# Articles - Cluster Validation Essentials

The cluster validation consists of measuring the goodness of clustering results. Before applying any clustering algorithm to a data set, the first thing to do is to assess the clustering tendency. That is, whether applying clustering is suitable for the data. If yes, then how many clusters are there. Next, you can perform hierarchical clustering or partitioning clustering (with a pre-specified number of clusters). Finally, you can use a number of measures, described in this part, to evaluate the goodness of the clustering results.

## Contents

Assessing Clustering Tendency

• Required R packages
• Data preparation
• Visual inspection of the data
• Why assessing clustering tendency?
• Methods for assessing clustering tendency
• Statistical methods
• Visual methods

Determining The Optimal Number Of Clusters

• Elbow method
• Average silhouette method
• Gap statistic method
• Computing the number of clusters using R
• Required R packages
• Data preparation
• fviz_nbclust() function: Elbow, Silhouhette and Gap statistic methods
• NbClust() function: 30 indices for choosing the best number of clusters

Cluster Validation Statistics

• Internal measures for cluster validation
• Silhouette coefficient
• Dunn index
• External measures for clustering validation
• Computing cluster validation statistics in R
• Required R packages
• Data preparation
• Clustering analysis
• Cluster validation
• External clustering validation

Choosing the Best Clustering Algorithms

• Measures for comparing clustering algorithms
• Compare clustering algorithms in R

Computing P-value for Hierarchical Clustering

• Description of pvclust() function
• Usage of pvclust() function

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## Computing P-value for Hierarchical Clustering

Clusters can be found in a data set by chance due to clustering noise or sampling error. This article describes the R package pvclust (Suzuki and Shimodaira 2015) which uses bootstrap resampling... [Read more]

## Choosing the Best Clustering Algorithms

Choosing the best clustering method for a given data can be a hard task for the analyst. This article describes the R package clValid (Brock et al. 2008), which can be used to compare... [Read more]

## Cluster Validation Statistics: Must Know Methods

The term cluster validation is used to design the procedure of evaluating the goodness of clustering algorithm results. This is important to avoid finding patterns in a random data, as well as,... [Read more]

## Determining The Optimal Number Of Clusters: 3 Must Know Methods

Determining the optimal number of clusters in a data set is a fundamental issue in partitioning clustering, such as k-means clustering (Chapter @ref(kmeans-clustering)), which requires the user... [Read more]

## Assessing Clustering Tendency: Essentials

Before applying any clustering method on your data, it’s important to evaluate whether the data sets contains meaningful clusters (i.e.: non-random structures) or not. If yes, then how many... [Read more]