## Description

Four datasets (Iris, YeastGene, Example, Utilities) are provided. In each dataset, each row

corresponds to an object and each column corresponds to an attribute. The attribute values are

comma-separated. You don’t need to do normalization for any of the datasets.

The initial centroids to be used in K-means for Iris and YeastGene datasets are provided. In each

file, each row denotes the initial centroid of a cluster.

In this assignment, you are asked to implement K-means algorithm and Agglomerative

algorithm (using Min to define inter-cluster distance). Templates (kmeans_template.py,

hierarchical_template.py) are for Python 3.

In kmeans_template.py, you are asked to fill in two functions: assignCluster and

getCentroid. In assignCluster, each object is assigned to the cluster whose centroid is the

closest to the object, based on Euclidean distance. In getCentroid, cluster centroids are

updated based on current assignment.

In hierarchical_template.py, you are asked to fill in merge_cluster and update_distance.

In merge_cluster, you need to merge two closest clusters. In update_distance, you need

to update the distance matrix after the merging using Min as the inter-cluster distance.

If you are not sure about whether it is OK to use a certain function, please post your

question on Piazza.

## Please take the following steps:

1. Implement K-means algorithm as follows:

Repeat T times:

• For each object xi

▪ Calculate Euclidean distance between xi and each of the K centroids

▪ Assign xi to the cluster whose centroid is the closest to xi

• For each cluster

▪ Calculate its centroid as the mean of all the objects in that cluster

2. Implement Hierarchical clustering algorithm (with Min as inter-cluster distance

definition):

• Obtain the distance matrix by computing Euclidean distance between each pair of

objects

• Let each object be a cluster (Assign the cluster index as 1 to N, where N is the

number of objects)

• Set the current index as T=N+1

• Repeat

▪ Find the smallest value in the distance matrix—suppose the entry is i-th

row and j-th column, so the i-th and j-th data points are the closest at the

current step

.

▪ Find the clusters that contain the i-th data point (the s-th cluster) and the jth data point (the t-th cluster).

▪ Merge the s-th and t-th clusters as a new cluster with index T and remove

the s-th and t-th clusters.

▪ For each pair of data points between the the s-th and t-th clusters (one

point in the s-th cluster, and one point in the t-th cluster), change their

distance to a big number.

▪ T=T+1

• Until only one cluster remains

3. Test your K-means on Iris dataset. Use the provided initial centroids, and set the

number of iterations (T) as 12, and the number of clusters (K) as 3. The final cluster

centroids should be:

Cluster 1: 5.006,3.418,1.464,0.244

Cluster 2: 6.8538,3.0769,5.7154,2.0538

Cluster 3: 5.8836,2.741,4.3885,1.4344

4. After running the filled kmeans_template.py code file, you can obtain a data file Iris_

kmeans_cluster.csv, which contains the Iris data and the assigned clusters. Then, apply

the PCA and plotting functions you used in Assignment 1 to project Iris data to 2

dimensions and draw the scatter plot. Use different colors for different clusters in the

scatter plot. The plot should look like the one below:

5. If you get the correct final cluster centroids and the plot, then repeat steps 3 and 4 on

the YeastGene dataset. Use the provided initial centroids, and set the number of iterations

(T) as 7, and the number of clusters (K) as 6.

6. Apply Hierarchical Clustering algorithm implemented in Step 2 on the Example

dataset. The order of the merging should be:

1 2 7

3 7 8

4 5 9

6 9 10

8 10 11

Each row here denotes an operation of merging two clusters to form a new cluster. The

first two indices denote the clusters to be merged, and the last one denotes the index of

the new cluster.

7. If you get the correct order in Step 6, then apply the hierarchical clustering algorithm

on the Utilities dataset.

8. Prepare your submission. Your final submission should be a zip file named as

Assignment3.zip. In the zip file, you should include:

• The Python code.

• Report: A WORD or PDF file named as Assignment3.docx or Assignment3.pdf.

The report should consist of the following parts: 1) The cluster centroids obtained

on YeastGene dataset after the T iterations. 2) The scatter plot obtained on

YeastGene dataset after applying PCA and plotting points using different colors for

different clusters. 3

) The order of merging in the hierarchical clustering on the

Utilities dataset. 4) The codes of your K-means and hierarchical clustering

algorithm implementation (i.e., the four functions: assignCluster, getCentroid,

merge_cluster and update_distance).

9. Submit the zip file under Assignment 3 on Brightspace.

Please refer to Course Syllabus for late submission policy and academic integrity policy. This

assignment must be done independently. Running your submitted code should be able to

reproduce the results in the report.