What Is Cluster Analysis Definition Types Methods and Solved Examples
What is Cluster Analysis?
Let us first know what is cluster analysis? Cluster Analysis is a technique that groups objects which are similar to groups known as clusters. The final effect of the cluster analysis is a group of clusters where each cluster is different from other clusters and the objects within each cluster are broadly identical to each other. For example, in the scatterplot given below, two clusters are shown, one cluster shows filled circles while the other cluster shows unfilled circles.
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The objective of the cluster analysis is to identify similar groups of objects where the similarity between each pair of objects means some overall measures over the whole range of characteristics. In this article, we will study cluster analysis, cluster analysis examples, types of cluster analysis, cluster CBSE etc.
Cluster CBSE
A cluster CBSE refers to a group of data points combined together because of certain similarities.
Types of Cluster Analysis.
Some of the different types of cluster analysis are:
1. Hierarchical Cluster Analysis
In hierarchical cluster analysis methods, a cluster is initially formed and then included in another cluster which is quite similar to the cluster which is formed to form one single cluster. This process is repeated until all subjects are found in one single cluster. This method is also known as the Agglomerative method. Agglomerative clustering also initiates with single objects and starts grouping them into clusters.
The divisive method is another type of Hierarchical cluster analysis method in which clustering initiates with the comprehensive data set and then starts grouping into partitions.
2. Centroid-based Clustering
In the centroid-based clustering, clusters are illustrated by a central entity, which may or may not be a component of the given data set. The K-Means method of clustering is used in centroid-based clustering where k are represented as the cluster centers and objects are allocated to the immediate cluster centers.
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3. Distribution -based Clustering
Distribution-based clustering model is strongly linked to statistics based on the models of distribution. Objects that are similar are grouped into a single cluster. This type of clustering analysis can represent some complex properties of objects such as correlation and dependence between elements.
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4. Density-based Clustering
In the density-based clustering analysis, clusters are identified by the areas of density that are higher than the remaining of the data set. Objects placed in scattered areas are usually required to separate clusters. The objects placed in these scattered areas are usually noisy and represented as broader points in the graph.
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Cluster Analysis Examples
Some cluster analysis examples are given below:
Markets- Cluster analysis helps marketers to find different groups in their customer bases and then use the information to introduce targeted marketing programs.
Land - It is used to identify areas of the same land used in an earth observation database.
Insurance - Cluster analysis helps to identify groups who hold a motor insurance policy with a high average claim cost.
Earthquake Studies - Cluster analysis helps to observe earthquakes.
City-Planning - Cluster analysis helps to recognize houses on the basis of their types, house value and geographical location.
Quiz Time
1. What are the Two Types of Hierarchical Clustering Analysis?
Top-down clustering ( Divisive)
Bottom-top clustering (Agglomerative)
Dendrogram
K-means
2. Which of the Following is Needed by K-means Clustering?
Defined distance metric
Number of clusters
Initial guess as to cluster centroids
All of the above answers are correct
3. Clustering Should be Initiated on Samples of 300 or More.
True
False
Fun Facts
Cluster analysis was first introduced in anthropology by Driver and Kroeber in 1932.
Cluster analysis was further introduced in psychology by Joseph Zubin in 1938 and Robert Tryon in 1939.
Cattell used cluster analysis in1943 for trait theory of classification in personality psychology.
FAQs on Cluster Analysis in Statistics and Data Science
1. What is cluster analysis in statistics?
Cluster analysis is a statistical technique used to group similar data points into clusters based on their characteristics. It is an unsupervised learning method, meaning there are no predefined labels. The goal is to maximize similarity within clusters and minimize similarity between clusters. It is widely used in data mining, machine learning, and pattern recognition.
2. What is the objective of cluster analysis?
The main objective of cluster analysis is to divide data into groups such that objects in the same cluster are more similar to each other than to those in other clusters. This is achieved by:
- Minimizing within-cluster variation
- Maximizing between-cluster variation
- Using a distance measure such as Euclidean distance
3. What are the main types of cluster analysis?
The main types of cluster analysis are hierarchical clustering and partitioning methods. Common approaches include:
- K-means clustering (partition-based)
- Hierarchical clustering (agglomerative or divisive)
- DBSCAN (density-based clustering)
- Mean shift clustering
4. How does K-means clustering work?
K-means clustering works by partitioning data into K clusters based on minimizing within-cluster variance. The steps are:
- Choose the number of clusters K
- Initialize K centroids randomly
- Assign each data point to the nearest centroid using Euclidean distance
- Recalculate centroids as the mean of assigned points
- Repeat until centroids stop changing
5. What is hierarchical clustering?
Hierarchical clustering is a method that builds clusters step-by-step in a tree-like structure called a dendrogram. It can be:
- Agglomerative (bottom-up, merging clusters)
- Divisive (top-down, splitting clusters)
6. What is the formula for Euclidean distance in cluster analysis?
The Euclidean distance between two points is given by d = √[(x₁ − x₂)² + (y₁ − y₂)²] in two dimensions. In n-dimensions, the formula is:
- d = √Σ (xᵢ − yᵢ)²
7. How do you choose the optimal number of clusters?
The optimal number of clusters is often chosen using the Elbow Method or Silhouette Score. Common techniques include:
- Elbow Method: Plot within-cluster sum of squares and look for a bend (elbow point).
- Silhouette Coefficient: Measures how well points fit within their cluster (ranges from −1 to 1).
8. What is the difference between supervised and unsupervised clustering?
Cluster analysis is an unsupervised learning method because it does not use labeled data. The difference is:
- Supervised learning: Uses known output labels (e.g., classification).
- Unsupervised learning: Finds hidden patterns without labels (e.g., clustering).
9. Can you give a simple example of cluster analysis?
A simple example of cluster analysis is grouping students based on marks in Math and Science. Suppose we have points (40, 45), (42, 43), (85, 90), and (88, 92). Using K-means with K = 2:
- Cluster 1: (40,45), (42,43)
- Cluster 2: (85,90), (88,92)
10. What are common applications of cluster analysis?
Cluster analysis is used to identify natural groupings in data across many fields. Common applications include:
- Market segmentation in business analytics
- Customer behavior analysis
- Image segmentation in computer vision
- Document clustering in text mining
- Biological classification in bioinformatics
