Statistical Modeling & Regression · Multivariate Analysis

Multivariate analysis: Cluster analysis (cluster analysis)

Public introduction · full guide in Eikos

Introduction

What this guide covers

A rigorous mathematical and algorithmic treatise on numerical taxonomy, the study of hyperspatial distances, variance decomposition, and clustering theory.

Overview

Topics covered

  • Introduction
  • Multivariate Cluster Analysis
  • Introduction and Axiomatic Foundations of Numerical Taxonomy
  • Formal Differentiation: Supervised Classification vs. Unsupervised Clustering
  • Formulation of Homogeneity and Separability
  • The Curse of Dimensionality in Metric Spaces

Related concepts

Main connections

  • Unsupervised learning & clustering
  • Linear algebra & matrices
  • Variance & standard deviation
  • Mean & expected value
  • Maximum likelihood estimation
  • Outliers & influence diagnostics

Compatible notation

Mathematical sample in LaTeX

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

minf1n∑i=1nℒ(f(𝐱i),yi)+λΩ(f)
View LaTeX source\min_{f} \frac{1}{n}\sum_{i=1}^n \mathcal{L}(f(\mathbf{x}_i), y_i) + \lambda \Omega(f)