You are working with a genomic dataset containing 50,000 features and 1,000 samples. Compare and contrast the application of Principal Component Analysis (PCA), t-Distributed Stochastic Neighbor Embedding (t-SNE), and Uniform Manifold Approximation and Projection (UMAP) for this dataset. Discuss the mathematical assumptions of each method, the preservation of local vs. global structure, and which method you would recommend for a clustering task. Justify your choice with specific metric examples (e.g., silhouette score).