Agglomerative Clustering Python Code From Scratch | Techniculus

Agglomerative Clustering Python Code From Scratch

Agglomerative clustering is a hierarchical clustering method that starts with each data point as its own cluster and then merges the closest clusters iteratively until only one cluster remains. The result of agglomerative clustering is a dendrogram, which is a tree-like structure that shows the sequence of mergers.

The algorithm for agglomerative clustering works as follows:

1) Begin by assigning each data point to its own cluster.

 
2) Compute the distance (or similarity) between each pair of clusters. There are several ways to compute the distance between clusters, such as single linkage, complete linkage, and average linkage.

 
3) Merge the two closest clusters into a single cluster, updating the distance matrix to reflect the new distances between the merged cluster and the remaining clusters.

 
4) Repeat step 3 until only one cluster remains.

The choice of distance metric and linkage criteria can greatly affect the resulting clusters. For example, single linkage tends to produce long, skinny clusters, while complete linkage tends to produce compact, spherical clusters.

Agglomerative clustering can be used for a variety of applications, such as image segmentation, document clustering, and market segmentation. One advantage of agglomerative clustering is that it can handle non-spherical and non-convex clusters, which is a limitation of some other clustering algorithms. However, agglomerative clustering can be computationally expensive for large datasets.

Agglomerative hierarchical clustering python code:

from sklearn.cluster import AgglomerativeClustering from sklearn.datasets import make_blobs import matplotlib.pyplot as plt # Generate some random data for clustering X, y_true = make_blobs(n_samples=300, centers=4, cluster_std=0.60, random_state=0) # Create an instance of AgglomerativeClustering agg = AgglomerativeClustering(n_clusters=4) # Fit the model and predict the clusters y_pred = agg.fit_predict(X) # Plot the data points with their corresponding cluster labels plt.scatter(X[:,0], X[:,1], c=y_pred) plt.title('Agglomerative Clustering') plt.xlabel('Feature 1') plt.ylabel('Feature 2') plt.show()

Let's go through this code step by step:

1) We first import the necessary libraries - scikit-learn for the agglomerative clustering algorithm and matplotlib for plotting the data.

 
2) Next, we generate some random data using the make_blobs function from scikit-learn. This function generates isotropic Gaussian blobs for clustering.

 
3) We create an instance of the AgglomerativeClustering class with the n_clusters parameter set to 4. This specifies the number of clusters we want the algorithm to find.

 
4) We fit the model to the data using the fit_predict method, which both fits the clustering model and returns the predicted cluster labels for each data point.

 
5) Finally, we plot the data points with their corresponding cluster labels using the scatter function from matplotlib.

Note that this is a simple example of agglomerative clustering, and there are many other parameters and options that can be tuned for more complex scenarios. For example, we can specify different linkage criteria (single, complete, or average), distance metrics (Euclidean, Manhattan, etc.), and more. Also, in some cases it may be necessary to preprocess the data before clustering, such as scaling or normalizing the features.

 

Difference between agglomerative and divisive clustering in tabular form:

Agglomerative and divisive clustering are two common hierarchical clustering algorithms. Here are the differences between them in tabular form:

Criteria	Agglomerative Clustering	Divisive Clustering
Starting point	Each data point is considered as a separate cluster.	All data points are considered to be in the same cluster.
Iterative process	Merges the two closest clusters at each iteration, until only one cluster remains.	Divides a cluster into two smaller clusters at each iteration, until each data point is its own cluster.
Complexity	Agglomerative clustering is generally less computationally expensive than divisive clustering, especially for large datasets.	Divisive clustering can be computationally expensive for large datasets, especially if the hierarchy is deep.
Resulting structure	Agglomerative clustering produces a dendrogram that shows the sequence of mergers.	Divisive clustering produces a tree-like structure that shows the sequence of divisions.
Number of clusters	Agglomerative clustering requires the user to specify the number of clusters in advance.	Divisive clustering does not require the user to specify the number of clusters in advance, but the hierarchy can be cut at any level to obtain a desired number of clusters.
Sensitivity to noise	Agglomerative clustering is more sensitive to noise and outliers, as they can affect the formation of clusters at earlier stages.	Divisive clustering is less sensitive to noise and outliers, as they can be split off into their own clusters.

In summary, agglomerative clustering starts with each data point as its own cluster and merges the closest clusters at each iteration, while divisive clustering starts with all data points in the same cluster and divides it into smaller clusters at each iteration. Agglomerative clustering is generally less computationally expensive and produces a dendrogram, but requires the number of clusters to be specified in advance and is more sensitive to noise. Divisive clustering can be computationally expensive, does not require the number of clusters to be specified in advance, and is less sensitive to noise.

Implementations of agglomerative clustering:

Agglomerative clustering is a popular hierarchical clustering algorithm that is used for a variety of applications in data analysis, pattern recognition, and machine learning. Here are some of the main uses of agglomerative clustering:

1) Market Segmentation: Agglomerative clustering can be used to segment customers into distinct groups based on their demographic or behavioral data. This can help companies tailor their marketing strategies to each group and improve customer engagement.

2) Image Segmentation: Agglomerative clustering can be used to segment images into regions with similar colors or textures. This is useful for tasks such as object recognition, image retrieval, and video surveillance.

3) Text Clustering: Agglomerative clustering can be used to group similar documents or text snippets based on their content. This can be useful for tasks such as topic modeling, sentiment analysis, and text classification.

4) Anomaly Detection: Agglomerative clustering can be used to detect anomalies or outliers in datasets. This is useful for detecting fraud, anomalies in sensor data, and other types of unusual patterns.

5) Neuroscience: Agglomerative clustering is used in neuroscience to identify distinct groups of neurons that exhibit similar firing patterns. This can help researchers understand the functional organization of the brain and how different regions of the brain are connected.

Overall, agglomerative clustering is a versatile algorithm that can be applied to many different types of data and problems. Its ability to handle non-spherical and non-convex clusters makes it a useful tool for clustering complex datasets, and its hierarchical structure provides a useful representation of the relationships between data points.

History of agglomerative clustering:

Here is a brief history of its development:

1) In 1963, S. S. Wilk and S. S. T. Gnanadesikan introduced the concept of hierarchical clustering in their paper "Probability plotting methods for the analysis of data". They used a divisive approach, where the dataset is initially treated as one cluster and is recursively divided into smaller clusters.

2) In 1967, J. L. Ward proposed a hierarchical clustering algorithm that follows an agglomerative approach. His method involves starting with each data point as a separate cluster and iteratively merging the two closest clusters until only one cluster remains.

3) In the following years, other agglomerative clustering algorithms were proposed, including the single linkage method by R. R. Sokal and C. D. Michener in 1958, the complete linkage method by P. J. Rousseeuw in 1987, and the average linkage method by A. J. S. McQuitty in 1966.

4) Since then, agglomerative clustering has become a widely-used clustering technique due to its simplicity, flexibility, and ability to handle non-spherical and non-convex clusters.

5) In recent years, there have been several extensions to agglomerative clustering, such as the use of hierarchical clustering in machine learning and deep learning algorithms. For example, hierarchical clustering is often used in convolutional neural networks (CNNs) for image segmentation and object detection.

 

Disadvantages of agglomerative clustering:

Agglomerative clustering is a popular clustering algorithm that has many advantages, such as its ability to handle non-spherical and non-convex clusters and its hierarchical structure. However, there are also some disadvantages to using agglomerative clustering:

1) Scalability: Agglomerative clustering can be computationally expensive, especially for large datasets. The time complexity of the algorithm is O(N^3) in the worst case, where N is the number of data points.

2) Sensitivity to noise and outliers: Agglomerative clustering can be sensitive to noise and outliers, as they can affect the formation of clusters at earlier stages. This can lead to the creation of suboptimal clusters or the merging of dissimilar clusters.

3) Sensitivity to initialization: The choice of linkage method and distance metric can have a significant impact on the resulting clusters. Different choices of parameters may result in very different clusters.

4) Need for prior knowledge of the number of clusters: Agglomerative clustering requires the user to specify the number of clusters in advance. This can be difficult if the number of clusters is unknown or if the data is complex and contains overlapping clusters.

5) Inability to handle large datasets with varying densities: Agglomerative clustering assumes that all clusters have similar densities. If the dataset contains clusters with varying densities, the algorithm may produce suboptimal results.

In summary, agglomerative clustering has several limitations that should be considered when choosing a clustering algorithm. While it can be effective for certain types of data, it may not be suitable for all datasets, especially those that are large or contain noisy or overlapping clusters.