Spectral clustering transforms the clustering problem into a graph-partitioning problem by treating each data point as a graph node. It constructs a similarity graph for all data points and embeds them into a low-dimensional space using the eigenvectors of the graph Laplacian, in which clusters are more obvious. Then a classical clustering algorithm like k-means is applied to partition the embedding. Spectral clustering is flexible and can handle various cluster shapes without assumptions, often outperforming other approaches.

1. SPECTRAL CLUSTERING
Prepared By
Ms.W.Ancy Breen,A.P/CSE
SRMIST

2. SPECTRAL CLUSTERING
 Spectral Clustering is a growing clustering algorithm which has performed
better than many traditional clustering algorithms in many cases.
 It treats each data point as a graph-node and thus transforms the clustering
problem into a graph-partitioning problem.
 Spectral clustering is a popular unsupervised machine learning algorithm which
often outperforms other approaches.
Why spectral clustring?
 Strength of spectral clustering
 Makes no assumptions on the shapes of clusters,can handled sprials,etc.
 EM or the like require an iterative process to find local minima and multiple
restarts.
Purpose of spectral clustering
 Spectral clustering is a technique with roots in graph theory, where the approach
is used to identify communities of nodes in a graph based on the edges
connecting them.
 The method is flexible and allows us to cluster non graph data as well.

3.  Construct a similarity graph(eg:KNN graph)for all the data points.
 Embed data points in a low-dimensional space(spectral
embedding),in which the clusters are more obvious,with the use of
the eigen vectors of the graph Laplacian.
 A classical clustering algorithm(eg:k-means)is applied to partition
the embedding.

4. 1)Pre-processing
 Construct a matrix representation of the graph.
2) Decomposition
 Compute eigen values and eigen vectors of the matrix .
 Map each point to a lower-dimensional representation
based on one or more eigen vectors.
3)Grouping
 Assign points to two or more clusters, based on the new
representation.

5. MATRIX REPRESENTATIONS OF A GRAPH

6. GRAPHS