So there's a fair amount of interconnection between a node's neighbors.

So just getting it correct to a couple of digits is probably sufficient.

Cluster ordered dither

So we'd like to have a way of getting a pretty good answer in time a lot less than this.

And the answer is 2.

And if you do that, you end up with K minus one clusters instead of k clusters.

Next I want to focus for a little while on the notion of a clustering coefficient.

I am going to say that the clustering coefficient for graph is just the average of the clustering coefficients of the nodes in the graph.

I actually have some friends who work on this too.

Suppose we're given the following data points in a 2 dimensional space.

Suppose you are given data like this, and you wish to learn that there's 2 clusters a cluster over here and a cluster over here.

And second, to narrow this down, it feels that there are clusters of data the way I do it.

K Means is an iterative algorithm and it does two things.

C6 equals to and similarly well c10 equals, too, right?

let's go through how this is often defined.

All the data points on the left correspond to the red cluster, and the ones on the right to the green cluster.

So as a concrete example, let's say that one of my cluster centroids, let's say cluster centroid two, has training examples, you know, 1, 5, 6, and 10 assigned to it.

The last question asked, what is the maximum clustering coefficient for a node in B?

I'm going to do. The first step is to randomly initialize two points, called the cluster centroids.

Next is lower case k.

And so in the earlier diagram, the cluster centroids corresponded to the

K means estimates for a fixed number of k. Here k 2.

So the optimal cluster center would be the halfway point in the middle.

It's likely somewhere over here where I drew the red dot.

So, let me do that now.

K means is a very simple almost binary algorithm that allows you to find cluster centers.

If we use k means, we shouldn't increase the number of cluster centers.

So just to remind you, here's some code for computing the clustering coefficient of a graph with respect to a particular node v.

Suppose we are giving you 4 data points, as indicated by those circles.

I'm going to color them either red or blue.

It is not the perfectly flat system like the disk of the Milky Way, but it is flat.

Order them from the lowest clustering coefficient to the highest clustering coefficient.

Who formatted this thing? And they used clusters instead of physical sectors for allocations,

For this problem we have 6 graphs, and we want you to order them with a clustering coefficient of the red node of each graph.

Two times the number of links divided by length of neighbors times length of neighbors minus one.

Both are prone to local minima.

So, if you could see stars as well, they would look somewhat like this but more condensed.

So, these two crosses here, these are called the Cluster Centroids and I have two of them because I want to group my data into two clusters.

In the M step we now figure out where these parameters should have been.

This one over here, we have a constant cost per cluster is new.

Step 1 Guess cluster centers at random, as shown over here with the 2 stars.

Let me illustrate this once again with the data set that has a different spectral clustering than a conventional clustering.

These are Hubble Space Telescope images of a particular cluster, that serves as a gravitational lens.

So the correct answer for the second question is 2.

So here's a first quiz for k means.