Now, we looked at something in the class called the clustering coefficient.

In the clustering problem we are given an unlabeled data set and we would like to have an algorithm automatically group the data into coherent subsets or into coherent clusters for us.

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

Cluster ordered dither

I actually have some friends who work on this too.

And the answer is 2.

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

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.

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

2 sigma, 3 sigma and you can see as you increase the threshold that they get to be clustered more and more strongly.

So.

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

They're not representative of physical property or dark matter in any way.

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

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

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,

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?

Well the secret society won't be so secret anymore.

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

What do you mean? You were set up to surveil an undercover operation. Your cover's been blown.

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.

Confidential?

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.

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.

Until they were still Until they were still Until they were still

What secret?

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

like that and the red one moved like that.

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

So, let me do that now.

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

So now that we can compute the clustering coefficient for any node V we can actually loop through all the nodes in the graph computing the total of their clustering coefficients and then divide by the number of nodes to get the clustering coefficient for the whole graph.

and what's your secret?

Why a secret?