{"id":24399,"date":"2020-06-11T06:00:00","date_gmt":"2020-06-11T13:00:00","guid":{"rendered":"https:\/\/insidebigdata.com\/?p=24399"},"modified":"2020-06-12T11:19:08","modified_gmt":"2020-06-12T18:19:08","slug":"book-review-linear-algebra-and-learning-from-data-by-gilbert-strang","status":"publish","type":"post","link":"https:\/\/insidebigdata.com\/2020\/06\/11\/book-review-linear-algebra-and-learning-from-data-by-gilbert-strang\/","title":{"rendered":"Book Review: Linear Algebra and Learning from Data by Gilbert Strang"},"content":{"rendered":"\n
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I’ve been a big fan of MIT mathematics professor Dr. Gilbert Strang for many years. A few years ago I reviewed the latest 5th edition of his venerable text on linear algebra<\/a>. Then last year I learned how he morphed his delightful mathematics book into a brand new title (2019) designed for data scientists – “Linear Algebra and Learning from Data.” I was intrigued, so after I received my review copy I did a deep dive without hesitation. I appreciate Strang’s approach to learning mathematics. His books are completely no-nonsense and no fluff. He gets down to business and the result is something mathematics lovers enjoy. This book resembles a collection of well-crafted, albeit dense, course notes for an honors section of a class designed for advanced undergraduate\/graduate level learners. Moreover, the breadth of material covered is impressive. I enjoyed the “Learning from Data” text immensely and this book review should serve to encourage all data scientists who may be lacking in the mathematical foundations of data science to make an investment in this great learning resource. <\/p>\n\n\n\n

As I tell my own data science students about the importance of learning the mathematical underpinnings of machine learning – while leading-edge machine learning applications can change in the short-term (e.g. CNNs, RNNs, reinforcement learning, NLP, LSTM, transfer learning, etc.) the underlying mathematical concepts do not. This book will help you establish a foundation. <\/p>\n\n\n\n

The text is divided into seven main parts, each with a special focus designed to provide the mathematical architecture important for data scientists to gain a firm understanding of machine learning. <\/p>\n\n\n\n

  1. Highlights of Linear Algebra<\/li>
  2. Computations with Large Matrices<\/li>
  3. Low Rank and Compressed Sensing<\/li>
  4. Special Matrices<\/li>
  5. Probability and Statistics<\/li>
  6. Optimization<\/li>
  7. Learning from Data<\/li><\/ol>\n\n\n\n

    Part I highlights the fundamental elements of linear algebra including such important topics for machine learning as: matrix multiplication, eigenvalues and eigenvectors, singular value decomposition (SVD), principal components, and many others topics needed for understanding what drives machine learning. Bear in mind, this content represents an overview of linear algebra and it is advised that the reader already have exposure to the material (e.g. vector spaces, subspaces, independence, bases, and linear operators). <\/p>\n\n\n\n

    In Part II discusses computation with large matrices with a focus on matrix factorization, iterative methods, along with insights into recent powerful algorithms for approximating matrix problem solutions using randomization and projection. <\/p>\n\n\n\n

    Part III discusses a variety of low-rank and sparse approximation techniques and ending with methods such as LASSO and matrix completion algorithms. <\/p>\n\n\n\n

    Part IV drills down into the topic of special matrices and constitutes a compilation of specially structured matrices that have applications in a variety of data and signal analysis areas. The matrices range from classical discrete Fourier transforms to graph node-adjacency matrices used for clustering. This section contains a tiny bit of MATLAB code on Page 249 that’s used in one example. I appreciated the section on Page 253, “Applications of Clustering” after a discussion of k-means. <\/p>\n\n\n\n

    Part V provides a good dose of probability and statistics, something I advise all my introductory data science students to absorb. The chapters include useful topics like: mean and variance, probability distributions, covariance matrices, multivariate Gaussian and weighted least squares, plus a discussion of Markov Chains. Also featured is the Central Limit Theorem<\/em>, something all data scientists need to know. Data scientists can limp along without knowledge of probability and statistics, but eventually you’ll hit the wall, and need to sit down and learn these fundamentals. This book’s coverage is pretty much all you’ll need.<\/p>\n\n\n\n

    One great reason to invest in this book is Part VI on optimization. Optimization techniques are the life blood of many machine learning algorithms. This part of the book examines several work-horse algorithms based on optimization including linear programming, gradient descent, and most relevant to machine learning, stochastic gradient descent. The chapter even has a definition of the ubiquitous “argmin” expression used in most machine learning theory texts. The problem is these books never define what argmin is! (hint: argmin are the values of arguments for a function F where F reaches its minimum). Kudos for Strang for completeness. <\/p>\n\n\n\n

    The crescendo of the book is reached in Part VII “Learning from Data” which contains all the meat for data scientists interested in truly taking command of what underlies machine learning algorithms. Here, Strang overviews the mathematics of machine learning including deep neural networks, convolutional neural networks (CNNs), recurrent neural networks (RNNs), the backprop algorithm, bias-variance tradeoff, use of hyperparameters, and how the chain rule in Calculus is king. <\/p>\n\n\n\n

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