Interpreting the output of Compare Single Cell Immune Repertoires

Compare Single Cell Immune Repertoires produces a report contrasting the immune repertoire properties, and optionally, a heat map and / or table summarizing the similarity of the immune repertoires.

The report

The report contains some of the same information provided in The report output from Single Cell Immune Repertoire Analysis, for each group of cells as defined by the configured options. It additionally contains:

Note that diversity is not reported for groups of cells containing more than one sample.

When a group of cells has a name that is too long to be suitable for figure legends, numbers are used in the legend, and the mapping between the numbers and the group names is listed below each figure.

If the "Group by" option leads to more than nine groups of cells, the figures will not have legends. The underlying information can be recovered by double-clicking on the desired figure and switching to the table view.

Heat map

For each pair of groups, the weighted Jaccard similarity between the two is computed. Let $ X_i$, $ Y_i$ denote the relative frequencies of the $ i$'th clonotype in the first and second group respectively. The weighted Jaccard similarity is defined as:

$\displaystyle J(X,Y) = \frac{\sum_{i=1}^n \operatorname{min}(X_i, Y_i)}{\sum_{i=1}^n \operatorname{max}(X_i, Y_i)} .$ (10.1)

The weighted Jaccard distance is defined as:

$\displaystyle D(X,Y) = 1-J(X,Y) .$    

The heat map is obtained using the Jaccard distance, where groups are clustered hierarchically.

Similarity table

A table showing the Jaccard similarity (eq. 10.1) between each pair of groups.