kmedoids code

Clustering

• Clustering is a type of unsupervised machine learning that involves grouping similar data points together into clusters.
• The goal of clustering is to partition a set of data points into groups (also called clusters) such that data points in the same group are more similar to each other than to those in other groups.
• Clustering is used in a wide range of applications, including market segmentation, image segmentation, document classification, and anomaly detection.
• The process of clustering can help to reveal patterns and relationships within the data, and can also be used to reduce the dimensionality of high-dimensional data.
• There are various algorithms for clustering, including K-means, K-medoid, hierarchical clustering, and density-based clustering.
• The choice of algorithm depends on the characteristics of the data and the requirements of the application.

K-Medoid Clustering

• K-medoid is a clustering algorithm that groups similar data points together into clusters.
• It is a variation of the K-means algorithm and is used to partition a set of data points into K clusters, where K is a user-defined parameter.
• The K-medoid algorithm works by selecting K data points as the initial medoids and then assigning each data point to the closest medoid.
• The algorithm then iteratively updates the medoids to minimize the sum of distances between data points and their cluster medoids.
• The quality of a clustering result depends on both the similarity measure used by the method and its implementation.

K-Medoid Clustering Algorithm

• Step 1: Initialization - Select K data points randomly as the initial medoids.
• Step 2: Assignment - For each data point, calculate the distance to all K medoids and assign the data point to the closest medoid.
• Step 3: Update - For each cluster, calculate the cost of replacing its medoid with each of its data points. If replacing the medoid with a data point results in a lower cost, update the medoid to that data point.
• Step 4: Repeat step 2 and 3 until the medoid no longer changes or the maximum number of iterations is reached.
• Step 5: Output - The final set of K medoids and the data points assigned to each cluster.

K-Medoid Clustering Numerical Example

• Let us consider a set of data with k=2 and the distance formula used is Dist =|𝑋2 − 𝑋1| + |𝑌2 − 𝑌1|.
• The data points are assigned to two clusters based on the distance calculation.
• The total cost involved in the initial assignment is calculated.
• The algorithm then iteratively updates the medoids to minimize the total cost.
• The final medoids and clusters are obtained.

K-Medoid Clustering in Python

• The data can be read from a list or a CSV file.
• The K-medoid clustering algorithm can be implemented using Python.

Questions

• Write a Python code to divide the data into clusters with k=2 using the K-Medoids clustering algorithm.
• Check the answer theoretically.