Data Set used

K Means

K Means Clusters

1. K Means begins with a user specified amount of clusters

2. Randomly places the K centroids on the data set3. Finds all the points closest to each centroid and

makes them clusters4. Changes the centroid of each cluster to the

mean of the subset of points5. Repeats step 5 until the change of the centroids

is minimal.

Kmeans Implementation Issues

• If K is too small the algorithm did not converge (no stable clusters)– Further investigation of this is needed

• If K is too small, some clusters were null

K- Means Matlab code

Ease of Doing Business vs Paying Taxes

Interesting case

• The border points are clearly defined by distance not density

• We ask for each point “What is the closest centroid?”

Why we like it

• It is relatively straight forward in concept and implementation

• Good for globular data• We can specify the amount of clusters

Why we don’t like it

• Subject to initialization problems and heterogeneous results.

• Not good for non-globular data (but can find clusters given a large enough K)

• Sensitive to outliers (cleaning data set helps)• Data must have the notion of a “center”

Variations

• Bisecting K-means• K-median• K - medoid• Several others

DBSCAN Algo

Pick a point P, find distance of every next point P' from P.

If(Dist < K Factor)P' is in same cluster as P.

else if (Dist = K Factor)P' is a border point.

else Allot P' a new cluster.

SNAPSHOTS

For K_Factor = 20

For K_Factor = 10

For K_Factor = 120

Calculation of K-Factor

Issues faced

When adding a new point P' to the present cluster, the whole cluster of P' has to be merged with the present cluster.

No lower bound on number of clusters.

Choice of K Factor

Further Enhancements

• Calculation for K-Factor and clustering could be integrated together.

• Dynamic programming could be made use of since many computations are being repeated.

• Static vs Dynamic data