`clValid`

reports validation measures for clustering
results. The function returns an object of class
`"'>clValid"`

, which
contains the clustering results in addition to the validation
measures. The validation measures fall into three general categories:
"internal", "stability", and "biological".

```
clValid(obj, nClust, clMethods = "hierarchical", validation =
"stability", maxitems = 600, metric = "euclidean", method = "average",
neighbSize = 10, annotation = NULL, GOcategory = "all",
goTermFreq=0.05, dropEvidence=NULL, verbose=FALSE, ...)
```

obj

Either a numeric matrix, a data frame, or an `ExpressionSet`

object. Data frames must contain all numeric columns. In all
cases, the rows are the items to be clustered (e.g., genes),
and the columns are the samples.

nClust

A numeric vector giving the numbers of clusters to be evaluated. e.g., 4:6 would evaluate the number of clusters ranging from 4 to 6.

clMethods

A character vector giving the clustering methods. Available options are "hierarchical", "kmeans", "diana", "fanny", "som", "model", "sota", "pam", "clara", and "agnes", with multiple choices allowed.

validation

A character vector giving the type of validation measures to use. Available options are "internal", "stability", and "biological", with multiple choices allowed.

maxitems

The maximum number of items (rows in matrix) which can be clustered.

metric

The metric used to determine the distance matrix. Possible choices are "euclidean", "correlation", and "manhattan".

method

For hierarchical clustering (`hclust`

and `agnes`

), the
agglomeration method used. Available choices are "ward", "single",
"complete", and "average".

neighbSize

For internal validation, an integer giving the neighborhood size used for the connectivity measure.

annotation

For biological validation, either a character string naming the Bioconductor annotation package for mapping genes to GO categories, or a list with the names of the functional classes and the observations belonging to each class.

GOcategory

For biological validation, gives which GO categories to use for biological validation. Can be one of "BP", "MF", "CC", or "all".

goTermFreq

For the BSI, what threshold frequency of GO terms to use for functional annotation.

dropEvidence

Which GO evidence codes to omit. Either NULL or a character vector, see 'Details' below.

verbose

Logical - if TRUE will produce detailed output on the progress of cluster validation.

…

Additional arguments to pass to the clustering functions.

`clValid`

returns an object of class
`"'>clValid"`

. See the help file for the class description.

This function calculates validation measures for a given set of clustering algorithms and number of clusters. A variety of clustering algorithms are available, including hierarchical, self-organizing maps (SOM), K-means, self-organizing tree algorithm (SOTA), and model-based. The available validation measures fall into the three general categories of "internal", "stability", and "biological". A brief description of each measure is given below, for further details refer to the package vignette and the references.

**Internal measures:**The internal measures include the connectivity, and Silhouette Width, and Dunn Index. The connectivity indicates the degree of connectedness of the clusters, as determined by the k-nearest neighbors. The

`neighbSize`

argument specifies the number of neighbors to use. The connectivity has a value between 0 and infinity and should be minimized. Both the Silhouette Width and the Dunn Index combine measures of compactness and separation of the clusters. The Silhouette Width is the average of each observation's Silhouette value. The Silhouette value measures the degree of confidence in a particular clustering assignment and lies in the interval [-1,1], with well-clustered observations having values near 1 and poorly clustered observations having values near -1. See the`silhouette`

function in package cluster for more details. The Dunn Index is the ratio between the smallest distance between observations not in the same cluster to the largest intra-cluster distance. It has a value between 0 and infinity and should be maximized.**Stability measures:**The stability measures are a special version of internal measures which evaluate the stability of a clustering result by comparing it with the clusters obtained by removing one column at a time. These measures include the average proportion of non-overlap (APN), the average distance (AD), the average distance between means (ADM), and the figure of merit (FOM). The APN, AD, and ADM are all based on the cross-classification table of the original clustering with the clustering based on the removal of one column. The APN measures the average proportion of observations not placed in the same cluster under both cases, while the AD measures the average distance between observations placed in the same cluster under both cases and the ADM measures the average distance between cluster centers for observations placed in the same cluster under both cases. The FOM measures the average intra-cluster variance of the deleted column, where the clustering is based on the remaining (undeleted) columns. In all cases the average is taken over all the deleted columns, and all measures should be minimized.

**Biological measures:**There are two biological validation measures, the biological homogeneity index (BHI) and biological stability index (BSI). The observations are typically taken to represent a `gene' (e.g., ORF, SAGE tag, affy ID). The BHI measures the average proportion of gene pairs that are clustered together which have matching biological functional classes. The BSI is similar to the other stability measures, but inspects the consistency of clustering for genes with similar biological functionality. Each sample is removed one at a time, and the cluster membership for genes with similar functional annotation is compared with the cluster membership using all available samples.

For biological validation, the user has two options. The first option is to explicity specify the functional clustering of the genes via either a named list or logical matrix. In ``list'' format, each item in the list is a vector giving genes belonging to a particular biological class. In ``matrix'' format, each column is a logical vector indicating which genes belong to the biological class.

`clValid`

will convert the biological annotation to matrix format internally if initially given in list format.The second option is to specify the appropriate annotation package from Bioconductor (http://www.bioconductor.org) and GO terms to determine the functional classes of the genes. To use the second option requires the Biobase, annotate, and GO packages from Bioconductor, in addition to the annotation package for the particular data type. If the annotation package cannot be loaded,

`clValid`

will attempt to automatically download the package from www.bioconductor.org (using the`biocLite.R`

installation script).The

`GOcategory`

options are "MF", "BP", "CC", or "all", corresponding to molecular function, biological process, cellular component, and all of the ontologies.The

`dropEvidence`

argument indicates which GO evidence codes to omit. For example, "IEA" is a relatively weak association based only on electronic information, and users may wish to omit this evidence when determining the functional annotation classes.

Brock, G., Pihur, V., Datta, S. and Datta, S. (2008) clValid: An R Package for Cluster Validation Journal of Statistical Software 25(4) http://www.jstatsoft.org/v25/i04

Datta, S. and Datta, S. (2003) Comparisons and validation of statistical clustering techniques for microarray gene expression data. Bioinformatics 19(4): 459-466

Datta, S. and Datta, S. (2006) Methods for evaluating clustering algorithms for gene expression data using a reference set of functional classes. BMC Bioinformatics 7:397 http://www.biomedcentral.com/1471-2105/7/397

Handl, J., Knowles, K., and Kell, D. (2005) Computational cluster validation in post-genomic data analysis. Bioinformatics 21(15): 3201-3212

For a description of the class 'clValid' and all available methods see `clValidObj`

or `clValid-class`

.

For help on the clustering methods see `hclust`

and
`kmeans`

in package stats,
`agnes`

, `clara`

, `diana`

,
`fanny`

, and `pam`

in package cluster,
`som`

in package kohonen, `Mclust`

in package mclust, and `sota`

(in this package).

For additional help on the validation measures see
`connectivity`

, `dunn`

,
`stability`

,
`BHI`

, and
`BSI`

.

```
# NOT RUN {
data(mouse)
## internal validation
express <- mouse[1:25,c("M1","M2","M3","NC1","NC2","NC3")]
rownames(express) <- mouse$ID[1:25]
intern <- clValid(express, 2:6, clMethods=c("hierarchical","kmeans","pam"),
validation="internal")
## view results
summary(intern)
optimalScores(intern)
plot(intern)
## stability measures
stab <- clValid(express, 2:6, clMethods=c("hierarchical","kmeans","pam"),
validation="stability")
optimalScores(stab)
plot(stab)
## biological measures
## first way - functional classes predetermined
fc <- tapply(rownames(express),mouse$FC[1:25], c)
fc <- fc[-match( c("EST","Unknown"), names(fc))]
bio <- clValid(express, 2:6, clMethods=c("hierarchical","kmeans","pam"),
validation="biological", annotation=fc)
optimalScores(bio)
plot(bio)
## second way - using Bioconductor
if(require("Biobase") && require("annotate") && require("GO.db") && require("moe430a.db")) {
bio2 <- clValid(express, 2:6, clMethods=c("hierarchical","kmeans","pam"),
validation="biological",annotation="moe430a.db",GOcategory="all")
optimalScores(bio2)
plot(bio2)
}
# }
```

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