spectral_clustering: Spectral Clustering

In arthans/SpectralClustering: Spectral Clustering

Description

Apply clustering to a projection of the normalized Laplacian.

Usage

spectral_clustering(X, n_clusters = 8, n_components = NULL,
affinity = "rbf", assign_labels = "kmeans", n_init = 10)

Arguments

X	Training instances to cluster.
n_clusters	Number of clusters to extract.
n_components	Number of eigenvectors to use for the spectral embedding.
affinity	How to construct the affinity matrix. - 'nearest_neighbors': construct the affinity matrix by computing a graph of nearest neighbors. - 'rbf': construct the affinity matrix using a radial basis function (RBF) kernel. - 'precomputed': interpret “X“ as a precomputed affinity matrix, where larger values indicate greater similarity between instances. - 'precomputed_nearest_neighbors': interpret “X“ as a sparse graph of precomputed distances, and construct a binary affinity matrix from the “n_neighbors“ nearest neighbors of each instance.
assign_labels	The strategy to use to assign labels in the embedding space. There are three ways to assign labels after the Laplacian embedding. k-means can be applied and is a popular choice. But it can also be sensitive to initialization. Discretization is another approach which is less sensitive to random initialization [3]_. The cluster_qr method [5]_ directly extracts clusters from eigenvectors in spectral clustering. In contrast to k-means and discretization, cluster_qr has no tuning parameters and is not an iterative method, yet may outperform k-means and discretization in terms of both quality and speed.
n_init	How many random sets should be chosen in k-means?

Details

In practice Spectral Clustering is very useful when the structure of the individual clusters is highly non-convex or more generally when a measure of the center and spread of the cluster is not a suitable description of the complete cluster. For instance, when clusters are nested circles on the 2D plane.

Value

The labels of the clusters.

References

[1] Normalized cuts and image segmentation, 2000 Jianbo Shi, Jitendra Malik http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.160.2324

[2] A Tutorial on Spectral Clustering, 2007 Ulrike von Luxburg http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.165.9323

[3] Multiclass spectral clustering, 2003 Stella X. Yu, Jianbo Shi https://www1.icsi.berkeley.edu/~stellayu/publication/doc/2003kwayICCV.pdf

[4] Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method, 2001. A. V. Knyazev SIAM Journal on Scientific Computing 23, no. 2, pp. 517-541. https://epubs.siam.org/doi/pdf/10.1137/S1064827500366124

[5] Simple, direct, and efficient multi-way spectral clustering, 2019 Anil Damle, Victor Minden, Lexing Ying <:doi:'10.1093/imaiai/iay008'>

Examples

data(X)

labels <- spectral_clustering(X,2)

plot(X, col=labels)

arthans/SpectralClustering documentation built on Dec. 19, 2021, 4:41 a.m.