From f6a5807fdd4194dab37bfefd3c021f1513b3eb8a Mon Sep 17 00:00:00 2001
From: Ethan Smith-Coss <ethan.sc@closedless.xyz>
Date: Fri, 30 May 2025 23:48:57 +0100
Subject: [PATCH] README.md

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+# Principal Component Analysis in C
+
+The committed files are a fully functioning implementation of the Karhunen–Loève
+transform (KLT) as defined on Wikipedia, and verified using multiple languages -
+Python, R and MATLAB. Note. It may be common for libraries to call this algorithm
+'covariance', 'eig' or similar to distinguish from the SVD alogrithm or 
+otherwise. The algorithm aims to solve the following system of linear
+expressions:
+
+$$
+\mathbf{Y} = \mathbb{KLT}\{\mathbf{X}\},
+C = \frac{1}{n-1}\mathbf{X}*\mathbf{X},
+\mathbf{V}^{-1}\matbf{C}\mathbf{V} = \mathbf{D},
+\mathit{W} \subset \mathit{V},
+T = \mathbf{B} \cdot \mathbf{W}.
+$$
+
+The initial dataset $\mathbf{X}$ is reduced in dimensionality by matrix
+$\mathit{W}$ which is a subset of eigenvectors, explicitly or intuitively
+selected. Matrix $\mathbf{T}$ is the newly reduced data with an explained
+variance ratio $\lt1.0$, though typically very high.
+
+The source code is built entirely on the GNU GSL (2.7) library, to
+utilise BLAS optimised functionality.