Perform Clustering on Universities data to make clusters of similar universities

1. Heirarchical Clustering

• It is a bottom to top approach.

• Find the euclidian distance between two points. Club closest point in one cluster.

• Then find the euclidian distance between two cluster / distance between one cluster and one point. We will again club the shortest distance in one cluster.

• Method to calculate euclidian distance

  • Single Linkage - shortest distance between 2 points in clusters.

  • Average Linkage - largest distance between 2 points in clusters.

  • Complete Linkage - Average of distance between all points in clusters.

  • Centroid Linkage - Find centroids of each clusters and find the distance between their centroids.

• If the data has both binary and numerical data. First convert the binary categorical data to 0 & 1 and standardize the numerical data. And perform heirarchical clustering on it.

2. K-Means Clustering

• Mostly used for practical uses. Will be used in industry frequently.

• Assume K = 3 (# of clusters)

• Find centroid for each partition

• Find distance between all data points to all cluster centroids.

• Move/Reassign datapoints to the nearest centroids.

• As the data has now changed so Recompute the centroids.

• Repeat step 3 - 5.

• Continue till we dont have to move any datapoint closer to any other centroid.

Cluster Profiling - Naming the cluster according to the common characteristics of the points in it.

How to select K-value

• Plot Elbow graph/ Scree Plot

3. DBSCAN

• DBSCAN - Density Based Spatial Clustering of Application with Noise.

Disadvantages of K-Means -

1. Cannot be used on data with noise(outliers).

2. K-Means does not perform well on non-spherical data. DBSCAN does.

3. We have to priorly determine the value of k in K-Means.

• DBSCAN is used for non-spherical data and also where data has lot of outliers, it will identify tehm seperately.

Important Terminology for DBSCAN

• epsilone - User given parameter - Defines size and borders of each neighbourhood. It will depend on domain and we have to trial and error dependeing how many outliers are we getting.

• Minpoints - User given parameters - Min number of points in neighnourhood to call it a dense region. Density Threshold. Generally choose minpoints >= D+1. D = no. of columns.

• Core point -

• Border point

• Noisy point

Disadvantage of DBSCAN

• Difficult with data whose density is low.

• It is an itterative procedure to determine eps and minpoints.

• computational complexity.