"Isomap" (Machine Learning Method)
- Method for DimensionReduction and DimensionReduce.
- Reduce the dimension of data using an isometric mapping.
Details & Suboptions
- "Isomap", which stands for isometric mapping, is a nonlinear neighbor-based dimensionality reduction method. The method attempts to find a low-dimensional embedding of data via a transformation that preserves geodesic distances.
- "Isomap" is able to learn nonlinear manifolds; however, it gives poor results on boundaries, can fail if data has high-density variations, and is computationally expensive.
- The following plots show two-dimensional embeddings learned by the "Isomap" method applied to the benchmark datasets Fisher's Irises, MNIST and FashionMNIST:
- "Isomap" constructs a neighborhood graph on data points given their nearest neighbors. The geodesic distances between all pairs of points on the manifold are estimated by the shortest path in the nearest neighbors graph, , which results in the matrix of graph distances . The method attempts to find the embedding for which the Euclidean distance (shortest distance) is equal to the geodesic distance. The lower-dimensional embeddings are computed by minimizing the embedding cost: min ∑ Ni=1 [||yi-yj||- dij]2
- The method is equivalent to performing the classical "MultidimensionalScaling" on the matrix of graph distances . Consequently, the Euclidean distances in the embedding space match the graph distances: ||yi-yj||≈ dijG.
- The following suboption can be given:
"NeighborsNumber" Automatic number of neighbors k
Examplesopen allclose all
Basic Examples (1)
Dataset Visualization (1)
Load the Fisher Iris dataset from ExampleData: