Lecture 55:- Agglomerative intuition 1

Agglomerative Hierarchical Clustering is a hierarchical clustering algorithm that aims to build a hierarchy of clusters by iteratively merging or "agglomerating" individual data points or existing clusters. This process results in a tree-like structure called a dendrogram, which provides insights into the relationships and hierarchical structure of the data.

Here's the intuition behind the Agglomerative Hierarchical Clustering algorithm:

1. Individual Data Points as Initial Clusters: At the beginning, each data point is considered as a separate cluster. This forms the initial set of clusters, where each cluster contains only one data point.

2. Pairwise Distance Calculation: The algorithm calculates pairwise distances (or dissimilarities) between all data points or clusters. Various distance metrics such as Euclidean distance, Manhattan distance, or other similarity measures can be used, depending on the type of data.

3. Merge Closest: The two closest clusters (measured by distance) are merged into a single cluster. This reduces the total number of clusters by one.

4. Update Distance Matrix: The distance matrix is updated to reflect the distances between the newly formed cluster and the remaining clusters.

5. Repeat: Steps 3 and 4 are repeated until all data points or clusters are merged into a single cluster, creating the hierarchical structure.

6. Dendrogram Construction: As clusters are merged, a dendrogram is constructed, where the vertical height represents the dissimilarity between merged clusters. The longer the branch, the more dissimilar the clusters.

7. Cutting the Dendrogram: To obtain a specific number of clusters or to identify clusters at different granularity levels, you can cut the dendrogram at a certain height. This determines the final clusters.

Agglomerative Hierarchical Clustering has several advantages, including its ability to handle different shapes of clusters and its interpretability through the dendrogram. It allows you to explore the data's structure at various scales. However, it can be computationally expensive for large datasets due to the need to calculate and update pairwise distances.

Here's a simplified Python example of how you might use the scikit-learn library to perform Agglomerative Hierarchical Clustering:

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import numpy as np from sklearn.datasets import make_blobs from sklearn.cluster import AgglomerativeClustering import matplotlib.pyplot as plt from scipy.cluster.hierarchy import dendrogram, linkage # Generate synthetic data data, _ = make_blobs(n_samples=300, centers=4, random_state=42) # Create AgglomerativeClustering model n_clusters = 4 model = AgglomerativeClustering(n_clusters=n_clusters) # Fit the model to the data labels = model.fit_predict(data) # Plot the data colored by cluster assignments plt.scatter(data[:, 0], data[:, 1], c=labels, cmap='rainbow') plt.xlabel('Feature 1') plt.ylabel('Feature 2') plt.title('Agglomerative Clustering') plt.show() # Create and plot the dendrogram linked = linkage(data, method='ward') # Ward linkage minimizes the variance within clusters dendrogram(linked, orientation='top', distance_sort='descending', show_leaf_counts=True) plt.title('Dendrogram') plt.show()

In this example, we generate synthetic data, create an AgglomerativeClustering model, fit it to the data, and plot the clustered data. We also construct and plot a dendrogram using the scipy library to visualize the hierarchical structure. Keep in mind that real-world applications might involve preprocessing, distance metric selection, and other adjustments to optimize clustering results.