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Spectral clustering has been successfully applied on large graphs by first identifying their community structure, and then clustering communities. [4] Spectral clustering is closely related to nonlinear dimensionality reduction, and dimension reduction techniques such as locally-linear embedding can be used to reduce errors from noise or ...
Algorithms capable of operating with kernels include the kernel perceptron, support-vector machines (SVM), Gaussian processes, principal components analysis (PCA), canonical correlation analysis, ridge regression, spectral clustering, linear adaptive filters and many others.
A spectral implementation of DBSCAN is related to spectral clustering in the trivial case of determining connected graph components — the optimal clusters with no edges cut. [12] However, it can be computationally intensive, up to (). Additionally, one has to choose the number of eigenvectors to compute.
Conductance also helps measure the quality of a Spectral clustering. The maximum among the conductance of clusters provides a bound which can be used, along with inter-cluster edge weight, to define a measure on the quality of clustering. Intuitively, the conductance of a cluster (which can be seen as a set of vertices in a graph) should be low.
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some specific sense defined by the analyst) to each other than to those in other groups (clusters).
Global approaches rely on properties of the entire graph and do not rely on an arbitrary initial partition. The most common example is spectral partitioning, where a partition is derived from approximate eigenvectors of the adjacency matrix, or spectral clustering that groups graph vertices using the eigendecomposition of the graph Laplacian ...
The Laplacian matrix of a directed graph is by definition generally non-symmetric, while, e.g., traditional spectral clustering is primarily developed for undirected graphs with symmetric adjacency and Laplacian matrices. A trivial approach to applying techniques requiring the symmetry is to turn the original directed graph into an undirected ...
Applications based on diffusion maps include face recognition, [7] spectral clustering, low dimensional representation of images, image segmentation, [8] 3D model segmentation, [9] speaker verification [10] and identification, [11] sampling on manifolds, anomaly detection, [12] [13] image inpainting, [14] revealing brain resting state networks ...