Data Science on IMTI

Linear Algebra in Go: High-Performance Computing

Wed, 25 May 2022 00:00:00 +0000

This final article in the series covers high-performance computing techniques for linear algebra in Go: BLAS/LAPACK integration, parallel operations, memory optimization, and benchmarking.

Linear Algebra in Go: PCA Implementation

Sat, 15 Jan 2022 00:00:00 +0000

This article implements Principal Component Analysis (PCA) from scratch in Go using gonum, covering both the covariance matrix and SVD approaches.

Linear Algebra in Go: Building a Regression Library

Wed, 10 Nov 2021 00:00:00 +0000

This article demonstrates building a regression library in Go from scratch using gonum: ordinary least squares, ridge regression, and cross-validation.

Linear Algebra in Go: Statistics and Data Analysis

Sun, 05 Sep 2021 00:00:00 +0000

This article covers statistics and data analysis in Go using gonum/stat and gonum/mat: descriptive statistics, covariance matrices, and correlation analysis.

Linear Algebra in Go: SVD and Decompositions

Wed, 30 Jun 2021 00:00:00 +0000

This article covers Singular Value Decomposition (SVD) and related matrix decompositions in Go. SVD is fundamental to many applications including dimensionality reduction, pseudoinverse computation, and low-rank approximation.

Linear Algebra in Go: Eigenvalue Problems

Sun, 25 Apr 2021 00:00:00 +0000

This article covers eigenvalue problems in Go using the gonum library. Eigenvalues and eigenvectors are fundamental to many algorithms including PCA, spectral clustering, and dynamical systems analysis.

Linear Algebra in Go: Solving Linear Systems

Sat, 20 Feb 2021 00:00:00 +0000

This article covers solving linear systems in Go using the gonum library, including direct methods with mat.Solve, LU decomposition, and Cholesky decomposition for positive-definite matrices.

Linear Algebra in Go: Matrix Fundamentals

Tue, 15 Dec 2020 00:00:00 +0000

This article covers matrix fundamentals in Go using the gonum library: matrix creation, basic arithmetic operations, and common matrix manipulations.

Linear Algebra in Go: Vectors and Basic Operations

Sat, 10 Oct 2020 00:00:00 +0000

This article begins a new series on linear algebra in Go, demonstrating how to perform numerical computations using the gonum library. If you’ve followed the Linear Algebra Crash Course in Python, this series provides a parallel implementation in Go with performance comparisons.

Advanced Platform Development with Kubernetes

Sun, 30 Aug 2020 00:00:00 +0000

I’ve been distracted for over a year now, writing a (~500 page) end-to-end tutorial on constructing data-centric platforms with Kubernetes. The book is titled “Advanced Platform Development with Kubernetes: Enabling Data Management, the Internet of Things, Blockchain, and Machine Learning”

Linear Algebra: Practical Applications in ML

Sun, 30 Aug 2020 00:00:00 +0000

This article covers practical machine learning applications, the final part of the series. I’ll show how the linear algebra concepts from previous articles apply to neural networks, gradient computation, and efficient vectorized operations.

Linear Algebra: Principal Component Analysis

Thu, 25 Jun 2020 00:00:00 +0000

This article covers Principal Component Analysis (PCA), part eleven of the series. PCA is one of the most widely used techniques for dimensionality reduction, data visualization, and feature extraction in machine learning.

Linear Algebra: Singular Value Decomposition

Mon, 20 Apr 2020 00:00:00 +0000

This article covers Singular Value Decomposition (SVD), part ten of the series. SVD is arguably the most important matrix decomposition, with applications in image compression, recommender systems, pseudoinverse computation, and dimensionality reduction.

Linear Algebra: Least Squares and Regression

Sat, 15 Feb 2020 00:00:00 +0000

This article covers least squares and regression, part nine of the series. Least squares is one of the most important applications of linear algebra and forms the foundation of regression analysis used throughout data science and machine learning.

Linear Algebra: Orthogonality and Projections

Tue, 10 Dec 2019 00:00:00 +0000

This article covers orthogonality and projections, part eight of the series. Orthogonality is fundamental to many algorithms including least squares regression, QR decomposition, and machine learning techniques like PCA.

Linear Algebra: Eigenvalues and Eigenvectors Part 2

Sat, 05 Oct 2019 00:00:00 +0000

This article continues the exploration of eigenvalues and eigenvectors, focusing on diagonalization, computing matrix powers, and handling complex eigenvalues. Part seven of the series.

Linear Algebra: Eigenvalues and Eigenvectors Part 1

Tue, 30 Jul 2019 00:00:00 +0000

This article on eigenvalues and eigenvectors is part six of an ongoing crash course on programming with linear algebra. Eigenvalues and eigenvectors are among the most important concepts in linear algebra, with applications ranging from differential equations to machine learning algorithms like PCA.

Linear Algebra: Vector Spaces and Subspaces

Sat, 25 May 2019 00:00:00 +0000

This article on vector spaces and subspaces is part five of an ongoing crash course on programming with linear algebra, demonstrating concepts and implementations in Python. Vector spaces provide the theoretical framework for understanding linear algebra, while subspaces help us analyze the structure of matrices and linear transformations.

Linear Algebra: Matrix Inverses and Determinants

Wed, 20 Mar 2019 00:00:00 +0000

This article on matrix inverses and determinants is part four of an ongoing crash course on programming with linear algebra, demonstrating concepts and implementations in Python. The inverse of a matrix and the determinant are fundamental concepts that reveal important properties about matrices and provide alternative methods for solving systems of linear equations.

Linear Algebra: Systems of Linear Equations

Tue, 15 Jan 2019 00:00:00 +0000

This article on systems of linear equations is part three of an ongoing crash course on programming with linear algebra, demonstrating concepts and implementations in Python. We’ll explore how matrices provide a powerful framework for solving systems of equations, a fundamental problem that appears throughout science, engineering, and machine learning.

Linear Algebra: Matrices

Sat, 08 Dec 2018 00:00:00 +0000

This article on matrices is part two of an ongoing crash course on programming with linear algebra, demonstrating concepts and implementations in Python. The following examples will demonstrate some of the various mathematical notations and their corresponding implementations, easily translatable to any programming language with mature math libraries.

Python Data Essentials - Matplotlib and Seaborn

Sun, 08 Jul 2018 00:00:00 +0000

There is an overwhelming number of options for developers needing to provide data visualization. The most popular library for data visualization in Python is Matplotlib, and built directly on top of Matplotlib is Seaborn. The Seaborn library is “tightly integrated with the PyData stack, including support for numpy and pandas data structures and statistical routines from scipy and statsmodels.”

Python Data Essentials - Pandas

Sun, 17 Jun 2018 00:00:00 +0000

Pandas bring Python a data type equivalent to super-charged spreadsheets. Pandas add two highly expressive data structures to Python, Series and DataFrame. Pandas Series and DataFrames provide a performant analysis and manipulation of “relational” or “labeled” data similar to relational database tables like MySQL or the rows and columns of Excel. Pandas are great for working with time series data as well as arbitrary matrix data, and unlabeled data.

Python Data Essentials - Numpy

Sat, 16 Jun 2018 00:00:00 +0000

Python is one of The Most Popular Languages for Data Science, and because of this adoption by the data science community, we have libraries like NumPy, Pandas and Matplotlib. NumPy at it’s core provides a powerful N-dimensional array objects in which we can perform linear algebra, Pandas give us data structures and data analysis tools, similar to working with a specialized database or powerful spreadsheets and finally Matplotlib to generate plots, histograms, power spectra, bar charts, error charts and scatterplots to name a few.