Distance Metrics
distance_metrics.RmdDownload a copy of the vignette to follow along here: distance_metrics.Rmd
The distance_metrics_list
metaSNF enables users to customize what distance metrics are used in
the SNF pipeline. All information about distance metrics are stored in a
distance_metrics_list object.
By default, batch_snf will create its own
distance_metrics_list by calling the
generate_distance_metrics_list function with no additional
arguments.
library(metasnf)
distance_metrics_list <- generate_distance_metrics_list()The list is a list of functions (euclidean_distance()
and gower_distance()), and printing them out directly can
be messy. The summarize_dml() function prints the object
with a nicer format.
summarize_dml(distance_metrics_list)
#>
#> Continuous distances:
#> 1. euclidean_distance
#>
#> Discrete distances:
#> 1. euclidean_distance
#>
#> Ordinal distances:
#> 1. euclidean_distance
#>
#> Categorical distances:
#> 1. gower_distance
#>
#> Mixed distances:
#> 1. gower_distanceThese lists must always contain at least 1 distance metric for each of the 5 recognized types of variables: continuous, discrete, ordinal, categorical, and mixed (any combination of the previous four).
By default, continuous, discrete, and ordinal data are converted to
distance matrices using simple Euclidean distance. Categorical and mixed
data are handled using Gower’s formula as implemented by the cluster
package (see ?cluster::daisy).
How the distance_metrics_list is used
To show how the distance_metrics_list is used, we’ll start by
extending our distance_metrics_list beyond just the default options.
metaSNF provides a Euclidean distance function that applies standard
normalization first, sn_euclidean_distance() (a wrapper
around SNFtool::standardNormalization +
stats::dist). Here’s how we can create a custom
distance_metrics_list that includes this metric for continuous and
discrete variables.
my_distance_metrics <- generate_distance_metrics_list(
continuous_distances = list(
"standard_norm_euclidean" = sn_euclidean_distance
),
discrete_distances = list(
"standard_norm_euclidean" = sn_euclidean_distance
)
)
summarize_dml(my_distance_metrics)
#>
#> Continuous distances:
#> 1. euclidean_distance
#> 2. standard_norm_euclidean
#>
#> Discrete distances:
#> 1. euclidean_distance
#> 2. standard_norm_euclidean
#>
#> Ordinal distances:
#> 1. euclidean_distance
#>
#> Categorical distances:
#> 1. gower_distance
#>
#> Mixed distances:
#> 1. gower_distanceNow, during settings_matrix generation, we can provide our distance_metrics_list to ensure our new distance metrics will be used on some of our SNF runs.
Before making the settings_matrix, we’ll quickly need to setup some data (as was done in A Simple Example).
library(SNFtool)
data(Data1)
data(Data2)
Data1$"patient_id" <- 101:(nrow(Data1) + 100) # nolint
Data2$"patient_id" <- 101:(nrow(Data2) + 100) # nolint
data_list <- generate_data_list(
list(Data1, "genes_1_and_2_exp", "gene_expression", "continuous"),
list(Data2, "genes_1_and_2_meth", "gene_methylation", "continuous"),
uid = "patient_id"
)And then the settings_matrix can be generated:
settings_matrix <- generate_settings_matrix(
data_list,
nrow = 10,
distance_metrics_list = my_distance_metrics
)
# showing just the columns that are related to distances
settings_matrix |> dplyr::select(dplyr::ends_with("dist"))
#> cont_dist disc_dist ord_dist cat_dist mix_dist
#> 1 2 2 1 1 1
#> 2 1 1 1 1 1
#> 3 2 2 1 1 1
#> 4 2 1 1 1 1
#> 5 1 2 1 1 1
#> 6 1 1 1 1 1
#> 7 2 1 1 1 1
#> 8 2 2 1 1 1
#> 9 1 1 1 1 1
#> 10 1 2 1 1 1The continuous and discrete distance metrics values randomly
fluctuate between 1 and 2, where 1 means that the first metric
(euclidean_distance()) will be used and 2 means that the
second metric (sn_euclidean_distance) will be used.
It’s important to note that the settings_matrix itself does
not store the distance metrics, just the pointers to which
position metric in the distance_metrics_list should be used for that SNF
run. Because of that, you’ll need to supply the distance_metrics_list
once again when calling batch_snf().
solutions_matrix <- batch_snf(
data_list,
settings_matrix,
distance_metrics_list = my_distance_metrics
)Removing the default distance_metrics
There are two ways to avoid using the default distance metrics if you don’t want to ever use them.
The first way is to use the keep_defaults parameter in
generate_distance_metrics_list():
no_default_metrics <- generate_distance_metrics_list(
continuous_distances = list(
"standard_norm_euclidean" = sn_euclidean_distance
),
discrete_distances = list(
"standard_norm_euclidean" = sn_euclidean_distance
),
ordinal_distances = list(
"standard_norm_euclidean" = sn_euclidean_distance
),
categorical_distances = list(
"standard_norm_euclidean" = sn_euclidean_distance
),
mixed_distances = list(
"standard_norm_euclidean" = sn_euclidean_distance
),
keep_defaults = FALSE
)
summarize_dml(no_default_metrics)
#>
#> Continuous distances:
#> 1. standard_norm_euclidean
#>
#> Discrete distances:
#> 1. standard_norm_euclidean
#>
#> Ordinal distances:
#> 1. standard_norm_euclidean
#>
#> Categorical distances:
#> 1. standard_norm_euclidean
#>
#> Mixed distances:
#> 1. standard_norm_euclideanFor this option, it is necessary to provide at least one distance metric for every variable type. A distance_metrics_list cannot have any of its variable types be completely empty (even if you have no data for that variable type in the first place).
The second way is to explicitly specify which indices you want to sample from during settings_matrix generation:
my_distance_metrics <- generate_distance_metrics_list(
continuous_distances = list(
"standard_norm_euclidean" = sn_euclidean_distance,
"some_other_metric" = sn_euclidean_distance
),
discrete_distances = list(
"standard_norm_euclidean" = sn_euclidean_distance,
"some_other_metric" = sn_euclidean_distance
)
)
summarize_dml(my_distance_metrics)
#>
#> Continuous distances:
#> 1. euclidean_distance
#> 2. standard_norm_euclidean
#> 3. some_other_metric
#>
#> Discrete distances:
#> 1. euclidean_distance
#> 2. standard_norm_euclidean
#> 3. some_other_metric
#>
#> Ordinal distances:
#> 1. euclidean_distance
#>
#> Categorical distances:
#> 1. gower_distance
#>
#> Mixed distances:
#> 1. gower_distance
settings_matrix <- generate_settings_matrix(
data_list,
nrow = 10,
distance_metrics_list = my_distance_metrics,
continuous_distances = 1,
discrete_distances = c(2, 3)
)
settings_matrix |> dplyr::select(dplyr::ends_with("dist"))
#> cont_dist disc_dist ord_dist cat_dist mix_dist
#> 1 1 2 1 1 1
#> 2 1 2 1 1 1
#> 3 1 3 1 1 1
#> 4 1 3 1 1 1
#> 5 1 3 1 1 1
#> 6 1 2 1 1 1
#> 7 1 3 1 1 1
#> 8 1 3 1 1 1
#> 9 1 2 1 1 1
#> 10 1 2 1 1 1The second option can be quite useful when paired with
add_settings_matrix_rows(), enabling you to build up
distinct blocks of rows in the settings matrix that have different
combinations of distance metrics. This can save you the trouble of
needing to manage several distinct distance metrics lists or manage your
solution space over separate runs of batch_snf.
settings_matrix <- generate_settings_matrix(
data_list,
nrow = 10,
distance_metrics_list = my_distance_metrics,
continuous_distances = 1,
discrete_distances = c(2, 3)
)
settings_matrix <- add_settings_matrix_rows(
settings_matrix,
nrow = 10,
distance_metrics_list = my_distance_metrics,
continuous_distances = 3,
discrete_distances = 1
)
settings_matrix |> dplyr::select(dplyr::ends_with("dist"))
#> cont_dist disc_dist ord_dist cat_dist mix_dist
#> 1 1 3 1 1 1
#> 2 1 2 1 1 1
#> 3 1 3 1 1 1
#> 4 1 3 1 1 1
#> 5 1 2 1 1 1
#> 6 1 2 1 1 1
#> 7 1 2 1 1 1
#> 8 1 2 1 1 1
#> 9 1 2 1 1 1
#> 10 1 2 1 1 1
#> 11 3 1 1 1 1
#> 12 3 1 1 1 1
#> 13 3 1 1 1 1
#> 14 3 1 1 1 1
#> 15 3 1 1 1 1
#> 16 3 1 1 1 1
#> 17 3 1 1 1 1
#> 18 3 1 1 1 1
#> 19 3 1 1 1 1
#> 20 3 1 1 1 1In rows 1 to 10, only continuous data will always be handled by the first continuous distance metric while discrete data will be handled by the second and third discrete distance metrics. In rows 11 to 20, continuous data will always be handled by the third continuous distance metric while discrete data will only be handled by the first distance metric.
Supplying weights to distance metrics
Some distance metric functions can accept weights. Usually, weights will be applied by direct scaling of specified variables. In some cases (e.g. categorical distance metric functions), the way in which weights are applied may be somewhat less intuitive. The bottom of this vignette outlines the available distance metric functions grouped by whether or not they accept weights. You can examine the documentation of those weighted functions to learn more about how the weights you provide will be used.
An important note on providing weights for a run of SNF is that the
specific form of the data may not be what you expect by the time it is
ready to be converted into a distance metric function. The “individual”
and “two-step” SNF schemes involve distance metrics only being applied
to the input dataframes in the data_list as they are. The
“domain” scheme, however, concatenates data within a domain before
converting that larger dataframe into a distance matrix. Anytime you
have more than one dataframe with the same domain label and you use the
domain SNF scheme, all the columns associated with that domain will be
in a single dataframe when the distance metric function is applied.
The first step in providing custom weights is to generate a
weights_matrix:
weights_matrix <- generate_weights_matrix(
data_list
)
weights_matrix
#> V1 V2 V3 V4
#> [1,] 1 1 1 1By default, this function will return a dataframe containing all the
columns in the data_list and a single row of 1s, which are
the weights that will be used for a single run of SNF.
To actually use the matrix during SNF, you’ll need to make sure that the number of rows in the weights matrix is the same as the number of rows in your settings matrix.
settings_matrix <- generate_settings_matrix(
data_list,
nrow = 10,
distance_metrics_list = my_distance_metrics,
continuous_distances = 1,
discrete_distances = c(2, 3)
)
weights_matrix <- generate_weights_matrix(
data_list,
nrow = nrow(settings_matrix)
)
weights_matrix[1:5, ]
#> V1 V2 V3 V4
#> [1,] 1 1 1 1
#> [2,] 1 1 1 1
#> [3,] 1 1 1 1
#> [4,] 1 1 1 1
#> [5,] 1 1 1 1
solutions_matrix_1 <- batch_snf(
data_list,
settings_matrix,
distance_metrics_list = my_distance_metrics,
weights_matrix = weights_matrix
)
#> [1] "Row: 1/10 | Time remaining: 4 seconds"
#> [1] "Row: 2/10 | Time remaining: 3 seconds"
#> [1] "Row: 3/10 | Time remaining: 3 seconds"
#> [1] "Row: 4/10 | Time remaining: 2 seconds"
#> [1] "Row: 5/10 | Time remaining: 2 seconds"
#> [1] "Row: 6/10 | Time remaining: 2 seconds"
#> [1] "Row: 7/10 | Time remaining: 1 seconds"
#> [1] "Row: 8/10 | Time remaining: 1 seconds"
#> [1] "Row: 9/10 | Time remaining: 0 seconds"
#> [1] "Row: 10/10 | Time remaining: 0 seconds"
#> [1] "Total time taken: 4 seconds."
solutions_matrix_2 <- batch_snf(
data_list,
settings_matrix,
distance_metrics_list = my_distance_metrics
)
#> [1] "Row: 1/10 | Time remaining: 3 seconds"
#> [1] "Row: 2/10 | Time remaining: 3 seconds"
#> [1] "Row: 3/10 | Time remaining: 3 seconds"
#> [1] "Row: 4/10 | Time remaining: 2 seconds"
#> [1] "Row: 5/10 | Time remaining: 2 seconds"
#> [1] "Row: 6/10 | Time remaining: 2 seconds"
#> [1] "Row: 7/10 | Time remaining: 1 seconds"
#> [1] "Row: 8/10 | Time remaining: 1 seconds"
#> [1] "Row: 9/10 | Time remaining: 0 seconds"
#> [1] "Row: 10/10 | Time remaining: 0 seconds"
#> [1] "Total time taken: 4 seconds."
identical(
solutions_matrix_1,
solutions_matrix_2
) # Try this on your machine - It'll evaluate to TRUE
#> [1] TRUEA weights_matrix of all 1s (the default
weights_matrix used when you don’t supply one yourself)
’won’t actually do anything to the data. You can either replace the 1s
with your own weights that you’ve calculated outside of the package, or
use some random weights following a uniform or exponential
distribution.
weights_matrix <- generate_weights_matrix(
data_list,
nrow = nrow(settings_matrix),
fill = "uniform" # or fill = "exponential"
)The default metrics (simple Euclidean for continuous, discrete, and ordinal data and Gower’s distance for categorical and mixed data) are both capable of applying weights to data before distance matrix generation.
Custom distance metrics
The remainder of this vignette deals with supplying custom distance metrics (including custom feature weighting). Making use of this functionality will require a good understanding of working with functions in R.
You can also supply your own custom distance metrics. Looking at the code from one of the package-provided distance functions shows some of the essential aspects of a well-formated distance function.
euclidean_distance
#> function (df, weights_row)
#> {
#> weights <- format_weights_row(weights_row)
#> weighted_df <- as.matrix(df) %*% weights
#> distance_matrix <- as.matrix(stats::dist(weighted_df, method = "euclidean"))
#> return(distance_matrix)
#> }
#> <bytecode: 0x561ebbac61d0>
#> <environment: namespace:metasnf>The function should accept two arguments: df and
weights_row, and only give one output,
distance_matrix. The function doesn’t actually need to make
use of those weights if you don’t want it to.
By the time your data reaches a distance metric function, it
(referred to as df) will always:
- have no UID column
- have at least one variable column
- have no missing values
- be a data.frame (not a tibble)
The variable column names won’t be altered from the values they had when they were loaded into the data_list.
For example, consider the abcd_anxiety raw data supplied
by metaSNF:
head(abcd_anxiety)
#> # A tibble: 6 × 2
#> patient cbcl_anxiety_r
#> <chr> <dbl>
#> 1 NDAR_INV0567T2Y9 3
#> 2 NDAR_INV0GLZNC2W 1
#> 3 NDAR_INV0IZ157F8 NA
#> 4 NDAR_INV0J4PYA5F 0
#> 5 NDAR_INV0OYE291Q 2
#> 6 NDAR_INV0SM1JLXQ 2Here’s how to make it look more like what the distance metric functions will expect to see:
processed_abcd_anxiety <- abcd_anxiety |>
na.omit() |> # no NAs
dplyr::rename("subjectkey" = "patient") |>
data.frame(row.names = "subjectkey")
head(processed_abcd_anxiety)
#> cbcl_anxiety_r
#> NDAR_INV0567T2Y9 3
#> NDAR_INV0GLZNC2W 1
#> NDAR_INV0J4PYA5F 0
#> NDAR_INV0OYE291Q 2
#> NDAR_INV0SM1JLXQ 2
#> NDAR_INV0Z87UJDR 0If we want to have a distance metric that calculates Euclidean distance, but also scales the resulting matrix down such that the biggest allowed distance is a 1, it would look like this:
my_scaled_euclidean <- function(df, weights_row) {
# this function won't apply the weights it is given
distance_matrix <- df |>
stats::dist(method = "euclidean") |>
as.matrix() # make sure it's formatted as a matrix
distance_matrix <- distance_matrix / max(distance_matrix)
return(distance_matrix)
}You’ll need to be mindful of any edge cases that your function will run into. For example, this function will fail if the pairwise distances for all patients is 0 (a division by 0 will occur). If that specific situation ever happens, there’s probably something quite wrong with the data.
Once you’re happy that you distance function is working as you’d like it to:
my_scaled_euclidean(processed_abcd_anxiety)[1:5, 1:5]
#> NDAR_INV0567T2Y9 NDAR_INV0GLZNC2W NDAR_INV0J4PYA5F
#> NDAR_INV0567T2Y9 0.0 0.2 0.3
#> NDAR_INV0GLZNC2W 0.2 0.0 0.1
#> NDAR_INV0J4PYA5F 0.3 0.1 0.0
#> NDAR_INV0OYE291Q 0.1 0.1 0.2
#> NDAR_INV0SM1JLXQ 0.1 0.1 0.2
#> NDAR_INV0OYE291Q NDAR_INV0SM1JLXQ
#> NDAR_INV0567T2Y9 0.1 0.1
#> NDAR_INV0GLZNC2W 0.1 0.1
#> NDAR_INV0J4PYA5F 0.2 0.2
#> NDAR_INV0OYE291Q 0.0 0.0
#> NDAR_INV0SM1JLXQ 0.0 0.0You can load it into a custom distance_metrics_list:
my_distance_metrics <- generate_distance_metrics_list(
continuous_distances = list(
"my_scaled_euclidean" = my_scaled_euclidean
)
)Requesting metrics
If there’s a metric you’d like to see added as a prewritten option included in the package, feel free to post an issue or make a pull request on the package’s GitHub.
List of prewritten distance metrics functions
These metrics can be used as is. They are all capable of accepting
and applying custom weights provided by a
weights_matrix.
-
euclidean_distance(Euclidean distance)- applies to continuous, discrete, or ordinal data
-
sn_euclidean_distance(Standard normalized Euclidean distance)- Standard normalize data, then use Euclidean distance
- applies to continuous, discrete, or ordinal data
-
gower_distance(Gower’s distance)- applies to any data
-
siw_euclidean_distance(Squared (including weights) Euclidean distance)- Apply weights to dataframe, then calculate Euclidean distance, then square the results
-
sew_euclidean_distance(Squared (excluding weights) Euclidean distance)- Apply square root of weights to dataframe, then calculate Euclidean distance, then square the results
-
hamming_distance(Hamming distance)- Distance between patients is (1 * variable weight) summed over all variables
References
Wang, Bo, Aziz M. Mezlini, Feyyaz Demir, Marc Fiume, Zhuowen Tu, Michael Brudno, Benjamin Haibe-Kains, and Anna Goldenberg. 2014. “Similarity Network Fusion for Aggregating Data Types on a Genomic Scale.” Nature Methods 11 (3): 333–37. https://doi.org/10.1038/nmeth.2810.