Matrices that contain mostly zero values are called sparse, distinct from matrices where most of the values are non-zero, called dense. Large sparse matrices are common in general and especially in applied machine learning, such as in data that contains counts, data encodings that map categories to counts, and even in whole subfields of machine […]

Arrays with different sizes cannot be added, subtracted, or generally be used in arithmetic. A way to overcome this is to duplicate the smaller array so that it is the dimensionality and size as the larger array. This is called array broadcasting and is available in NumPy when performing array arithmetic, which can greatly reduce […]

Linear algebra is a sub-field of mathematics concerned with vectors, matrices, and linear transforms. It is a key foundation to the field of machine learning, from notations used to describe the operation of algorithms to the implementation of algorithms in code. Although linear algebra is integral to the field of machine learning, the tight relationship […]

There are many books that provide an introduction to the field of linear algebra. Most are textbooks targeted at undergraduate students and are full of theoretical digressions that are barely relevant and mostly distracting to a beginner or practitioner to the field. In this post, you will discover the book “No bullshit guide to linear […]

Linear regression is a method for modeling the relationship between one or more independent variables and a dependent variable. It is a staple of statistics and is often considered a good introductory machine learning method. It is also a method that can be reformulated using matrix notation and solved using matrix operations. In this tutorial, […]

An important machine learning method for dimensionality reduction is called Principal Component Analysis. It is a method that uses simple matrix operations from linear algebra and statistics to calculate a projection of the original data into the same number or fewer dimensions. In this tutorial, you will discover the Principal Component Analysis machine learning method […]

Fundamental statistics are useful tools in applied machine learning for a better understanding your data. They are also the tools that provide the foundation for more advanced linear algebra operations and machine learning methods, such as the covariance matrix and principal component analysis respectively. As such, it is important to have a strong grip on […]

Matrix decomposition, also known as matrix factorization, involves describing a given matrix using its constituent elements. Perhaps the most known and widely used matrix decomposition method is the Singular-Value Decomposition, or SVD. All matrices have an SVD, which makes it more stable than other methods, such as the eigendecomposition. As such, it is often used […]

All of the Linear Algebra Operations that You Need to Use in NumPy for Machine Learning. The Python numerical computation library called NumPy provides many linear algebra functions that may be useful as a machine learning practitioner. In this tutorial, you will discover the key functions for working with vectors and matrices that you may […]

How to Get Help with Linear Algebra for Machine Learning? Linear algebra is a field of mathematics and an important pillar of the field of machine learning. It can be a challenging topic for beginners, or for practitioners who have not looked at the topic in decades. In this post, you will discover how to […]