Microarray Two-way Clustering

This menu can be used to perform a two-way clustering of probes (which may be thought of as representing genes) and slides or targets effects. The clustering method can be either hierarchical or non-hierarchical using the k-means algorithm. A range of clustering criteria are available for each method. The probes are grouped together so that the responses of each group are similar, with the groups as distinct as possible, and similarly the slides or target effects are grouped together. For the hierarchical clustering, the allocation to groups is specified by providing a threshold for the levels of similarity within a group, and the dendrogram is cut at this level generating an unknown number of groups. For the k-means algorithm, the number of groups must be specified.

The dendrogram for a hierarchical cluster analysis may be plotted, but for a large number of probes this may not be useful as individual probes cannot be read. The responses of each probe across the targets/slides can also be plotted, but again with large numbers of probes this is slow, in which case the mean response for each group can be plotted. A spreadsheet containing the grouped data can also be generated using the Store button.

With large numbers of probes, the limit of RAM on a PC can be quickly reached, so an option to only cluster probes with the largest mean absolute response is available.

Available Data

This lists data structures appropriate for the edit box which currently has focus. You can double-click a name to enter it in the edit box.

Data Format

The data can be supplied in either of the following formats:

Single Variate for Log-ratios with Slide Factor - All the log-ratios are stacked into a single variate, with factors that index the slide and probe/gene
Pointer to Log-ratio Variates for each Slide - Each slide has its data in a variate, and a pointer which points to this set of variates is provided. The Slides factor is not required, but if supplied it should just have one entry for each slide in the order of the variates in the pointer. The Probes/Genes factor is that for a single slide, and all slides must have a common layout.

The spreadsheet stack and unstack menus can be used to reorganise the data between these two formats.

Log-ratios

The log-ratios to cluster the probes and targets on.

Probes/Genes

The factor that identifies the probes or genes on a slide. If the data are in pointer format, this has just one entry per probe, but if the data are in variate (stacked) format, this factor indexes the probes in the log-ratio variate.

Targets or Slides

The factor that identifies the slides. If the data are in pointer format, this has just one entry per slide, but if the data are in variate (stacked) format, this factor indexes the slides in the log-ratio variate.

Clustering Method

The type of clustering to be used:

Hierarchical	Hierarchical clustering using the method selected within the Link Method option.
K-Means	Non-hierarchical clustering using k-means method

When a clustering method is selected the options and controls change to allow you to specify settings for the chosen method.

Link Method (Hierarchical only)

A number of methods for clustering are available and vary according to the way in which 'closest' is defined at each stage of merging groups. The following possibilities are available:

Single Link	defines the similarity between two clusters as the maximum similarity between any two samples in those clusters
Nearest Neighbour	synonym for Single link
Complete Link	defines the similarity between two clusters as the minimum similarity between any two samples in those clusters
Furthest Neighbour	synonym for Complete Link
Average Link	defines the similarity between a cluster and two merging clusters as the average of the similarities with each of the original clusters. It therefore replaces two merging clusters by their mean, unweighted by cluster size
Group Average	an average is taken over all the samples in the two merging clusters. Thus, the original clusters are replaced by their mean, weighted by cluster size
Median Sorting	can be thought of in terms of clusters being represented by points in a multidimensional space; when two clusters join, the new cluster is represented by the midpoint of the original cluster points

Distance Method (Hierarchical only)

The number of clusters to group the probes into.

Probe Groups Threshold% (Hierarchical only)

The minimum percentage similarity within probe/gene groups.

Target Groups Threshold% (Hierarchical only)

The minimum percentage similarity within slide/target groups.

Criterion (K-means only)

The criterion to be optimized by the clustering. This can be set to one of the following four choices:

Within-class dispersion	Minimizes the determinant of the pooled within-class dispersion matrix (W). Under the assumption that the data originated from a mixture of k multivariate Normal distributions, with equal variance-covariance matrix V, the MLE of V is obtained when the grouping into k classes minimizes det(W). Obtains compact groups.
Mahalanobis squared distance	Maximizes the total between-groups Mahalanobis squared distance. This will obtain separation of groups, possibly at the cost of compactness. Equivalent to the Within-class dispersion criterion when there are only two groups.
Between-group sum of squares	Minimizes the trace of the pooled within-class dispersion matrix (W). Equivalent to maximizing the total between-group sum of squares, or Euclidean distance between groups.
Maximal predictive classification	Maximal predictive classification is suitable for binary data. Each group has a class predictor, a binary indicator for each variate set to 0 or 1 according to whichever value is more frequent in the group. The criterion to be maximized is the total number of agreements between units and their respective class predictors.

Number of Probe Groups (K-means only)