# Hierarchical Clustering in Machine Learning

# What is Hierarchical Clustering?

In machine learning, hierarchical clustering is a method of clustering data points into groups. It is a type of unsupervised learning, which means that it does not require any labels or target values. Hierarchical clustering can be used to cluster data points in any type of dataset, including numerical, categorical, and text data.

There are two main types of hierarchical clustering: Agglomerative and Divisive. Agglomerative clustering starts with each data point in its own group and then merges groups together until all data points are in one group. Divisive clustering starts with all data points in one group and then splits the group into smaller groups until each data point is in its own group.

There are many different algorithms for hierarchical clustering, but the most common are Ward’s method, complete-linkage clustering, and single-linkage clustering. Ward’s method minimizes the within-cluster variance, complete-linkage clustering minimizes the maximum distance between data points, and single-linkage clustering minimizes the minimum distance between data points.

Hierarchical clustering is a powerful tool for data analysis because it can be used to find patterns and relationships in data that would not be apparent using other methods. It is also relatively easy to implement and is not sensitive to outliers. However, hierarchical clustering can be slow for large datasets and can be affected by the order of the data points.

In statistics and data mining, hierarchical clustering is a method of cluster analysis which seeks to build a hierarchy of clusters. In a hierarchical clustering algorithm, data is divided into a set of clusters, where each cluster is distinct from each other cluster, and each data point is assigned to a single cluster. The algorithm then proceeds to create a hierarchy of clusters, where each cluster is a subset of the data points in the previous cluster.

The most common form of hierarchical clustering is agglomerative clustering, which starts with each data point as its own cluster, and then proceeds to merge clusters until there is only one cluster remaining. The algorithm then proceeds to create a hierarchy of clusters, where each cluster is a subset of the data points in the previous cluster.

There are a number of different ways to measure the similarity between data points, which in turn determines how the clusters are formed. The most common similarity measure is Euclidean distance, which is the straight-line distance between two data points. Other similarity measures include Manhattan distance, which is the sum of the absolute values of the difference between two data points; and Cosine similarity, which is the cosine of the angle between two data points.

Once the similarity measure has been chosen, the algorithm must then determine the order in which to merge the clusters. There are a number of different ways to do this, but the most common is to use the similarity between the clusters as the criterion. The algorithm then proceeds to create a hierarchy of clusters, where each cluster is a subset of the data points in the previous cluster.

The advantages of hierarchical clustering include the fact that it can be used with any similarity measure, and that it is relatively easy to understand and interpret the results. The disadvantages of hierarchical clustering include the fact that it can be slow, and that it can be sensitive to outliers.

# How Does Hierarchical Clustering Work?

In machine learning, hierarchical clustering is a method of cluster analysis which seeks to build a hierarchy of clusters. In a hierarchy, there is a designated parent cluster for every child cluster. The distinction between child and parent cluster is arbitrary and depends on the particular algorithm being used.

The main advantage of hierarchical clustering is that it can be used to obtain a relatively good approximation of the global optimum, especially when the number of clusters is small. The main disadvantage is that it is very sensitive to outliers.

There are two main types of hierarchical clustering: agglomerative and divisive. Agglomerative clustering starts with each data point as its own cluster and then successively merges pairs of clusters until all points are in one cluster. Divisive clustering starts with all points in one cluster and then successively splits clusters until each point is in its own cluster.

Most hierarchical clustering algorithms are agglomerative. The most popular agglomerative algorithms are single-linkage, complete-linkage, and average-linkage. Single-linkage clustering is the simplest and most commonly used agglomerative algorithm. It merges two clusters by finding the shortest distance between them. Complete-linkage clustering is more robust to outliers but is more computationally expensive. It merges two clusters by finding the longest distance between them. Average-linkage clustering is a compromise between single-linkage and complete-linkage and is the most commonly used agglomerative algorithm. It merges two clusters by finding the average distance between them.

There are many different ways to measure the distance between two clusters. The most common are the Euclidean distance, the squared Euclidean distance, the Manhattan distance, and the cosine similarity.

The choice of distance metric is important because it can have a big impact on the results of the clustering. In general, the Euclidean distance is the best choice if the clusters are well-separated and the cosine similarity is the best choice if the clusters are not well-separated.

The number of clusters is another important parameter. In general, it is best to start with a small number of clusters and then increase it if the results are not satisfactory.

Hierarchical clustering is a powerful tool for cluster analysis but it is important to understand the limitations of the algorithm and the parameters that need to be tuned in order to obtain good results.

# Types of Hierarchical Clustering

There are two types of hierarchical clustering in machine learning:

>> Agglomerative

>> Divisive.

Agglomerative clustering begins with each data point as its own cluster. The algorithm then repeatedly merges the closest clusters until only one cluster remains. This process is similar to building a tree from the bottom up.

Divisive clustering begins with all data points in one cluster. The algorithm then repeatedly splits the largest cluster until each data point is in its own cluster. This process is similar to building a tree from the top down.

Agglomerative clustering is more common because it is easier to implement and typically produces more accurate results. Divisive clustering can be more difficult to implement and may produce less accurate results.

# Advantages of Hierarchical Clustering

Hierarchical clustering is a powerful tool for data analysis and machine learning. It can be used to find groups of similar data points, or to identify outliers. Hierarchical clustering can be used on data of any type, including numerical, categorical, and text data.

There are many advantages to using hierarchical clustering. Hierarchical clustering can find groups of data points that are not linearly separable. This means that it can find groups of data points that are not easily separable by a line or a plane. Hierarchical clustering can also find groups of data points that are not easily separable by any other means.

Hierarchical clustering is also very efficient. It can be used on large datasets, and it can find groups of data points very quickly. Hierarchical clustering is also very flexible. It can be used with any number of data points, and it can be used with any number of clusters.

Overall, hierarchical clustering is a powerful tool for data analysis and machine learning. It has many advantages, and it is very flexible. It can be used on large datasets, and it can find groups of data points very quickly. However, it can be sensitive to outliers and the order of the data.

-Hierarchical clustering can be used to find patterns in data that are not easily found by other methods.

-Hierarchical clustering can be used to group data that is not linearly separable.

-Hierarchical clustering can be used to find clusters of different sizes and shapes.

-Hierarchical clustering is a fast and efficient method for clustering large datasets.

# Disadvantages of Hierarchical Clustering

There are a few disadvantages of hierarchical clustering:

Hierarchical clustering is a type of unsupervised learning algorithm that is used to cluster data points into groups. The main advantage of hierarchical clustering is that it can be used to find clusters of any shape, since it does not assume that the data points are spherical. However, there are some disadvantages to using hierarchical clustering:

1. Hierarchical clustering can be slow for large datasets.

2. It can be difficult to interpret the results of hierarchical clustering, since it produces a dendrogram that can be hard to read.

3. Hierarchical clustering can be biased towards finding clusters of similar size.

4. If the data contains outliers, they can often dominate the results of hierarchical clustering.

5. It can be difficult to determine the appropriate number of clusters.

6. It can be computationally expensive.

7. It can be sensitive to outliers.

# Applications of Hierarchical Clustering

1. Grouping customers by buying behavior

2. Organizing computer files into folders

3. Dividing a large city into neighborhoods

4. Classifying documents by topic

5. Grouping genes with similar function

6. Identifying clusters of galaxies

7. Segmenting an image into regions

8. Detecting unusual patterns in financial data

9. Grouping employees by job function

10. Partitioning a social network into communities

11. Identifying trends in stock market data

12. Grouping songs by style

13. Clustering images by similarity

14. Classifying websites by content

15. Grouping news articles by topic

16. Grouping blog posts by topic

17. Segmenting a market by customer needs

18. Grouping products by sales volume

19. Dividing a city into boroughs

20. Identifying clusters of crime

21. Identifying customer segments for targeted marketing

22. Grouping genes with similar expression profiles

23. discovering structure in high-dimensional data

24. Image segmentation

26. Object recognition in computer vision

26. Identifying similar documents for information retrieval

27.Discovering structure in social networks

28. detecting crime hotspots in a city

29. Discovering patterns in stock market data

30. Forecasting demand for a product

# Hierarchical Clustering Algorithms

There are two types of clustering algorithms:

1. Hierarchical clustering

2. Partitional clustering

In hierarchical clustering, we create clusters that have a predetermined ordering. In partitional clustering, we define a set of clusters with no predefined ordering.

There are two types of hierarchical clustering algorithms:

1. Agglomerative

2. Divisive

In agglomerative algorithms, we start with each data point as a single cluster and then merge them together. In divisive algorithms, we start with all data points in one cluster and then split them up.

There are two types of agglomerative algorithms:

1. Bottom-up

2. Top-down

In bottom-up algorithms, we start with each data point as a single cluster and then merge them together. In top-down algorithms, we start with all data points in one cluster and then split them up.

There are two types of divisive algorithms:

1. Bottom-up

2. Top-down

In bottom-up algorithms, we start with each data point as a single cluster and then merge them together. In top-down algorithms, we start with all data points in one cluster and then split them up.

# The algorithm for Agglomerative Hierarchical Clustering is

1. Calculate the similarity of one cluster with all the other clusters (calculate proximity matrix).

2. Consider every data point as an individual cluster.

3. Merge the clusters which are highly similar or close to each other.

4. Recalculate the proximity matrix for each cluster.

5. Repeat Steps 3 and 4 until only a single cluster remains.

8. Agglomerative Hierarchical Clustering

It is a bottom-up approach. In this approach, we start with each data point as a separate cluster. At each iteration, we find the closest pair of clusters and merge them into a new cluster. We repeat this process until there is only one cluster left in the dataset.

# Divisive Hierarchical Clustering:

It is a top-down approach. In this approach, we start with the whole dataset as one cluster. At each iteration, we find the largest cluster and split it into two new clusters. We repeat this process until each data point is a separate cluster.

# Dendrograms:

Dendrograms are tree-like diagrams that show how clusters are related to each other.

# Types of Linkage Methods:

There are three types of linkage methods that we use in hierarchical clustering:

1. Single Linkage Method:

In this method, we define the similarity between two clusters by finding the similarity between the two closest points in each cluster.

2. Complete Linkage Method:

In this method, we define the similarity between two clusters by finding the similarity between the two furthest points in each cluster.

3. Average Linkage Method:

In this method, we define the similarity between two clusters by finding the average similarity between all points in each cluster.

# Types of clustering:

There are different types of clustering which depend on the type of data:

1. Exclusive Clustering:

In exclusive clustering, a data point can belong to only one cluster.

2. Overlapping Clustering:

In overlapping clustering, a data point can belong to more than one cluster.

3. Hierarchical Clustering:

In hierarchical clustering, we create a hierarchy of clusters.

4. Fuzzy Clustering:

In fuzzy clustering, a data point can belong to more than one cluster with a certain degree of membership.

**K-Means Clustering:**

K-means clustering is a type of exclusive clustering where each data point belongs to only one cluster.

In k-means clustering, we first randomly initialize k cluster centroids. We then assign each data point to the cluster whose centroid is closest to it. We then find the new centroid of each cluster. We repeat this process until the centroids do not change.

We can also use k-means clustering for data that is not linearly separable.

K-means clustering is a heuristic algorithm and it is not guaranteed to find the global optimum.

**Types of K-Means Clustering:**

There are two types of k-means clustering:

*1. Hard K-Means Clustering:*

In hard k-means clustering, a data point can only belong to one cluster.

*2. Soft K-Means Clustering:*

In soft k-means clustering, a data point can belong to more than one cluster.

**Advantages of K-Means Clustering:**

1. K-means clustering is simple to implement.

2. K-means clustering is easy to interpret.

3. K-means clustering is fast and efficient.

4. K-means clustering can be used for data that is not linearly separable.

**Disadvantages of K-Means Clustering:**

1. K-means clustering is a heuristic algorithm and it is not guaranteed to find the global optimum.

2. K-means clustering is sensitive to outliers.

3. K-means clustering is sensitive to the initialization of cluster centroids.

4. K-means clustering might not be able to find clusters with non-convex shapes.

**Fuzzy C-Means Clustering:**

Fuzzy c-means clustering is a type of soft k-means clustering where each data point can belong to more than one cluster.

In fuzzy c-means clustering, we first randomly initialize cluster centroids. We then assign each data point to the clusters whose centroids are closest to it. We then find the new centroid of each cluster. We repeat this process until the centroids do not change.

**Advantages of Fuzzy C-Means Clustering:**

1. Fuzzy c-means clustering can find clusters with non-convex shapes.

2. Fuzzy c-means clustering is not sensitive to outliers.

**Disadvantages of Fuzzy C-Means Clustering:**

1. Fuzzy c-means clustering is a heuristic algorithm and it is not guaranteed to find the global optimum.

2. Fuzzy c-means clustering is sensitive to the initialization of cluster centroids.

3. Fuzzy c-means clustering is slower than k-means clustering.

**DBSCAN Clustering:**

DBSCAN clustering is a type of density-based clustering where each data point can belong to more than one cluster.

In DBSCAN clustering, we first randomly select a data point. We then find all data points that are within a certain radius of the selected data point. If there are at least a certain number of data points within the radius, we label the selected data point as a core point. We then label all data points within the radius as members of the same cluster. If a data point is not a core point, we label it as an outlier. We then repeat this process for all data points.

**Advantages of DBSCAN Clustering:**

1. DBSCAN clustering can find clusters with non-convex shapes.

2. DBSCAN clustering is not sensitive to outliers.

**Disadvantages of DBSCAN Clustering:**

1. DBSCAN clustering is sensitive to the parameter values.

2. DBSCAN clustering might not be able to find all clusters in a dataset.

3. DBSCAN clustering is not guaranteed to find the global optimum.

**Expectation Maximization:**

Expectation maximization is a type of density-based clustering where each data point can belong to more than one cluster.

In expectation maximization, we first randomly initialize the parameters of the clusters. We then assign each data point to the cluster that it is most likely to belong to. We then find the new parameters of the clusters. We repeat this process until the parameters do not change.

**Advantages of Expectation Maximization:**

1. Expectation maximization is not sensitive to outliers.

2. Expectation maximization can find clusters with non-convex shapes.

**Disadvantages of Expectation Maximization:**

1. Expectation maximization is a heuristic algorithm and it is not guaranteed to find the global optimum.

2. Expectation maximization is sensitive to the initialization of the cluster parameters.

3. Expectation maximization might not be able to find all clusters in a dataset.

# Conclusion

Hierarchical clustering is a type of unsupervised learning that does not require labels or target values . Ward’s method minimizes the within-cluster variance . There are two main types of hierarchical clustering: Agglomerative and Divisive . There are two types of hierarchical clustering in machine learning: Agglomerative and Divisive . The algorithm begins with each data point as its own cluster and merges the closest clusters until only one cluster remains . This process is similar to building a tree from the bottom up . Hierarchical clustering can be biased towards finding clusters of similar size . Clusters of galaxies can be used to identify clusters of galaxies, galaxies and social networks . There are two types of clustering algorithms: Agglomerative algorithms and divisive algorithms . Exclusive clustering is a type of clustering where each data point belongs to only one cluster . Overlapping clustering, a data point can belong to more than one cluster with a certain degree of membership . DBSCAN clustering can find clusters with non-convex shapes . There are two types of k-means clustering: hard and soft . Expectation Maximization involves finding all data points within a certain radius of the selected data point . Advantages include finding clusters with non-convex shapes . It is a heuristic algorithm and it is not guaranteed to find the global optimum .