The BIRCH Clustering Feature essentially is suppose you get these five

points into one cluster.

okay?

Then suppose these are the five points, their positions, okay?

Then the CF vector contains three components.

One is the number of data points.

The second is a linear sum of the points in the cluster.

The third one is square sum of the N points.

Okay.

So you probably can see the, the first one, 5 means there are 5 points.

The second one acts as a linear sum of each dimension.

Okay.

The third one actually is the squared sum of each dimension.

So the Clustering Feature essentially is the summary of the statistics of

a given sub-cluster, which you can consider the number is the zeroth,

the first one is the linear, the second one is the second moments

of the sub-cluster from the statistic point of view.

That means it will register the crucial measurements of the, for

computing cluster and utilizes storage quite efficiently.

So we can look at the,

the general concepts of centroid, radius, and diameter.

Okay.

The centroid essentially is the center of the cluster, okay?

Then, suppose we have a vector of N dimensions, x sub i.

Okay.

Then, the centroid is essentially computed by the sum of

all the points in this cluster divided by the number of points in the cluster,

so that what we get is a centroid of the cluster.

Okay.

Then the radius actually is the average distance from the member

objects to the centroid.

That essentially is every one you get a difference with the centroid,

then we use the sum of their square distance.

Divide by the number of points in the cluster.

Take their square root.

Essentially it's the square root of the average distance

from any point of the cluster to its centroid.