Homework 5

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Jan 9, 2024

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Homework 5: Cluster Analysis and Anomaly Detection Question 1: Assume we have a simple dataset with 10 two-dimensional points (x, y). Dataset: (2, 3), (3, 3), (3, 4), (4, 4), (7, 5), (9, 4), (6, 8), (8, 8), (9, 9), (8, 10) Use KMeans algorithm and group data points into two clusters. Initial centroids are Centroid 1: (3, 3), Centroid 2: (8, 8) Solution: Points Centroid 1: (3,3) Centroid 2(8,8) cluster (2,3) 1 7.81 1 (3,3) 0 7.07 1 (3,4) 1 6.40 1 (4,4) 1.41 5.65 1 (7,5) 4.47 3.16 2 (9,4) 6.08 4.12 2 (6,8) 5.83 2 2 (8,8) 7.07 0 2 (9,9) 8.48 1.41 2 (8,8) 8.60 2 2 Next centroids New Centroid 1 = (2+3+3+4)/4, (3+3+4+4)/4 = (3,3.5) New Centroid 2= (7+9+6+8+9+8)/6, (5+4+8+8+9+8)/6 = (7.8, 7.3) Points Centroid 1: (3,3.5) Centroid 2: (7.8,7.3) New cluster (2,3) 1.11 7.2 1 (3,3) 0.5 6.44 1 (3,4) 0.5 5.82 1 (4,4) 1.11 5.03 1 (7,5) 4.27 2.43 2 (9,4) 6.02 3.51 2 (6,8) 5.4 2.15 2 (8,8) 6.7 0.72 2 (9,9) 8.1 2.08 2 (8,8) 8.2 2.70 2 Final clusters: Cluster 1: (2,3), (3,3), (3,4), (4,4) Cluster 2: (7,5), (9,4), (6,8), (8,8), (9,9), (8, 10)
Homework 5: Cluster Analysis and Anomaly Detection Question 2: A data scientist plans to use DBSCAN with the minimum number of points set to 5. Identify each labeled point in the scatter plot as a border point, core point, or outlier. (Discuss it). Solution: A is considered a core point since it meets the criteria for the minimum number of points within the specified ε range. On the other hand, B and C are identified as outliers because they fail to meet the minimum number of points requirement and also fall outside the range of a core point to be classified as a border point. Question 3: Determine whether each labeled point in the figure below is a core point, a boundary point, or an outlier given ε = 2 and the minimum number of points for a core point is 4. (Discuss it).
Homework 5: Cluster Analysis and Anomaly Detection Solution : For a point to be a core point, it should satisfy the min_points condition within the given ε . So, A is a core point which has 4 samples within ε = 2. Point B though it has 2 points within the ε , it doesn ’ t have 4 samples so it is a boundary point. Point C doesn’t have any points within the ε limit. So, C is an outlier. Question 4: What is the distance between the two clusters using centroid linkage? Solution: Centroid of cluster A = (1+2+0)/3, (6+4+2)/3 = (1,4) Centroid of cluster B = (6+8)/2, (8+4)/2 = (7,4) distance between the two clusters = √ ( ? 1 − ? 2 ) 2 + (? 1 − ? 2 ) 2 = √ ( 1 − 7 ) 2 + (4 − 4 ) 2 = 6 Question 5: Create a dendrogram from the following figure. (Height of dendrogram in your solution is not important.)
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