SPECTRAL CLUSTERING AND VISUALIZATION: A ... - Carl Meyer

BENSON-PUTNINS, BONFARDIN, MAGNONI, AND MARTIN
Fig. 2.1. Graph corresponding to consensus matrix from Section 2.2
origins of spectral graph partitioning methods; methods that use the spectral, or
eigen, properties of a matrix to identify clusters.
3.1. Example of Fiedler Clustering. Consider the small graph in Figure 3.1
with 10 vertices along with its associated adjacency matrix. Note: each edge has
weight 1.
Fig. 3.1. Graph with 10 vertices and its adjacency matrix
The corresponding Laplacian matrix L is defined as
(3.1)
L = D − A,
where A is the adjacency matrix, or matrix of weights, and D is a diagonal matrix
containing the row sums of A. Figure 3.2 shows the Laplacian matrix for the graph
in Figure 3.1.
Fig. 3.2. Finding Laplacian matrix for adjacency matrix in Figure 3.1
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