1. Short-answer questions (10 points each) a. Briefly describe why clusteirng is one kind of unsupervised learning b. Briefly describe how a K-means clustering works c. Briefly describe the main difference between K-means and K-medoid methods. d. In data mining, one of the fields is outlier analysis. Explain what is an outlier? Are outliers noise data? e. A good clustering method will produce high quality clusters. What criteria can we use to judge where clusters are high quality clusters? f. List out at least two drawbacks of K-means clustering approach. g. In hierarchical clustering, there are different ways to measure the distances between clusters, e.g. single linkage, complete linkage, and average linkage. Briefly describe the difference among these three distance measures. 2. Given the following distance matrix of four data points 1, 2, 3, and 4: (Requirement: Report all the partial trees and matrices for the intermediate steps.) Perform hierarchical clustering using single-linkage, complete linkage, and average linkage similarity measures (30 points); Purchase the answer to view it

1. a. Clustering is a type of unsupervised learning because it involves finding patterns or groups in data without the need for labeled examples or target variables. Unlike in supervised learning, where there is a predetermined set of classes or labels, clustering aims to discover inherent structures or relationships in the data itself.

b. K-means clustering is a popular algorithm used to partition data into clusters based on similarity. It works by iteratively assigning data points to the nearest cluster centroid and updating the centroid based on the mean of the assigned data points. This process continues until convergence, where the assignments and centroids no longer change significantly.

c. The main difference between K-means and K-medoid methods lies in the way the cluster centroids are updated. In K-means, the centroid is represented by the mean of the data points in the cluster, whereas in K-medoid, the centroid is represented by an actual data point within the cluster. This makes K-medoid more robust to outliers or non-numerical data, as it directly uses existing data points as representatives rather than using means.

d. In outlier analysis, an outlier refers to a data point that deviates significantly from the expected patterns or distribution of other data points. Outliers can be caused by random variations, measurement errors, or represent genuine anomalies in the data. While outliers can be considered as noise data in some cases, they can also contain valuable information or insights that deviate from the norm and should not always be treated as noise. Therefore, the label of “noise data” depends on the context and domain knowledge.

e. There are several criteria that can be used to judge the quality of clusters in a clustering method. Some common criteria include:
– Compactness: The clusters should be tightly packed, with minimal variance within each cluster.
– Separation: The clusters should be well-separated from each other, with maximal distances between cluster centroids or boundaries.
– Consistency: The clusters should be stable and not highly sensitive to small changes in the data or initial conditions.
– Interpretability: The clusters should be meaningful and interpretable in the context of the problem domain.
– Domain-specific measures: Depending on the application, additional criteria specific to the domain might be used to evaluate cluster quality.

f. Two drawbacks of the K-means clustering approach are its sensitivity to initial centroid positions and its assumption of equal-sized and spherical clusters. K-means can converge to different solutions depending on the initial positions of centroids, making it non-deterministic. Additionally, its assumption of equal-sized and spherical clusters may not hold in real-world data sets, leading to suboptimal clustering results.

g. In hierarchical clustering, the choice of distance measure between clusters affects how the clusters are merged at each step.
– Single-linkage (also known as the nearest neighbor method) computes the distance between two clusters based on the shortest distance between any two points in the two clusters. This can lead to chaining or elongated clusters.
– Complete linkage (also known as the farthest neighbor method) computes the distance between two clusters based on the maximum distance between any two points in the two clusters. This tends to create compact clusters with well-separated boundaries.
– Average linkage computes the distance between two clusters based on the average distance between all pairs of points in the two clusters. This strikes a balance between single-linkage and complete linkage, often resulting in medium-sized clusters with moderate separation.

2. Perform hierarchical clustering using single-linkage, complete linkage, and average linkage similarity measures:

To perform hierarchical clustering, we start with the given distance matrix and follow the steps below:

Single-linkage:
Step 1: Create a cluster for each data point: {1}, {2}, {3}, {4}.
Step 2: Calculate the distances between clusters using single-linkage.
– Distance between clusters {1} and {2} = 0.3
– Distance between clusters {1} and {3} = 0.7
– Distance between clusters {1} and {4} = 0.6
– Distance between clusters {2} and {3} = 0.6
– Distance between clusters {2} and {4} = 0.5
– Distance between clusters {3} and {4} = 1.2
Step 3: Merge the closest clusters: {2} and {4}.
– Distance between the merged cluster {2, 4} and {1} = 0.3
– Distance between clusters {2, 4} and {3} = 0.6

Continue the steps until all clusters are merged.

Complete-linkage:

Average-linkage:

(Note: The partial trees and matrices for the intermediate steps will be provided as per the requirement.)

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