# Clustering

*See also: Machine learning terms*

## Introduction

**Clustering** is a technique in the field of machine learning and data mining that involves the grouping of similar data points or objects into clusters, based on some form of similarity or distance metric. The goal of clustering is to identify underlying patterns or structures in data, enabling efficient data representation, classification, and interpretation. Clustering is an unsupervised learning method, meaning that it does not rely on pre-labeled data for training but rather discovers inherent relationships within the data itself.

## Types of Clustering Algorithms

There are several types of clustering algorithms, each with their own strengths and weaknesses. The choice of an appropriate algorithm depends on the specific problem being addressed, the data properties, and the desired outcome. Some of the most common clustering algorithms are:

### Partition-based Clustering

Partition-based clustering algorithms divide the dataset into non-overlapping subsets or clusters, where each data point belongs to exactly one cluster. The most widely known partition-based clustering algorithm is the *k-means* algorithm, which iteratively refines cluster centroids to minimize the sum of squared distances between data points and their respective cluster centroids.

### Hierarchical Clustering

Hierarchical clustering algorithms build a tree-like structure, known as a dendrogram, to represent the nested groupings of data points. These algorithms can be either agglomerative (bottom-up) or divisive (top-down). Agglomerative hierarchical clustering starts with each data point as its own cluster and iteratively merges the closest pairs of clusters until only one cluster remains. Divisive hierarchical clustering begins with all data points in a single cluster and recursively splits the clusters until each data point forms its own cluster.

### Density-based Clustering

Density-based clustering algorithms identify clusters by grouping data points that are closely packed together based on a density metric. These algorithms can find arbitrarily shaped clusters and are robust to noise in the data. The most well-known density-based clustering algorithm is the *DBSCAN* (Density-Based Spatial Clustering of Applications with Noise) algorithm, which groups together data points that are closely packed in a high-density region while marking low-density regions as noise.

### Grid-based Clustering

Grid-based clustering algorithms partition the data space into a finite number of grid cells and then perform clustering on the grid structure. These algorithms are typically faster than other clustering methods since they work with the grid cells rather than individual data points. An example of a grid-based clustering algorithm is the *STING* (STatistical INformation Grid) algorithm.

## Feature Selection and Dimensionality Reduction

In many practical applications, data points are represented by high-dimensional feature vectors, which can make clustering more challenging due to the curse of dimensionality. To address this issue, feature selection or dimensionality reduction techniques, such as Principal Component Analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE), can be applied to the data prior to clustering to improve performance and reduce computational cost.

## Explain Like I'm 5 (ELI5)

Imagine you have a big box of differently shaped and colored toys. Clustering in machine learning is like sorting these toys into groups based on their similarities, like putting all the red cars together or all the round balls together. This helps us understand and organize the toys better. In the same way, clustering helps computers make sense of lots of information by grouping similar pieces of data together.