decomposition
- Cholesky Decomposition
- Extensions
- Further Reading
- Summary
- Eigendecomposition
- Tutorial Overview
- Eigendecomposition of a Matrix
- Eigenvectors and Eigenvalues
- Calculation of Eigendecomposition
- Confirm an Eigenvector and Eigenvalue
- Reconstruct Matrix
- Extensions
- Further Reading
- Summary
- Singular Value Decomposition
- Tutorial Overview
- What is the Singular-Value Decomposition
- Calculate Singular-Value Decomposition
- Reconstruct Matrix
- Pseudoinverse
- Dimensionality Reduction
- Extensions
- Further Reading
- Summary
- VI Statistics
- Introduction to Multivariate Statistics
- Tutorial Overview
- Expected Value and Mean
- Variance and Standard Deviation
- Covariance and Correlation
- Covariance Matrix
- Extensions
- Further Reading
- Summary
- Principal Component Analysis
- Tutorial Overview
- What is Principal Component Analysis
- Calculate Principal Component Analysis
- Principal Component Analysis in scikit-learn
- Extensions
- Further Reading
- API
- Articles
- Summary
- Linear Regression
- Tutorial Overview
- What is Linear Regression
- Matrix Formulation of Linear Regression
- Linear Regression Dataset
- Solve via Inverse
- Solve via QR Decomposition
- Solve via SVD and Pseudoinverse
- Solve via Convenience Function
- Extensions
- Further Reading
- Summary
- VII Appendix
- Getting Help
- Linear Algebra on Wikipedia
- Linear Algebra Textbooks
- Linear Algebra University Courses
- Linear Algebra Online Courses
- NumPy Resources
- Ask Questions About Linear Algebra
- How to Ask Questions
- Contact the Author
- How to Setup a Workstation for Python
- Overview
- Download Anaconda
- Install Anaconda
- Start and Update Anaconda
- Further Reading
- Summary
- Linear Algebra Cheat Sheet
- Array Creation
- Vectors
- Matrices
- Types of Matrices
- Matrix Operations
- Factorization
- Statistics
- Basic Math Notation
- Tutorial Overview
- The Frustration with Math Notation
- Arithmetic Notation
- Greek Alphabet
- Sequence Notation
- Set Notation
- Other Notation
- Tips for Getting More Help
- Further Reading
- Summary
- VIII Conclusions
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