LaTeX Documentation

Comprehensive mathematical notes and formal documentation

About the Documentation

This section contains our formal LaTeX documentation, including detailed mathematical notes, proofs, and theoretical foundations for manifold learning. All documents are compiled weekly and maintain rigorous academic standards.

The documentation follows the structure of our study group meetings and provides comprehensive coverage of topics from foundational mathematics to advanced manifold learning algorithms.

Explore the individual member contributions below to dive into specialised topics we're studying together.

Member Notes

Personal study dossiers prepared by members to deepen and share understanding beyond the main syllabus.

Member Note

Repeated Eigendirection Problem (REP)

Oğuzhan Recep Akkol examines repeated eigendirections, their impact on embeddings, and ways to mitigate artefacts.

Oğuzhan Recep Akkol PDF · 11 pages
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Laplace–Beltrami and Graph Laplacians

Oğuzhan Recep Akkol links physical intuition, discrete graphs, and eigenmaps to show how graph Laplacians converge to their Laplace–Beltrami counterparts.

Oğuzhan Recep Akkol PDF · 6 pages
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Member Note

Local Linear Approximations

Oğuzhan Recep Akkol reviews the manifold assumption, random projections, and local PCA to motivate neighbourhood-based dimensionality reduction.

Oğuzhan Recep Akkol PDF · 5 pages
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Local Tangent Space Alignment (LTSA)

Oğuzhan Recep Akkol outlines the LTSA pipeline, from tangent patch construction to aligning affine charts into a coherent embedding.

Oğuzhan Recep Akkol PDF · 4 pages
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Principal Curves and d-Manifolds

Naki Eren Şengezer revisits principal curves and intrinsic dimensionality, connecting geometric intuition with manifold learning objectives.

Naki Eren Şengezer PDF · 3 pages
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Riemannian Metrics in Context

An exploration by Naki Eren Şengezer on framing Riemannian metrics for data-driven manifolds, with annotated derivations and references.

Naki Eren Şengezer PDF · 6 pages
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Member Note

Statistical Basis of Sampling Biases

Naki Eren Şengezer formalises Section 5 intuitions with statistical tools that explain sampling-density bias and its interaction with graph construction.

Naki Eren Şengezer PDF · 6 pages
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