Statistical Modeling & Regression · Multivariate Analysis

Multivariate analysis · Computational implementation and practical interpretation

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Chart from the original guide

Overview

Topics covered

  • Introduction
  • Multivariate Analysis: Implementation and Practice
  • Fundamentals of matrix algebra and multivariate geometry
  • Multivariate Metric Geometry: Mahalanobis Distance
  • Essential Matrix Decompositions
  • The Multivariate Normal Distribution

Related concepts

Main connections

  • Linear algebra & matrices
  • Variance & standard deviation
  • Principal component analysis (PCA)
  • Normal (Gaussian) distribution
  • Regularization (Lasso / Ridge / Elastic Net)
  • Unsupervised learning & clustering

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

𝐗=( x11x12…x1p x21x22…x2p ⋮⋮⋱⋮ xn1xn2…xnp )=(𝐱1T𝐱2T⋮𝐱nT),
View LaTeX source\mathbf{X} = \begin{pmatrix} x_{11} & x_{12} & \dots & x_{1p} \\ x_{21} & x_{22} & \dots & x_{2p} \\ \vdots & \vdots & \ddots & \vdots \\ x_{n1} & x_{n2} & \dots & x_{np} \end{pmatrix} = \begin{pmatrix} \mathbf{x}_1^T \\ \mathbf{x}_2^T \\ \vdots \\ \mathbf{x}_n^T \end{pmatrix},