| Algorithm | Approach | Goal | Strengths | Weaknesses | Computational Cost | Global/Local |
|---|
| MDS (Multi-dimensional Scaling) | Preserving pairwise distances | Embed data points in a lower dimension while preserving distances | Works well when pairwise distances are meaningful, classic method | Computationally expensive for large datasets, sensitive to noise in distance measurements, global optimization can be hard | High | Global |
| IsoMap | Geodesic distance on neighborhood graph | Preserve global geodesic distances | Robust to outliers, captures global structure well | Sensitive to “shortcuts” in graph construction, computationally expensive for large datasets | High | Global |
| Locally Linear Embedding | Local linear reconstruction of points | Preserve local linear relationships | Computationally efficient, good for locally smooth manifolds | Sensitive to noise, can have issues with non-convex manifolds, requires careful neighborhood selection | Medium | Local |
| MLLE (Modified LLE) | Multiple local linear reconstructions | Improve robustness of LLE to noise and sampling density variations | More robust to noise and sampling variations than LLE | More computationally expensive than LLE, still sensitive to neighborhood selection | Medium-High | Local |
| HLLE (Hessian Eigenmapping) | Hessian of the manifold | Capture local curvature information | Less sensitive to parameter tuning than LLE variants, can handle some non-convexities | Computationally expensive, can be sensitive to noise | High | Local |
| LTSA (Local Tangent Space Alignment) | Aligning local tangent spaces | Preserve local geometry by aligning tangent spaces | Robust to noise, can handle some non-convexities | Computationally more expensive than LLE, requires careful parameter tuning | Medium-High | Local |
| Spectral Embedding (Laplacian Eigenmaps) | Graph Laplacian Eigenvectors | Preserve local neighborhood relationships (similar to LLE in spirit) | Computationally efficient, widely applicable | Sensitive to noise, can have issues with disconnected graphs | Medium | Local |
| t-SNE (t-distributed Stochastic Neighbor Embedding) | Probabilistic similarity based on t-distribution | Visualize high-dimensional data in 2D or 3D | Excellent for visualization, reveals clusters well | Computationally intensive, sensitive to parameter tuning (perplexity), global structure is not well preserved, can create misleading “clusters” | High | Primarily Local, with some global tendencies |