Cluster analysis

Cluster-2

SLINK-Gaussian-data

SLINK-density-data

KMeans-Gaussian-data

KMeans-density-data

Cluster analysis or clustering is a statistical analysis technique used to group a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of exploratory data analysis (EDA), and a common technique for statistical data analysis, used in many fields, including machine learning, pattern recognition, image analysis, information retrieval, bioinformatics, data compression, and computer graphics.

Overview

Cluster analysis itself is not one specific algorithm, but the general task to be solved. It can be achieved by various algorithms that differ significantly in their notion of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with small distances among the cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering can therefore be formulated as a multi-objective optimization problem. The appropriate clustering algorithm and parameter settings (including parameters such as the distance measure to use, a density threshold, or the number of expected clusters) depend on the individual data set and intended use of the results. Cluster analysis as such is not an automatic task, but an iterative process of knowledge discovery or interactive multi-objective optimization that involves trial and error. It is often necessary to modify data preprocessing and model parameters until the result achieves the desired properties.

Types of Clustering

Cluster analysis is broadly divided into two subgroups:

Hierarchical Clustering

Hierarchical clustering methods build a hierarchy of clusters where each node is a cluster consisting of the clusters of its daughter nodes. Strategies for hierarchical clustering generally fall into two types:

• Agglomerative: This is a "bottom-up" approach where each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy.
• Divisive: This is a "top-down" approach where all observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.

Partitional Clustering

Partitional clustering divides the data set into non-overlapping subsets (clusters) such that each data point is in exactly one subset. The most well-known method in this category is the K-means clustering algorithm.

Applications

Cluster analysis is used in many fields:

• In marketing, to identify distinct groups of customers based on their purchasing behavior.
• In biology, for classifying genes with similar expression patterns or grouping species in taxonomy.
• In library and information science for book classification or organizing articles for literature review.
• In cybersecurity, for identifying patterns of attacks that represent a new type of exploit.

Challenges

The main challenges in cluster analysis include:

• Determining the number of clusters. Many clustering algorithms require the number of clusters to be specified.
• Scalability to large data sets.
• Dealing with different types of attributes.
• Interpreting the clustering results.
• Dealing with noisy data and outliers.

See also

• Data mining
• Dimensionality reduction
• Principal component analysis

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