computeStructuralMetrics {msImpute} | R Documentation

## Metrics for the assessment of post-imputation structural preservation

### Description

For an imputed dataset, it computes within phenotype/experimental condition similarity (i.e. preservation of local structures), between phenotype distances (preservation of global structures), and the Gromov-Wasserstein (GW) distance between original (source) and imputed data.

### Usage

    computeStructuralMetrics(x, group = NULL, y = NULL, k = 2)

### Arguments

`x` | numeric matrix. An imputed data matrix of log-intensity.
`group` | factor. A vector of biological groups, experimental conditions or phenotypes (e.g. control, treatment).
`y` | numeric matrix. The source data (i.e. the original log-intensity matrix), preferably subsetted on highly variable peptides (see `findVariableFeatures`).
`k` | numeric. Number of Principal Components used to compute the GW distance. default to 2.

### Details

For each group of experimental conditions (e.g. treatment and control), the group centroid is calculated as the average of observed peptide intensities. Withinness for each group is computed as sum of the squared distances between samples in that group and the group centroid. Betweenness is computed as sum of the squared distances between group centroids. When comparing imputation approaches, the optimal imputation strategy should minimize the within group distances, hence smaller withinness, and maximizes between group distances, hence larger betweenness. The GW metric considers preservation of both local and global structures simultaneously. A small GW distance suggests that imputation has introduced small distortions to global and local structures overall, whereas a large distance implies significant distortions. When comparing two or more imputation methods, the optimal method is the method with smallest GW distance. The GW distance is computed on Principal Components (PCs) of the source and imputed data, instead of peptides. Principal components capture the geometry of the data, hence GW computed on PCs is a better measure of preservation of local and global structures. The PCs in the source data are recommended to be computed on peptides with high biological variance. Hence, users are recommended to subset the source data only on highly variable peptides (hvp) (see `findVariableFeatures`). Since the hvp peptides have high biological variance, they are likely to have enough information to discriminate samples from different experimental groups. Hence, PCs computed on those peptides should be representative of the original source data with missing values. If the samples cluster by experimental group in the first couple of PCs, then a choice of k=2 is reasonable. If the desired separation/clustering of samples occurs in later PCs (i.e. the first few PCs are dominated by batches or unwanted variability), then it is recommended to use a larger number of PCs to compute the GW metric. If you are interested in how well the imputed data represent the original data in all possible dimensions, then set k to the number of samples in the data (i.e. the number of columns in the intensity matrix). GW distance estimation requires `python`. See example. All metrics are on log scale.

### Value

list of three metrics: withinness (sum of squared distances within a phenotype group), betweenness (sum of squared distances between the phenotypes), and gromov-wasserstein distance (if `xna` is not NULL). if `group` is NULL only the GW distance is returned. All metrics are on log scale.

### References

Hediyeh-zadeh, S., Webb, A. I., & Davis, M. J. (2020). MSImpute: Imputation of label-free mass spectrometry peptides by low-rank approximation. bioRxiv.

### Examples

    data(pxd010943)
    y <- log2(data.matrix(pxd010943))
    y <- y[complete.cases(y),]
    group <- as.factor(gsub("_[1234]", "", colnames(y)))
    computeStructuralMetrics(y, group, y=NULL)

[Package msImpute version 1.4.0 Index]