Dimensionality-Reduction

Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Every applied account of PCA triages components by the share of variance they carry, and stability does not work that way: an eigenvector is determined by the distance from its eigenvalue to the nearest other one, so the largest component in a decomposition can be the least trustworthy axis in it....

Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Eckart and Young settled which rank-k matrix is closest to yours — your own truncated SVD — and said nothing about which k. The scree plot fills that gap with a judgement about a shape and no reference distribution, and on a matrix with no structure in it that judgement returns a number every time....

Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. On raw breast-cancer measurements the first principal component holds 98.2% of the variance and is led by worst area, the feature with the largest units; the 95% variance rule keeps 1 component, against 10 on standardised features....