An Overview on Clustering Methods (1205.1117v1)

Abstract: Clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics. Clustering is the process of grouping similar objects into different groups, or more precisely, the partitioning of a data set into subsets, so that the data in each subset according to some defined distance measure. This paper covers about clustering algorithms, benefits and its applications. Paper concludes by discussing some limitations.

• The paper comprehensively surveys clustering algorithms, categorizing them into hierarchical and partitional methods while detailing their mathematical foundations and diverse applications.
• It compares techniques such as k-means, DBSCAN, and Gaussian mixtures, highlighting the trade-offs between computational efficiency and sensitivity to outliers.
• It outlines the importance of selecting appropriate distance measures and cluster-count criteria, offering practical guidance for applications in machine learning and data mining.

An Overview on Clustering Methods

The paper "An Overview on Clustering Methods" by T. Soni Madhulatha provides a comprehensive survey of clustering algorithms, their applications, benefits, and limitations. This manuscript serves both as an educational resource and an insightful analysis for researchers and practitioners in fields such as machine learning, data mining, and pattern recognition.

Clustering is identified as a fundamental unsupervised learning problem that involves finding a structure in a collection of unlabeled data by grouping similar objects together while ensuring the objects in different groups are dissimilar. The author systematically categorizes clustering algorithms into hierarchical and partitional methods, expanding on the nuances and mathematical foundations of each type.

Types of Clustering Algorithms

Hierarchical Clustering:

Hierarchical clustering is further subdivided into agglomerative (bottom-up) and divisive (top-down) methods. Agglomerative algorithms begin with each data point as a single cluster and merge them iteratively, while divisive algorithms start with the whole dataset and partition it into smaller clusters. The choice of distance measure, such as Manhattan or Euclidean distance, is crucial. Various strategies like complete linkage, single linkage, and average linkage are used to define inter-cluster distances. A key limitation of hierarchical clustering is its rigidity; once a merge or split is performed, it cannot be undone.

Partitional Clustering:

Partitional or flat clustering algorithms, such as k-means and k-medoids, partition the data into a predefined number of clusters. The k-means algorithm minimizes intra-cluster variance but is sensitive to outliers. K-medoids, on the other hand, is more robust to noise. Both methods have efficient time complexities and are order-independent given a fixed initial seed set.

Density-Based Clustering:

Density-based algorithms like DBSCAN and SSN are adept at identifying clusters of arbitrary shapes based on point density. DBSCAN defines clusters as high-density regions separated by low-density regions, efficiently managing noise and varying cluster sizes. The SSN algorithm extends DBSCAN by incorporating the shared nearest neighbour concept, enhancing its ability to handle clusters of varying densities.

Grid-Based Clustering:

Grid-based clustering divides the data space into a finite number of cells, as seen in approaches like STING and CLIQUE. This method is computationally efficient due to its spatial data structure, though it is limited by the grid resolution and cannot easily detect diagonal cluster boundaries.

Model-Based Clustering:

Model-based methods assume that the data is generated by a mixture of underlying probability distributions, typically Gaussian. These methods optimize the fit between the data and a probabilistic model, offering a sophisticated approach to clustering but at the cost of increased computational complexity.

Determining the Number of Clusters

A crucial aspect of clustering is determining the appropriate number of clusters. Methods such as the Elbow Criterion, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Deviance Information Criterion (DIC) provide heuristics to identify the optimal number of clusters. These criteria measure the balance between model complexity and goodness of fit.

Comparison of Clustering Algorithms

Clustering algorithms are compared on several factors including dataset size, number of clusters, dataset type, and the software used for implementation. Hierarchical and partitional methods have distinct advantages and limitations based on these criteria. The paper emphasizes the importance of contextual factors in selecting an appropriate clustering technique:

• Hierarchical algorithms are more suitable for smaller datasets and when the number of clusters is large.
• Partitional algorithms excel in handling large datasets and moderate to small numbers of clusters.
• Grid-based methods offer computational efficiency but are restricted by grid resolution.
• Density-based clustering methods are optimal for discovering clusters of varying shapes and densities but can struggle with differing density clusters.
• Model-based clustering provides probabilistic interpretability and is robust for complex cluster distributions.

Applications and Practical Implications

Clustering has a wide array of applications across different domains including but not limited to:

• Marketing: Grouping customers based on purchasing behavior.
• Finance: Risk management and fraud detection.
• Biology: Taxonomy and classification of species.
• Urban Planning: Identifying housing patterns.
• Web Analysis: Classifying web documents and analyzing user access patterns.

Conclusion

Clustering serves as a crucial analytical tool in extracting meaningful patterns from unlabeled data. The choice of clustering method heavily depends on data characteristics and the specific requirements of the analysis. This paper underscores the importance of understanding the underlying mechanics and appropriate contexts for each clustering algorithm.

The exploratory nature of clustering underscores the necessity for empirical validation and careful consideration of the assumptions inherent in each method. Future research may further optimize these algorithms, explore new distance measures, and better handle large-scale, high-dimensional data.