Spectral clustering focuses on affinity (how relatively close the neighbouring points are from each other), rather than absolute position of the data points (i.e. what K-means and Expectation Maximization clustering algorithms focus on).
This Udacity video summarizes Spectral clustering very nicely.
The Expectation Maximization is somewhat similar to K-means, with this core difference:
In the corresponding step:
k-means uses “hard correspondence” – estimated centerpoint A only compares with the data points in cluster A in the revision of new estimated centerpoint A location. It does not compare with data points from other clusters (e.g. cluster B, etc.)
Expectation Maximization uses “soft correspondence” – estimated centerpoint A compares with the data points in cluster A and other clusters in the revision of new estimated centerpoint A location. It does compare with data points from other clusters (e.g. cluster B, etc.).
This video by Udacity summarizes this very nicely.
A quick memory refresh on understanding how K-means work in Unsupervised Learning:
Pick how many clusters we wish to find. K = 2 means “finding two clusters”. K = 3 means “finding three clusters”. etc.
Algorithm (assumd K=2 for simplicity sake).
Assign two ramdom cluster center points: A and B.
Link up the A and B with a straight line. Pick the mid-point. Draw a perpendicular line. This is the dividing line between cluster A and cluster B.
Now our goal is to find a revised A and B locations. Do this by picking an A location that has the minimum straight-line distances between all the points in cluster A. Do the same for B. i.e. Now we have the new A and B locations.
Repeat step 2 and step 3 iteratively. Until the A and B locations are more or less stable. i.e. we have two defined clusters.
This short video by Udacity summarizes this very nicely: