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So far we've been picturing K Means and applying it to data sets like that shown here where we have three pretty well separated clusters, and we'd

Valued point cloud visualisation and analysis

But for now I'm going to give you 4 choices.

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.

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.

And the line that separates the space between the left and right cluster center is the equidistant line, often called a Voronoi graph.

Chemical Data

Nevertheless, the matter is well understood now and a lot of good data have been obtained.

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Given now we have a correspondence between the data points and cluster centers, find the optimal cluster center that corresponds to the points associated with the cluster center.

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

One of the nice things here is this algorithm also overcomes local minima problems to some extent.

It doesn't make any sense, so the only way to understand it is visually and relatively.

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

In a corresponding step, we correspond all the data points to the nearest cluster center, and then we calculate the new cluster center by the mean of the corresponding data points.

Let's do a very quick quiz for EM.

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

One is a parameter K, which is the number of clusters you want to find in the data.

So let's look at this example again let me redraw the data.

The main new thing in Unit 3 was lists.

And then we introduced the hash table.

In the adjustment step or the maximization step the cluster centers are being optimized just like before but now the correspondence is a soft variable and they correspond to all data points in different strengths not just the nearest ones.

The sound of the waves and other environmental sounds that you can hear in the space are translated into data and visualized as light.

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

Golan Levin, who is going to be making his interpretation and visualization of the data.

I work as a theoretical physicist.

Step 3

I'm not talking about digitizing, and bits, and re mastering.

It's kind of living.

And the way they represent information is they break up that data into little pieces that are represented by pulses and different neurons.

Thrun Here is another EM quiz.

SPM data visualization and analysis

But the problem is that things in the upper right corner there personalized data, it's been pretty hard to come by.

learning algorithms that we'll talk about later that finds other types of structure or other types of patterns in the data other than clusters.

The data must have been erased.

And I've taken the liberty, just for clarity, to translate that to data slices.

Or put differently do you think there's something to be learned about data like this, or is it entirely random?

Cluster ordered dither

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.

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And the answer is 2.