"Spectral" (Machine Learning Method)
- Method for FindClusters, ClusterClassify and ClusteringComponents.
- Partitions data into clusters of similar elements using a "Spectral" method.
Details & Suboptions
- "Spectral" is a hybrid neighbor-based/centroid-based clustering method. "Spectral" works for arbitrary cluster shapes but requires clusters to have similar sizes. Since the method solves an eigenvalue problem, it is computationally expensive for large datasets.
- The following plots show the results of the "Spectral" method applied to toy datasets:
- To identify k clusters, the "Spectral" method uses the "KMeans" algorithm after reducing the data to k-dimensions. The dimensionality reduction is a neighbor-based nonlinear method similar to "Isomap": The adjacency matrix, is computed for every data point i, j. is the distance between the points, and is a scale parameter. is then centered, normalized and linearly reduced to dimension k. Mathematically speaking, the centered and renormalized adjacency matrix is given by , where is the diagonal matrix defined as . The largest k eigenvectors of constitute the reduced data.
- The option DistanceFunction can be used to define .
- The following suboption can be given:
"NeighborhoodRadius" Automatic value for scale parameter
Examplesopen allclose all
Basic Examples (3)
Find clusters of numbers using the "Spectral" method:
Find up to four clusters using the "Spectral" method:
Train the ClassifierFunction on a list of colors using the "Spectral" method:
Gather the elements by their class number:
Create and visualize noisy 2D moon-shaped training and test datasets:
Train a ClassifierFunction using the "Spectral" method; find and visualize clusters in the test set:
Perform cluster analysis of a computed tomography scan image using the "Spectral" method:
Create a ClassifierFunction from a list of images and classify examples using the "Spectral" method:
Find the cluster assignments and gather the elements by their corresponding clusters: