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Marxist Philosophy of Science: The Newspaper — 2026-11-14
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Marxist Philosophy of Science: The Newspaper — 2026-11-13
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METRIC EMBEDDINGS, PART I: PRINCIPAL COMPONENT ANALYSIS AND CLUSTER ANALYSIS. THEIR CONCEPTUAL INTERPRETATION, GEOMETRIC LOGIC-INTUITION, MATHEMATICAL FORMALISM, AND COMPUTATIONAL APPLICATIONS
This article develops PCA from geometric and algebraic foundations, explaining transformations, eigenvalues, variance, reconstruction, and variable relevance. It connects dimensionality reduction with k-means and hierarchical clustering, demonstrates applications using decathlon and USArrests data in R and Minitab, discusses validation and interpretation, and introduces random projections through the Johnson–Lindenstrauss lemma.