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**What is Clustering ?**

Clustering is the process of assembling a set of observations under different groups based on some similarity criteria. Clustering is very essential in Machine learning since it helps to categorize our data set and helps us to understand our data well without the help of any sort of labeling of data. These algorithms do this by identifying underlying patterns in the feature set. However, different algorithms take different approach towards clustering the data points. The most common and widely used clustering algorithm is K-Means Clustering. But discussing about the algorithms in detail, let me introduce you to the method by which we measure the similarity between the observations

**Similarity criteria**

The similarity between the observations in the data set is generally done by distance metrics. There are three well-known and widely used distance metrics, namely, Manhattan, Euclidean and Minkowski distance.

If (x1, x2, …, xn) and (y1, y2, …, yn) are two given data points/ observations :

Manhattan Distance :

Euclidean Distance :

Minkowski Distance with order of norm = p :

The smaller is the value of a distance metric, the higher is the similarity between the two observations.

**K-Means Clustering**

The idea behind the algorithm is to group all the points to one of the K clusters with K cluster centroids. The entire clustering algorithm is based on the concept of Expectation-Maximization.

Steps involved in the algorithm :

However, the most important downside of this algorithm is that the algorithm is prone to find local optimum based on the starting points of cluster centroids. An effective solution to this issue is to repeat the algorithm for multiple times and take the results of that particular run which has the minimum Sum Squared Error (SSE). Sum squared error is defined as the sum of the distances of all the observations from their respective cluster centers.

One other down-side of this algorithm is that it tends to form globular clusters and are not suitable for grouping clusters with non-globular structures. To address these issues, we have other clustering algorithms known as hierarchical clustering algorithms.

**Hierarchical Clustering**

These clustering algorithms are based on the concept of hierarchy. It tries to find a hierarchical pattern in the unlabeled data. There are two kinds of hierarchical clustering :

**What is Proximity Matrix ?**

A matrix that stores the distances between each points. The distance can be based on any distance metric. If we have n observations in our data set, proximity matrix is of size n x n, with diagonal elements equal to 0.

**Steps involved in Agglomerative Hierarchical clustering :**

**Types of Linkages :**

**What is a Dendrogram ?**

A Dendrogram is a pictorial representation of the hierarchical tree formed as a result of hierarchical clustering. It aptly represents the clusters formed at different stages of the algorithm. It also gives a rough idea about the pint at which we need to terminate algorithm in order to get the right number of clusters.

**Advantages of Hierarchical Clustering**

However the biggest disadvantage of this algorithm is that, the performance of this algorithm degrades with increasing number of observations in the data set, since it becomes computationally expensive to calculate the huge n x n proximity matrix.

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