"LLE" (Machine Learning Method)
- Method for DimensionReduction, DimensionReduce, FeatureSpacePlot and FeatureSpacePlot3D.
- Reduce the dimension of data using a locally linear embedding.
Details & Suboptions
- "LLE", which stands for locally linear embedding, is a nonlinear neighborhood-preserving dimensionality reduction method.
- "LLE" is able to learn nonlinear manifolds; however, it can fail if data has high-density variations and tends to collapse large portions of the data close together.
- The following plots (see FeatureSpacePlot) show two-dimensional embeddings learned by the "LLE" method applied to the benchmark datasets Fisher's Irises, MNIST and FashionMNIST:
- "LLE" seeks to find a low-dimensional embedding that locally preserves the intrinsic geometry (such as angles and relative distances) of the data. To do so, "LLE" first defines the neighborhood of each data point by its nearest neighbors. Then, it computes the optimal "reconstruction weights" Wij by minimizing the reconstruction error (xj is a neighbor of xi): ∑ Ni=1|xi-∑jWijxj|2, subject to the constraint ∑jWij=1 (this constraint enforces the invariance of Wij to rotations, rescalings and translations of the data). Once Wij are computed, the lower-dimensional embeddings are computed by minimizing the embedding cost: ∑ Ni=1|yi-∑jWijyj|2 .
- "LLE" attempts to have the same reconstruction weights in the original and embedding space, which is why the local geometric properties of the data points are approximately preserved.
- The following suboption can be given:
"NeighborsNumber" Automatic number of nearest neighbors
Examplesopen allclose all
Basic Examples (1)
Dataset Visualization (1)
Load the Fisher Iris dataset from ExampleData and perform a train/test split: