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

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

Cluster ordered dither

And the answer is 2.

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

But so, Ci is going to, I'm going to minimize over my values of k and find the value of K that minimizes this distance between Xi and the cluster centroid, and then, you know, the value of k that minimizes this, that's what gets set in

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.

We were just happy with the number of cluster centers, and using more will make the situation worse.

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

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

This is a really useful thing to do if the exact answer doesn't matter very much which often when you're doing social network analysis it doesn't really matter that much exactly what something like the clustering coefficient is.

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

I actually have some friends who work on this too.

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.

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.

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?

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

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.

let's go through how this is often defined.

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.

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

So you get for e ij the probability that the j th data point corresponds to cluster center number i

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.

So, let me do that now.

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

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

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.

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

let mu k be the average of the points assigned to the cluster.

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

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

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

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.

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

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

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.

In particular, you're going to minimize the negative log likelihood of your data given the model plus a constant penalty per cluster.