Last Updated on October 18, 2019 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 in a wide array of applications including compressing, denoising, and data reduction. In this tutorial, you will discover the […]

Last Updated on November 16, 2019 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 fundamental statistics in the context of linear algebra notation. In this tutorial, you will discover how fundamental statistical operations […]

Last Updated on August 9, 2019 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 for dimensionality reduction and how to implement it from scratch in Python. After completing this tutorial, you will know: […]

Last Updated on August 9, 2019 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, you will discover the matrix formulation of linear regression and how to solve it using direct and matrix factorization […]

Last Updated on August 9, 2019 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 algebra” that provides a gentle introduction to the field of linear algebra and assumes no prior mathematical knowledge. After […]

Last Updated on August 9, 2019 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 is often left unexplained or explained using abstract concepts such as vector spaces or specific matrix operations. In this […]

Last Updated on August 9, 2019 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 and simplify your code. In this tutorial, you will discover the concept of array broadcasting and how to implement […]

Last Updated on August 9, 2019 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 learning such as natural language processing. It is computationally expensive to represent and work with sparse matrices as though […]

Last Updated on August 9, 2019 Linear algebra is a field of applied mathematics that is a prerequisite to reading and understanding the formal description of deep learning methods, such as in papers and textbooks. Generally, an understanding of linear algebra (or parts thereof) is presented as a prerequisite for machine learning. Although important, this area of mathematics is seldom covered by computer science or software engineering degree programs. In their seminal textbook on deep learning, Ian Goodfellow and others […]

Last Updated on August 9, 2019 Numerical linear algebra is concerned with the practical implications of implementing and executing matrix operations in computers with real data. It is an area that requires some previous experience of linear algebra and is focused on both the performance and precision of the operations. The company fast.ai released a free course titled “Computational Linear Algebra” on the topic of numerical linear algebra that includes Python notebooks and video lectures recorded at the University of […]