Puneet Mangla

Table of Contents Solving Ordinary Least Squares Using QR Decomposition Overview of Ordinary Least Squares The Linear Regression Model Solving the Ordinary Least Squares Problem What Is QR Decomposition? Orthogonal Matrix Q Upper Triangular Matrix R Gram-Schmidt Process for QR…

Table of Contents Diagonalize Matrix for Data Compression with Singular Value Decomposition What Is Matrix Diagonalization? Mathematical Definition Singular Value Decomposition How to Diagonalize Matrix with Singular Value Decomposition Power Iteration Algorithm Step 1: Start with a Random Vector Step…

Table of Contents Solving System of Linear Equations with LU Decomposition System of Linear Equations What Are Systems of Linear Equations? The Role of Matrix Factorization Understanding LU Decomposition The Role of Gaussian Elimination Solving Linear Equations Using LU Decomposition…

Table of Contents Hessian Matrix, Taylor Series, and the Newton-Raphson Method Higher-Order Derivatives: The Hessian Matrix Higher-Order Gradients The Hessian Matrix Taylor Series Linearization Taylor Series Expansion Newton-Raphson Method Summary Citation Information Hessian Matrix, Taylor Series, and the Newton-Raphson Method…

Table of Contents Partial Derivatives and Jacobian Matrix in Stochastic Gradient Descent Basics of Vector Calculus Vectors Differentiation of Univariate Functions What Are Derivatives? Derivatives of Common Functions Central Difference Formula Partial Derivatives and Gradients Multivariate Functions Partial Derivatives Gradients,…

Table of Contents Approximate Nearest Neighbor with Locality Sensitive Hashing (LSH) What Is Locality Sensitive Hashing (LSH)? Mathematical Foundation of LSH How LSH Works SimHash: LSH for Vector Databases Random Projection Computing Binary Fingerprint Creating Hash Table Mathematical Trade-Off Querying…

Table of Contents Implementing Huffman Encoding for Lossless Compression Lossy vs. Lossless Compression Lossy Compression Lossless Compression What Is Huffman Encoding? Frequency Analysis Build a Priority Queue Construct the Huffman Tree Generate Huffman Code Encode the Data Decode the Data…

Table of Contents Anomaly Detection: How to Find Outliers Using the Grubbs Test What Is an Outlier? How to Find Outliers with Grubbs Test Formulating the Hypotheses Null Hypothesis Alternative Hypothesis Calculate the Test Statistic Determining the Critical Value with…

Table of Contents Implementing Approximate Nearest Neighbor Search with KD-Trees Introduction to Approximate Nearest Neighbor Search Mathematical Foundation KD-Trees for Approximate Nearest Neighbor Search Construction of KD-Trees Querying with KD-Trees Step 1: Forward Traversal Step 2: Computing the Best Estimate…