| Title: | Lining Up Two Sets of Measurements |
|---|---|
| Description: | Tools for detecting and correcting sample mix-ups between two sets of measurements, such as between gene expression data on two tissues. This is a revised version of the 'lineup' package, to be more general and not tied to the 'qtl' package. |
| Authors: | Karl W Broman [aut, cre]
|
| Maintainer: | Karl W Broman <[email protected]> |
| License: | GPL-3 |
| Version: | 0.6 |
| Built: | 2024-11-14 04:30:12 UTC |
| Source: | https://github.com/kbroman/lineup2 |
Align the columns of two matrices using their column names, omitting columns that are not present in both.
align_matrix_cols(x, y)align_matrix_cols(x, y)
x |
A matrix |
y |
Another matrix |
A list with the input x and y matrices, with the
columns aligned using their names. Columns not in both matrices
are omitted.
# using the provided lineup2ex data (a list of two matrices) # reduces to the common columns and puts the columns in the same order # (using the column names) aligned <- align_matrix_cols(lineup2ex$gastroc, lineup2ex$islet)# using the provided lineup2ex data (a list of two matrices) # reduces to the common columns and puts the columns in the same order # (using the column names) aligned <- align_matrix_cols(lineup2ex$gastroc, lineup2ex$islet)
Align the rows of two matrices using their row names, omitting rows that are not present in both.
align_matrix_rows(x, y)align_matrix_rows(x, y)
x |
A matrix |
y |
Another matrix |
A list with the input x and y matrices, with the rows
aligned using their names. Rows not in both matrices are
omitted.
# using the provided lineup2ex data (a list of two matrices) # reduces to the common rows and puts the rows in the same order # (using the row names) aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet)# using the provided lineup2ex data (a list of two matrices) # reduces to the common rows and puts the rows in the same order # (using the row names) aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet)
For matrices x and y, calculate the correlation between columns of x and columns of y.
corr_betw_matrices( x, y, what = c("paired", "bestright", "bestpairs", "all"), corr_threshold = 0.9, align_rows = TRUE, cores = 1 )corr_betw_matrices( x, y, what = c("paired", "bestright", "bestpairs", "all"), corr_threshold = 0.9, align_rows = TRUE, cores = 1 )
x |
A numeric matrix. |
y |
A numeric matrix with the same number of rows as |
what |
Indicates which correlations to calculate and return. See value, below. |
corr_threshold |
Threshold on correlations if |
align_rows |
If TRUE, align the rows in the two matrices by the row names. |
cores |
Number of CPU cores to use, for parallel calculations.
(If |
Missing values (NA) are ignored, and we calculate the correlation
using all complete pairs, as in stats::cor() with
use="pairwise.complete.obs".
If what="paired", the return value is a vector of
correlations, between columns of x and the corresponding column of
y. x and y must have the same number of columns.
If what="bestright", we return a data frame of size ncol(x) by
3, with the th row being the maximum correlation between
column of x and a column of y, and then the
y-column index and y-column name with that correlation. (In
case of ties, we give the first one.)
If what="bestpairs", we return a data frame with five columns,
containing all pairs of columns (with one in x and one in y)
with correlation corr_threshold. Each row corresponds to a
column pair, and contains the correlation and then the x- and
y-column indices followed by the x- and y-column names.
If what="all", the output is a matrix of size ncol(x) by
ncol(y), with all correlations between columns of x and
columns of y.
dist_betw_matrices(), dist_betw_arrays()
# use the provided data, and first align the rows aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # correlations for each column in x with each in y result_pairs <- corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") # subset columns to those with correlation > 0.75 gastroc <- lineup2ex$gastroc[,result_pairs > 0.75] islet <- lineup2ex$islet[,result_pairs > 0.75] # similarity matrix for the two sets of rows # (by transposing and using what="all") corr_betw_samples <- corr_betw_matrices(t(gastroc), t(islet), "all") # for each column in x, find most correlated column in y # (max in each row of result_all) bestright <- corr_betw_matrices(t(gastroc), t(islet), "bestright") # correlations that exceed a threshold bestpairs <- corr_betw_matrices(t(gastroc), t(islet), "bestpairs", corr_threshold=0.8)# use the provided data, and first align the rows aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # correlations for each column in x with each in y result_pairs <- corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") # subset columns to those with correlation > 0.75 gastroc <- lineup2ex$gastroc[,result_pairs > 0.75] islet <- lineup2ex$islet[,result_pairs > 0.75] # similarity matrix for the two sets of rows # (by transposing and using what="all") corr_betw_samples <- corr_betw_matrices(t(gastroc), t(islet), "all") # for each column in x, find most correlated column in y # (max in each row of result_all) bestright <- corr_betw_matrices(t(gastroc), t(islet), "bestright") # correlations that exceed a threshold bestpairs <- corr_betw_matrices(t(gastroc), t(islet), "bestpairs", corr_threshold=0.8)
Calculate the distances between the rows of two multi-dimensional arrays.
dist_betw_arrays(x, y, distance = c("rmsd", "mad", "propdiff"), cores = 1)dist_betw_arrays(x, y, distance = c("rmsd", "mad", "propdiff"), cores = 1)
x |
A numeric array. |
y |
A second numeric array, with the same dimensions as |
distance |
Indicates whether to use Euclidean distance
( |
cores |
Number of CPU cores to use, for parallel calculations.
(If |
The two arrays need to have the same dimensions, except for the
leading dimension (rows). They are turned into matrices by merging
all but the leading dimension, and then they're sent to
dist_betw_matrices().
If x and y have m and n rows, respectively, the
result is an m by n matrix whose (i,j)th element is the
distance between the ith row of x and the jth row of
y.
dist_betw_matrices(), corr_betw_matrices()
p <- 10 k <- 6 n <- 5 m <- 3 x <- array(stats::rnorm(n*k*p), dim=c(n,k,p)) rownames(x) <- LETTERS[1:n] y <- array(stats::rnorm(m*k*p), dim=c(m,k,p)) rownames(y) <- letters[1:m] d <- dist_betw_arrays(x, y)p <- 10 k <- 6 n <- 5 m <- 3 x <- array(stats::rnorm(n*k*p), dim=c(n,k,p)) rownames(x) <- LETTERS[1:n] y <- array(stats::rnorm(m*k*p), dim=c(m,k,p)) rownames(y) <- letters[1:m] d <- dist_betw_arrays(x, y)
Calculate the distances between the rows of one matrix and the rows of a second matrix.
dist_betw_matrices( x, y, distance = c("rmsd", "mad", "propdiff"), align_cols = TRUE, cores = 1 )dist_betw_matrices( x, y, distance = c("rmsd", "mad", "propdiff"), align_cols = TRUE, cores = 1 )
x |
A numeric matrix. |
y |
A second numeric matrix, with the same number of columns as |
distance |
Indicates whether to use Euclidean distance
( |
align_cols |
If TRUE, align the columns in the two matrices by the column names. |
cores |
Number of CPU cores to use, for parallel calculations.
(If |
If x is m by p and y is n by p, then the result
is an m by n matrix whose (i,j)th element is the distance
between the ith row of x and the jth row of y.
corr_betw_matrices(), dist_betw_arrays()
p <- 10 n <- 5 m <- 3 x <- matrix(stats::rnorm(n*p), ncol=p) rownames(x) <- LETTERS[1:n] y <- matrix(stats::rnorm(m*p), ncol=p) rownames(y) <- letters[1:m] d <- dist_betw_matrices(x, y)p <- 10 n <- 5 m <- 3 x <- matrix(stats::rnorm(n*p), ncol=p) rownames(x) <- LETTERS[1:n] y <- matrix(stats::rnorm(m*p), ncol=p) rownames(y) <- letters[1:m] d <- dist_betw_matrices(x, y)
For each individual represented in a distance matrix, find the 2nd-smallest entry (with NAs for individuals present in only the rows or only the columns).
get_2ndbest(d, dimension = c("row", "column"), get_min = TRUE)get_2ndbest(d, dimension = c("row", "column"), get_min = TRUE)
d |
A distance matrix |
dimension |
Whether to get the 2nd-best by row or by column |
get_min |
If TRUE, get the 2nd-minimum; if FALSE, get the 2nd-maximum |
A vector with all distinct individuals, with the
2nd-smallest (or largest) value by row or column. We include
all individuals so that the results are aligned with the
results of get_self().
get_self(), get_best(), which_2ndbest(), get_nonself()
# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # second-biggest value by row secbest_byrow <- get_2ndbest(similarity, get_min=FALSE) # second-biggest value by column secbest_bycol <- get_2ndbest(similarity, get_min=FALSE, dimension="column")# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # second-biggest value by row secbest_byrow <- get_2ndbest(similarity, get_min=FALSE) # second-biggest value by column secbest_bycol <- get_2ndbest(similarity, get_min=FALSE, dimension="column")
For each individual represented in a distance matrix, find the smallest entry (with NAs for individuals present in only the rows or only the columns).
get_best(d, dimension = c("row", "column"), get_min = TRUE)get_best(d, dimension = c("row", "column"), get_min = TRUE)
d |
A distance matrix |
dimension |
Whether to get the minimum by row or by column |
get_min |
If TRUE, get the minimum; if FALSE, get the maximum |
A vector with all distinct individuals, with the
minimum (or maximum) value by row or column. We include all
individuals so that the results are aligned with the results of
get_self().
get_self(), get_2ndbest(), which_best(), get_nonself()
# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # maximum value by row best_byrow <- get_best(similarity, get_min=FALSE) # maximum value by column best_bycol <- get_best(similarity, get_min=FALSE, dimension="column")# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # maximum value by row best_byrow <- get_best(similarity, get_min=FALSE) # maximum value by column best_bycol <- get_best(similarity, get_min=FALSE, dimension="column")
Return the distance matrix with all self-self distances replaced with NAs (and so just containing the self-self distances).
get_nonself(d)get_nonself(d)
d |
A distance matrix |
The input distance matrix with all self-self distances replaced with NAs.
get_self(), get_best(), get_2ndbest()
# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # pull out the non-self similarities nonself <- get_nonself(similarity)# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # pull out the non-self similarities nonself <- get_nonself(similarity)
For the inviduals represented in a distance matrix, collect the self-self, best, and 2nd best distances, and summarize the results in a data frame.
get_problems( d, dimension = c("row", "column"), get_min = TRUE, subset = c("problems", "all"), threshold = 0 )get_problems( d, dimension = c("row", "column"), get_min = TRUE, subset = c("problems", "all"), threshold = 0 )
d |
A distance or similarity matrix |
dimension |
Whether to determine the best distances within rows or columns |
get_min |
If TRUE, get the minimum (for a distance matrix); if FALSE, get the maximum (for a similarity matrix) |
subset |
Whether to return just the rows with potential problems, or all of the rows. |
threshold |
If |
A data frame containing individual ID, distance to self, best distance and corresponding individual, 2nd best distance and the corresponding individual.
get_self(), get_best(), get_2ndbest(), which_best(), get_nonself()
# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # pull out the problems, looking by row (where best > self + 0.3) problems_byrow <- get_problems(similarity, get_min=FALSE, threshold=0.3) # pull out the problems, looking by column (where best > self + 0.3) problems_bycol <- get_problems(similarity, get_min=FALSE, threshold=0.3, dimension="column")# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # pull out the problems, looking by row (where best > self + 0.3) problems_byrow <- get_problems(similarity, get_min=FALSE, threshold=0.3) # pull out the problems, looking by column (where best > self + 0.3) problems_bycol <- get_problems(similarity, get_min=FALSE, threshold=0.3, dimension="column")
For each individual represented in a distance matrix, pull the self-self entry (with NAs for individuals present in only the rows or only the columns).
get_self(d)get_self(d)
d |
A distance matrix |
A vector with all distinct individuals, with the self-self values
get_best(), get_2ndbest(), get_nonself()
# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # pull out the self-self similarities self <- get_self(similarity)# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # pull out the self-self similarities self <- get_self(similarity)
Plot histograms of self-self and self-nonself distances
hist_self_nonself(d, breaks = NULL, rug = TRUE, xlabel = "distance")hist_self_nonself(d, breaks = NULL, rug = TRUE, xlabel = "distance")
d |
A distance matrix |
breaks |
Histogram breaks (default is to use 100 intervals) |
rug |
If TRUE, use |
xlabel |
Label on x-axes (e.g., "similarity" vs "distance") |
We use the mfrow arg for graphics::par() to make a
two-panel figure.
None.
# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # histograms of the self and non-self distances hist_self_nonself(similarity)# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # histograms of the self and non-self distances hist_self_nonself(similarity)
Example dataset for lineup2 package, with gene expression data for a selected set of 200 genes on two tissues on a set of about 500 mice, with 100 genes chosen to be highly correlated between the two tissues and 100 chosen at random.
data(lineup2ex)data(lineup2ex)
List of two matrices, with gene expression data for gastrocnemius
muscle (gastroc) and pancreatic islets (islet), at a selected
set of 200 genes (100 are highly correlated between the two
tissues, and 100 others chosen at random). The matrices have
samples as rows and genes as columns. The row names are sample
identifiers. There are 498 samples for gastroc and 499 samples for
islet, with 497 samples in common.
https://phenome.jax.org/projects/Attie1
Broman KW, Keller MP, Broman AT, Kendziorski C, Yandell BS, Sen Ś, Attie AD (2015) Identification and correction of sample mix-ups in expression genetic data: A case study. G3 5:2177–2186
Tian J, Keller MP, Oler AT, Rabaglia ME, Schueler KL, Stapleton DS, Broman AT, Zhao W, Kendziorski C, Yandell BS, Hagenbuch B, Broman KW, Attie AD (2015) Identification of the bile acid transporter Slco1a6 as a candidate gene that broadly affects gene expression in mouse pancreatic islets. Genetics 201:1253–1262
data(lineup2ex) common_ind <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet)data(lineup2ex) common_ind <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet)
Plot the distances for a given sample, highlighting itself and the closest sample
plot_sample( d, sample, dimension = c("row", "column"), get_min = TRUE, add_labels = TRUE, ... )plot_sample( d, sample, dimension = c("row", "column"), get_min = TRUE, add_labels = TRUE, ... )
d |
A distance or similarity matrix |
sample |
Sample ID (in row or column names) |
dimension |
Whether to look at the row or column |
get_min |
If TRUE, get the minimum (for a distance matrix); if FALSE, get the maximum (for a similarity matrix) |
add_labels |
If TRUE, label the individual sample and the optimal sample |
... |
Passed to |
None.
# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") plot_sample(similarity, "Mouse3659", get_min=FALSE) plot_sample(similarity, "Mouse3655", "column", get_min=FALSE)# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") plot_sample(similarity, "Mouse3659", get_min=FALSE) plot_sample(similarity, "Mouse3655", "column", get_min=FALSE)
For each individual represented in a distance matrix, find the individual giving the 2nd-smallest entry (with NAs for individuals present in only the rows or only the columns).
which_2ndbest(d, dimension = c("row", "column"), get_min = TRUE)which_2ndbest(d, dimension = c("row", "column"), get_min = TRUE)
d |
A distance matrix |
dimension |
Whether to get the 2nd-best by row or by column |
get_min |
If TRUE, get the 2nd-minimum; if FALSE, get the 2nd-maximum |
A vector with all distinct individuals, with the
character string labels for the individuals giving the
2nd-smallest (or largest) value by row or column. We include
all individuals so that the results are aligned with the
results of get_self().
get_2ndbest(), get_self(), get_best(), which_best()
# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # which sample gives second-biggest value by row secbest_byrow <- which_2ndbest(similarity, get_min=FALSE) # which sample gives second-biggest value by column secbest_bycol <- which_2ndbest(similarity, get_min=FALSE, dimension="column")# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # which sample gives second-biggest value by row secbest_byrow <- which_2ndbest(similarity, get_min=FALSE) # which sample gives second-biggest value by column secbest_bycol <- which_2ndbest(similarity, get_min=FALSE, dimension="column")
For each individual represented in a distance matrix, find the individual giving the smallest entry (with NAs for individuals present in only the rows or only the columns).
which_best(d, dimension = c("row", "column"), get_min = TRUE)which_best(d, dimension = c("row", "column"), get_min = TRUE)
d |
A distance matrix |
dimension |
Whether to get the minimum by row or by column |
get_min |
If TRUE, get the minimum; if FALSE, get the maximum |
A vector with all distinct individuals, with the
character string labels for the individuals giving the minimum
(or maximum) value by row or column. We include all individuals
so that the results are aligned with the results of
get_self().
get_best(), get_self(), get_2ndbest(), which_2ndbest()
# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # which sample gives maximum value by row best_byrow <- which_best(similarity, get_min=FALSE) # which sample gives maximum value by column best_bycol <- which_best(similarity, get_min=FALSE, dimension="column")# align rows in the provided dataset, lineup2ex aligned <- align_matrix_rows(lineup2ex$gastroc, lineup2ex$islet) # find correlated columns selected_genes <- (corr_betw_matrices(aligned[[1]], aligned[[2]], "paired") > 0.75) # calculate correlation between rows similarity <- corr_betw_matrices(t(lineup2ex$gastroc[,selected_genes]), t(lineup2ex$islet[,selected_genes]), "all") # which sample gives maximum value by row best_byrow <- which_best(similarity, get_min=FALSE) # which sample gives maximum value by column best_bycol <- which_best(similarity, get_min=FALSE, dimension="column")