Understanding Hierarchical Clustering and its Role in K-means Clustering

As machine learning practitioners, we often find ourselves working with datasets that contain natural groupings or clusters. One popular method for identifying these clusters is hierarchical clustering, which has gained significant attention in recent years due to its flexibility and interpretability. In this article, we will explore how to extract cluster centers from a hierarchical clustering output (agnes) and use them as input to the k-means clustering algorithm.

Introduction to Agnes and Hierarchical Clustering

Agnes is a package in R that performs hierarchical clustering using the Ward’s minimum variance method. It is an extension of the popular cluster package, which provides an interface to various clustering algorithms. When we run agnes on a dataset, it generates a dendrogram, which represents the hierarchical relationships between observations based on their similarity.

The output of agnes includes several components:

• ag.a: This contains the distance matrix used in the clustering process.
• clust: A list containing information about the clusters, including the cluster indices and membership assignments for each observation.
• cutree: The final cutree object, which provides a binary classification of observations into different clusters.

Extracting Cluster Centers from Agnes

Given that we have obtained our cluster assignments using agnes, the next step is to calculate the mean values within each cluster. This can be achieved by aggregating the coordinates (x and y) of all observations assigned to each cluster.

We will use the aggregate function in R to perform this calculation. The aggregate function allows us to specify a formula that defines the aggregation process. In our case, we want to calculate the mean values for both x and y coordinates within each cluster.

Here is an example:

library(cluster)
data(animals)

# Run agnes on the agriculture dataset with k = 2
ag.a <- agnes(agriculture, method = "ward")
ag.2 <- cutree(ag.a, k = 2)

# Calculate the mean values for all observations in each cluster
cent <- aggregate(cbind(x,y) ~ ag.2, agriculture, mean)

In this code:

• agriculture is our dataset.
• ag.2 contains the binary classification of our observations into different clusters.
• We use aggregate to calculate the mean values for both x and y coordinates within each cluster (cent <- aggregate(cbind(x,y) ~ ag.2, agriculture, mean)).
• The result is stored in cent, which contains a matrix where each row corresponds to an observation (with its class label as index), and each column represents either the x or y coordinate.

Passing Cluster Centers to K-means

The next step involves passing these cluster centers to the kmeans function for reapplication. We will use this to demonstrate how to extract clusters from a hierarchical clustering output using agnes.

To do so, we need to specify an initial set of points (cent) to start the iterative process of finding the optimal centroids.

Here is an example:

# Pass the cluster centers as initial centroids for k-means
kmeans(agriculture, cent[,-1])

In this code:

• agriculture remains our original dataset.
• We pass only the cluster centers (cent[,-1]) to the k-means algorithm using cent[,-1]. The -1 denotes all but the first column (i.e., the class labels).
• The result is stored in the output of kmeans.

Using Clustering for Data Preprocessing and K-means

Hierarchical clustering has found its place in various applications, including data preprocessing. When applying clustering to preprocess a dataset:

1. Handling Noisy Data: By grouping similar values together, hierarchical clustering can help filter out noisy or outlier data points.
2. Dimensionality Reduction: Clustering can be used as an intermediate step for dimensionality reduction techniques such as PCA (Principal Component Analysis) or t-SNE (t-distributed Stochastic Neighbor Embedding).
3. Data Visualization: By grouping observations based on their similarity, hierarchical clustering provides a meaningful way to visualize high-dimensional data.
4. Robustness: Clustering algorithms can be robust against missing values, outliers, and other types of noisy data.

Applications of Hierarchical Clustering

Hierarchical clustering has been used in various applications across different domains:

1. Customer Segmentation: In marketing, hierarchical clustering can help segment customers based on their buying behavior, demographics, or loyalty.
2. Gene Expression Analysis: Researchers use hierarchical clustering to identify gene expression patterns and groups of genes that are co-regulated.
3. Image Processing: Clustering is used in image processing for object recognition, denoising, and feature extraction.

Example Use Case: Identifying Patterns in Iris Dataset

Suppose we want to analyze the iris dataset to identify its natural clusters. We can use hierarchical clustering to group the sepal and petal measurements based on their similarity.

# Load the iris dataset
data(iris)

# Convert the factor variable 'species' into a numeric vector for hierarchical clustering
iris$species <- as.numeric(factor(iris$species))

# Perform hierarchical clustering using ward's linkage method
hclust_data <- hclust(dist(iris[, 1:4]), method = "ward")

# Visualize the dendrogram
plot(hclust_data, main = "Iris Dendrogram", xlab = "Sample Index", ylab = "Distance")

Conclusion

In this article, we explored how to extract cluster centers from a hierarchical clustering output (agnes) and use them as input to the k-means clustering algorithm. This is an example of using machine learning techniques for data preprocessing.

Hierarchical clustering has found its place in various applications across different domains, including customer segmentation, gene expression analysis, image processing, and more. By applying clustering algorithms like agnes, we can gain a deeper understanding of our data and make more informed decisions.

Last modified on 2024-04-20