Manifold Öğrenme Tekniklerinin Uygulaması ve Karşılaştırmalı Analizi

Year 2025, Volume: 25 Issue: 6, 1348 - 1358

Hatice Çoban Eroğlu

Abstract

Bu makalede, İzomap, Yerel Doğrusal Gömme (LLE), Hessian LLE (HLLE), t-dağıtımlı Stokastik Komşu Gömme (t-SNE) ve Boyut Azaltma için Düzgün Manifold Yaklaşımı ve Projeksiyonu (UMAP) manifold öğrenme tekniklerinin parametre uzayı konveks ve konveks olmayan manifoldlar üzerindeki veri setlerine uygulamaları yapılmıştır. Ayrıca bu tekniklerin performansları sayısal büyüklükler ve gömme sonuçlarının görselleri açısından incelenerek bir analiz sunulmaktadır. Bu çalışmada, kullanılan parametre uzayı konveks ve konveks olmayan manifoldlar Swiss Roll ve delikli Swiss Roll olarak adlandırılan manifoldlardır.

Keywords

Manifold öğrenmesi , konveks ve konveks olmayan manifoldlar , boyut azaltma teknikleri , makine öğrenmesi

Application and Comparative Analysis of Manifold Learning Techniques

Abstract

In this paper, Isomap, Local Linear Embedding (LLE), Hessian LLE (HLLE), t-distributed Stochastic Neighbour Embedding (t-SNE) and Uniform Manifold Approximation and Projection for Dimensionality Reduction (UMAP) manifold learning techniques are applied to data sets on manifolds with convex and non-convex parameter spaces. In addition, an analysis of the performance of these techniques in terms of numerical quantities and visualizations of the embedding results are presented. The parameter space convex and non-convex manifolds used in this study are the so-called Swiss Roll and Swiss Roll with a rectangular hole.

Keywords

manifold learning , convex and nonconvex manifolds , dimensionality reduction , machine learning

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