# A tibble: 6 × 6
University TLR RP GO OI PR
<chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Indian Institute of Science 89.8 98.6 92.3 85 90.1
2 Jawaharlal Nehru University 78.5 85.2 86.4 82.1 88.7
3 Banaras Hindu University 75.4 82.1 85.7 80 85.9
4 University of Delhi 70.3 75.5 80.2 79.5 84.5
5 Amrita Vishwa Vidyapeetham 77.6 70.3 79.8 81.3 83
6 Jadavpur University 72.1 68.7 78.1 77.6 81.2LA Assignment 26
Shyam Kumar M, Saurav K S
Use dendrograms and hierarchical clustering to analyze similarity between universities based on ranking metrics.
Step 1: Load required packages
- tidyverse: For data manipulation and visualization
- cluster: For clustering algorithms
- factoextra: For enhanced visualization of clustering
Step 2: Import the CSV File
This reads the CSV file.
head() to preview 6 rows of data.
Step 3: Preprocess the Data
na.omit: used to remove rows with missing values.
Sets university names as row identifies for use in the dendogram.
Only keep numeric columns (metrics) for clustering.
Step 4: Scale the Data
TLR RP GO OI PR
[1,] 2.45162099 2.0973214 1.94256682 1.7366701 1.62919733
[2,] 0.54367904 0.9785273 1.00924889 0.9606542 1.31802730
[3,] 0.02026133 0.7197018 0.89851625 0.3987116 0.69568726
[4,] -0.84084522 0.1686540 0.02847411 0.2649158 0.38451724
[5,] 0.39171906 -0.2655049 -0.03480169 0.7465808 0.05112079
[6,] -0.53692526 -0.3990922 -0.30372380 -0.2435084 -0.34895495
[7,] -0.06416088 -0.6913145 -0.58846487 -0.8322101 -0.54899282
[8,] -0.68888524 -1.0837274 -0.80993014 -1.4209119 -0.81570998
[9,] -0.28365863 -0.5994732 -0.99975752 -0.4843410 -0.97129500
[10,] -0.99280520 -0.9250924 -1.14212805 -1.1265610 -1.39359717
attr(,"scaled:center")
TLR RP GO OI PR
75.28 73.48 80.02 78.51 82.77
attr(,"scaled:scale")
TLR RP GO OI PR
5.922612 11.977182 6.321533 3.737037 4.499148 - Scales all columns to have a mean of 0 and standard deviation of 1
Step 5: Compute Distance Matrix
1 2 3 4 5 6 7
2 2.5420567
3 3.4001413 1.0277670
4 4.6839227 2.2113829 1.3845070
5 4.1480998 2.0764463 1.5862454 1.4334807
6 5.2956118 3.0030444 2.1239732 1.1495805 1.4466797
7 5.6440613 3.5228762 2.6969620 1.9489804 1.8837199 0.8812278
8 6.5959067 4.3938836 3.5027683 2.5645727 2.8084583 1.5336887 1.0054964
9 5.9251311 3.8130942 2.9991074 2.0874264 2.0147735 1.0168908 0.7246570
10 6.9173534 4.7246533 3.8193517 2.7726487 3.0288620 1.7488521 1.4225239
8 9
2
3
4
5
6
7
8
9 1.1559052
10 0.8052850 1.1045233Calculates Euclidean distance between universities.
This distance matrix is the input for the clustering algorithm
Step 6: Apply Hierarchical Clustering
Call:
hclust(d = dist_matrix, method = "ward.D2")
Cluster method : ward.D2
Distance : euclidean
Number of objects: 10 Performs hierarchical clustering
Ward’s method minimizes within-cluster variance.
Step 7: Plot Dendrogram
Visualizes the clustering result
k gives the no. of clusters.
Step 8: Add Cluster Assignments
# A tibble: 10 × 6
TLR RP GO OI PR Cluster
<dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 89.8 98.6 92.3 85 90.1 1
2 78.5 85.2 86.4 82.1 88.7 2
3 75.4 82.1 85.7 80 85.9 2
4 70.3 75.5 80.2 79.5 84.5 2
5 77.6 70.3 79.8 81.3 83 2
6 72.1 68.7 78.1 77.6 81.2 3
7 74.9 65.2 76.3 75.4 80.3 3
8 71.2 60.5 74.9 73.2 79.1 3
9 73.6 66.3 73.7 76.7 78.4 3
10 69.4 62.4 72.8 74.3 76.5 3- Assigning cluster number to each university