kldist {bapred} R Documentation

## Kullback-Leibler divergence between density of within and between batch pairwise distances

### Description

This metric estimates the Kullback-Leibler divergences between the distributions of the within and that of the between batch euclidian distances of pairs of observations. These distributions should be similar in the abscence of stronger batch effects.

### Usage

```kldist(xba, batch)
```

### Arguments

 `xba` matrix. The covariate matrix, raw or after batch effect adjustment. observations in rows, variables in columns. `batch` factor. Batch variable. Currently has to have levels: '1', '2', '3' and so on.

### Details

For two batches j and j* (see next paragraph for the case with more batches): 1) the distances between all pairs of observations in batch j - denoted as {dist_j} - and the distances between all such pairs in batch j* - denoted as {dist_j*} - are calculated; 2) for each observation in j the distances to all observations in j* are calculated, resulting in n_j x n_j* distances denoted as {dist_jj*}; calculate the Kullback-Leibler divergence between the densities of {dist_j} and {dist_jj*} and that between the densities of {dist_j*} and {dist_jj*} - using the k-nearest neighbours based method by Boltz et al (2009) with k=5; 3) take the weighted mean of the values of these two divergences with weights proportional to n_j and n_j*.

For more than two batches: 1) for all possible pairs of batches: calculate the metric as described above; 2) calculate the weighted average of the values in 1) with weights proportional to the sum of the sample sizes in the two respective batches.

The variables are standardized before the calculation to make the metric independent of scale.

### Value

Value of the metric

### Note

The smaller the values of this metric, the better.

Roman Hornung

### References

Lee, J. A., Dobbin, K. K., Ahn, J. (2014) Covariance adjustment for batch effect in gene expression data. Statistics in Medicine, 33, 2681-2695.

Boltz, S., Debreuve, E., Barlaud, M. (2009) High-dimensional statistical measure for region-of-interest tracking. Transactions in Image Processing, 18(6), 1266-1283.

Hornung, R., Boulesteix, A.-L., Causeur, D. (2016) Combining location-and-scale batch effect adjustment with data cleaning by latent factor adjustment. BMC Bioinformatics 17:27.

### Examples

```data(autism)

kldist(xba=X, batch=batch)
```

[Package bapred version 1.0 Index]