A Complete Example

Download a copy of the vignette to follow along here: a_complete_example.Rmd

We recommend you go through the simple example before working through this one.

This vignette walks through how the core functionality of this package, including:

1. Setting up the data
2. Building a space of settings to cluster over
3. Running SNF
4. Identifying and visualizing meta clusters
5. Characterizing and selecting top meta clusters
6. Selecting a representative cluster solution from a meta cluster
7. Cluster solution characterization
8. Cluster solution validation

Data Set-up

Pre-processing

Your data should be loaded into the R environment in the following format:

1. The data is in one or more data.frame objects
2. The data is in wide form (one row per observation to cluster)
3. All dataframes should have exactly one column that uniquely identifies each observation
4. All data should be complete (no missing values)

If you wish to use imputation to handle missingness in your data, you can take a look at the imputation vignette which outlines a basic workflow for meta clustering across multiple imputations of the same dataset.

The package comes with a few mock dataframes based on real data from the Adolescent Brain Cognitive Development study:

• anxiety (anxiety scores from the CBCL)
• depress (depression scores from the CBCL)
• cort_t (cortical thicknesses)
• cort_sa (cortical surface areas in mm^2)
• subc_v (subcortical volumes in mm^3)
• income (household income on a 1-3 scale)
• pubertal (pubertal status on a 1-5 scale)

Here’s what the cortical thickness data looks like:

library(metasnf)

class(cort_t)
#> [1] "tbl_df"     "tbl"        "data.frame"

dim(cort_t)
#> [1] 188 152

str(cort_t[1:5, 1:5])
#> Classes 'tbl_df', 'tbl' and 'data.frame':    5 obs. of  5 variables:
#>  $ unique_id: chr  "NDAR_INV0567T2Y9" "NDAR_INV0GLZNC2W" "NDAR_INV0IZ157F8" "NDAR_INV0J4PYA5F" ...
#>  $ mrisdp_1 : num  2.6 2.62 2.62 2.6 2.53
#>  $ mrisdp_2 : num  2.49 2.85 2.29 2.67 2.76
#>  $ mrisdp_3 : num  2.8 2.78 2.53 2.68 2.83
#>  $ mrisdp_4 : num  2.95 2.85 2.96 2.94 2.99

cort_t[1:5, 1:5]
#>          unique_id mrisdp_1 mrisdp_2 mrisdp_3 mrisdp_4
#> 1 NDAR_INV0567T2Y9    2.601    2.487    2.801    2.954
#> 2 NDAR_INV0GLZNC2W    2.619    2.851    2.784    2.846
#> 3 NDAR_INV0IZ157F8    2.621    2.295    2.530    2.961
#> 4 NDAR_INV0J4PYA5F    2.599    2.670    2.676    2.938
#> 5 NDAR_INV0OYE291Q    2.526    2.761    2.829    2.986

The first column unique_id is the unique identifier (UID) for all subjects in the data.

Here’s the household income data:

dim(income)
#> [1] 275   2

str(income[1:5, ])
#> Classes 'tbl_df', 'tbl' and 'data.frame':    5 obs. of  2 variables:
#>  $ unique_id       : chr  "NDAR_INV0567T2Y9" "NDAR_INV0GLZNC2W" "NDAR_INV0IZ157F8" "NDAR_INV0J4PYA5F" ...
#>  $ household_income: num  3 NA 1 2 1

income[1:5, ]
#>          unique_id household_income
#> 1 NDAR_INV0567T2Y9                3
#> 2 NDAR_INV0GLZNC2W               NA
#> 3 NDAR_INV0IZ157F8                1
#> 4 NDAR_INV0J4PYA5F                2
#> 5 NDAR_INV0OYE291Q                1

Putting everything in a list will help us get quicker summaries of all the data.

data <- list(
    anxiety,
    depress,
    cort_t,
    cort_sa,
    subc_v,
    income,
    pubertal
)

# The number of rows in each dataframe:
lapply(data, dim)
#> [[1]]
#> [1] 275   2
#> 
#> [[2]]
#> [1] 275   2
#> 
#> [[3]]
#> [1] 188 152
#> 
#> [[4]]
#> [1] 188 152
#> 
#> [[5]]
#> [1] 174  31
#> 
#> [[6]]
#> [1] 275   2
#> 
#> [[7]]
#> [1] 275   2

# Whether or not each dataframe has missing values:
lapply(data,
    function(x) {
        any(is.na(x))
    }
)
#> [[1]]
#> [1] TRUE
#> 
#> [[2]]
#> [1] TRUE
#> 
#> [[3]]
#> [1] FALSE
#> 
#> [[4]]
#> [1] FALSE
#> 
#> [[5]]
#> [1] FALSE
#> 
#> [[6]]
#> [1] TRUE
#> 
#> [[7]]
#> [1] TRUE

Some of our data has missing values and not all of our dataframes have the same number of participants. SNF can only be run with complete data, so you’ll need to either use complete case analysis (removal of observations with any missing values) or impute the missing values to proceed with the clustering. As mentioned above, metasnf can be used to visualize changes in clustering results across different imputations of the data.

For now, we’ll just examine the simpler complete-case analysis approach by reducing our dataframes to only common and complete observations. This can be made easier using the get_complete_uids function.

complete_uids <- get_complete_uids(data, uid = "unique_id")

print(length(complete_uids))
#> [1] 87

# Reducing dataframes to only common subjects with no missing data
anxiety <- anxiety[anxiety$"unique_id" %in% complete_uids, ]
depress <- depress[depress$"unique_id" %in% complete_uids, ]
cort_t <- cort_t[cort_t$"unique_id" %in% complete_uids, ]
cort_sa <- cort_sa[cort_sa$"unique_id" %in% complete_uids, ]
subc_v <- subc_v[subc_v$"unique_id" %in% complete_uids, ]
income <- income[income$"unique_id" %in% complete_uids, ]
pubertal <- pubertal[pubertal$"unique_id" %in% complete_uids, ]

Generating the data list

The data_list structure is a structured list of dataframes (like the one already created), but with some additional metadata about each dataframe. It should only contain the input dataframes we want to directly use as inputs for the clustering. Out of all the data we have available to us, we may be working in a context where the anxiety and depression data are especially important outcomes, and we want to know if we can find subtypes using the rest of the data which still do a good job of separating out subjects by their anxiety and depression scores.

We’ll start by creating a data list that stores our input features.

# Note that you do not need to explicitly name every single named element
# (data = ..., name = ..., etc.)
data_list <- generate_data_list(
    list(
        data = cort_t,
        name = "cortical_thickness",
        domain = "neuroimaging",
        type = "continuous"
    ),
    list(
        data = cort_sa,
        name = "cortical_surface_area",
        domain = "neuroimaging",
        type = "continuous"
    ),
    list(
        data = subc_v,
        name = "subcortical_volume",
        domain = "neuroimaging",
        type = "continuous"
    ),
    list(
        data = income,
        name = "household_income",
        domain = "demographics",
        type = "continuous"
    ),
    list(
        data = pubertal,
        name = "pubertal_status",
        domain = "demographics",
        type = "continuous"
    ),
    uid = "unique_id"
)

This process removes any observations that did not have complete data across all provided input dataframes. If you’d like to keep track of that information, you can set the “return_missing” parameter to TRUE and receive a list containing the data_list as well as the removed observations. The structure of the data list is a nested list tracking the data, the name of the dataframe, what domain (broader source of information) the data belongs to, and the type of feature stored in the dataframe. Options for feature type include “continuous”, “discrete”, “ordinal”, and “categorical”.

The “uid” parameter is the name of the column in the dataframes that uniquely identifies each observation. Upon data list creation, the UID will be converted to “subjectkey” for consistency across other functions in the package.

We can get a summary of our constructed data_list with the summarize_dl function:

summarize_dl(data_list)
#>                    name       type       domain length width
#> 1    cortical_thickness continuous neuroimaging     87   152
#> 2 cortical_surface_area continuous neuroimaging     87   152
#> 3    subcortical_volume continuous neuroimaging     87    31
#> 4      household_income continuous demographics     87     2
#> 5       pubertal_status continuous demographics     87     2

Each input dataframe now has the same 87 subjects with complete data. The width refers to the number of columns in each dataframe, which equals 1 for the UID (subjectkey) column + the number of features in the dataframe.

data_list now stores all the features we intend on using for the clustering. We’re interested in knowing if any of the clustering solutions we generate can distinguish children apart based on their anxiety and depression scores. To do this, we’ll also create a data list storing only features that we’ll use for evaluating our cluster solutions and not for the clustering itself. We’ll refer to this as the “target_list”.

target_list <- generate_data_list(
    list(anxiety, "anxiety", "behaviour", "ordinal"),
    list(depress, "depressed", "behaviour", "ordinal"),
    uid = "unique_id"
)

summarize_dl(target_list)
#>        name    type    domain length width
#> 1   anxiety ordinal behaviour     87     2
#> 2 depressed ordinal behaviour     87     2

Note that it is not necessary to make use of a partition of input and out-of-model measures in this way. If you’d like to have no target list and instead use every single feature of interest for the clustering, you can stick to just using one data list.

Defining sets of hyperparameters to use for SNF and clustering

The settings_matrix stores all the information about the settings we’d like to use for each of our SNF runs. Calling the generate_settings_matrix function with a specified number of rows will automatically build a randomly populated settings_matrix.

set.seed(42)
settings_matrix <- generate_settings_matrix(
    data_list,
    nrow = 20,
    min_k = 20,
    max_k = 50
)

settings_matrix[1:5, ]
#>   row_id alpha  k  t snf_scheme clust_alg cont_dist disc_dist ord_dist cat_dist
#> 1      1   0.5 29 20          2         1         1         1        1        1
#> 2      2   0.4 26 20          1         1         1         1        1        1
#> 3      3   0.3 44 20          2         2         1         1        1        1
#> 4      4   0.3 43 20          1         1         1         1        1        1
#> 5      5   0.5 29 20          2         2         1         1        1        1
#>   mix_dist inc_cortical_thickness inc_cortical_surface_area
#> 1        1                      1                         0
#> 2        1                      1                         1
#> 3        1                      1                         0
#> 4        1                      1                         1
#> 5        1                      1                         1
#>   inc_subcortical_volume inc_household_income inc_pubertal_status
#> 1                      1                    0                   1
#> 2                      1                    1                   1
#> 3                      0                    1                   1
#> 4                      0                    1                   1
#> 5                      1                    1                   1

The columns are:

• row_id: Integer to keep track of which row is which
• alpha - A hyperparameter for SNF (feature that influences the subtyping process)
• k - A hyperparameter for SNF
• t - A hyperparameter for SNF
• snf_scheme - the specific way in which input data gets collapsed into a final fused network (discussed further in the SNF schemes vignette)
• clust_alg - Which clustering algorithm will be applied to the final fused network produced by SNF
• *_dist - Which distance metric will be used for the different types of data (discussed further in the distance metrics vignette)
• inc_* - binary columns indicating whether or not an input dataframe is included (1) or excluded (0) from the corresponding SNF run (discussed further in the settings matrix vignette)

Without specifying any additional parameters, generate_settings_matrix randomly populates these columns and ensures that no generated rows are identical.

What’s important for now is that the matrix (technically a dataframe in the R environment) contains several rows which each outline a different but reasonable way in which the raw data could be converted into a cluster solution. Further customization of the settings_matrix will enable you to access the broadest possible space of reasonable cluster solutions that your data can produce using SNF and ideally get you closer to a generalizable and useful solution for your context. More on settings_matrix customization can be found in the settings matrix vignette.

Setting the optional seed parameter (which will affect the seed of your entire R session) ensures that the same settings matrix is generated each time we run the code.

While we end up with a random set of settings here, there is nothing wrong with manually altering the settings matrix to suit your needs. For example, if you wanted to know how much of a difference one input dataframe made, you could ensure that half of the rows included this input dataframe and the other half didn’t. You can also add random rows to an already existing dataframe using the add_settings_matrix_rows function (further discussed in the vignette).

Running SNF and clustering

The batch_snf function integrates the data in the data_list using each of the sets of settings contained in the settings_matrix. The resulting structure is an solutions_matrix which is an extension of the settings_matrix that contains columns specifying which cluster each subject was assigned for the corresponding settings_matrix row.

solutions_matrix <- batch_snf(data_list, settings_matrix)

colnames(solutions_matrix)[1:30]
#>  [1] "row_id"                    "alpha"                    
#>  [3] "k"                         "t"                        
#>  [5] "snf_scheme"                "clust_alg"                
#>  [7] "cont_dist"                 "disc_dist"                
#>  [9] "ord_dist"                  "cat_dist"                 
#> [11] "mix_dist"                  "inc_cortical_thickness"   
#> [13] "inc_cortical_surface_area" "inc_subcortical_volume"   
#> [15] "inc_household_income"      "inc_pubertal_status"      
#> [17] "nclust"                    "subject_NDAR_INV0567T2Y9" 
#> [19] "subject_NDAR_INV0J4PYA5F"  "subject_NDAR_INV10OMKVLE" 
#> [21] "subject_NDAR_INV15FPCW4O"  "subject_NDAR_INV19NB4RJK" 
#> [23] "subject_NDAR_INV1HLGR738"  "subject_NDAR_INV1KR0EZFU" 
#> [25] "subject_NDAR_INV1L3Y9EOP"  "subject_NDAR_INV1TCP5GNM" 
#> [27] "subject_NDAR_INV1ZHRDJ6B"  "subject_NDAR_INV2EJ41YSZ" 
#> [29] "subject_NDAR_INV2PK6C85M"  "subject_NDAR_INV2XO1PHCT"

It goes on like this for some time.

Just like that, 20 different cluster solutions have been generated!

In practice, you may end up wanting to create hundreds or thousands of cluster solutions at a time. If you have access to a multi-core system, batch_snf can be run with parallel processing enabled. See ?batch_snf or the parallel processing vignette for more information.

You can pull the clustering results out of each row using the get_cluster_solutions function:

cluster_solutions <- get_cluster_solutions(solutions_matrix)

head(cluster_solutions)
#>                 subjectkey 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
#> 1 subject_NDAR_INV0567T2Y9 5 3 1 1 1 1 1 3 3  2  6  1  1  3  2  1  1  1  1  1
#> 2 subject_NDAR_INV0J4PYA5F 2 3 7 2 6 2 4 4 3  4  5  7  2  3  2  4  2  7  2  3
#> 3 subject_NDAR_INV10OMKVLE 1 2 3 1 4 2 3 1 2  2  7  2  2  2  1  1  3  4  2  2
#> 4 subject_NDAR_INV15FPCW4O 1 2 5 2 5 2 3 1 2  3  7  5  2  2  1  1  2  5  2  3
#> 5 subject_NDAR_INV19NB4RJK 4 2 9 1 7 2 3 2 2  3  8  6  2  2  1  6  3  2  2  2
#> 6 subject_NDAR_INV1HLGR738 4 2 9 1 7 2 3 2 2  1  8  6  2  2  1  6  3  2  2  2

Identifying and visualizing meta clusters

Now that we have access to 20 different clustering solutions, we’ll need to find some way to pick an optimal one to move forward with for additional characterization. In this case, plotting or running stats manually on each of the solutions might be a reasonable way to determine which ones we like the most. But when the number of solutions generated goes up into the hundreds (or thousands), we’re going to need some more automated approaches.

The main approach we recommend using is the meta clustering approach described in Caruana et al., 2016. Meta clustering is a good approach to use when the criterion for what makes one cluster solution better than another is hard to formalize quantitatively (and hence, hard to fully automate).

The idea is to cluster the clustering solutions themselves to arrive at a manageable number of qualitatively similar meta clusters. From there, characterization of representative solutions from each meta cluster can be done to efficiently identify the top choice.

The first step is to calculate the adjusted Rand index (ARI) between each pair of cluster solutions. This metric tells us how similar the solutions are to each other, thereby allowing us to find clusters of cluster solutions.

solutions_matrix_aris <- calc_aris(solutions_matrix)

We can visualize the resulting inter-cluster similarities with a heatmap. First, call get_matrix_order to get a hierarchical clustering-based ordering of the rows in the adjusted rand indices.

meta_cluster_order <- get_matrix_order(solutions_matrix_aris)

# Just a vector of numbers
meta_cluster_order
#>  [1] 10 19  6 13  3 18  5 12  7 17 20  4 15  9  2 14  1  8 11 16

This order can be passed into the adjusted_rand_index_heatmap function to get a clearer view of existing meta clusters.

ari_hm <- adjusted_rand_index_heatmap(
    solutions_matrix_aris,
    order = meta_cluster_order
)

save_heatmap(
    heatmap = ari_hm,
    path = "./adjusted_rand_index_heatmap.png",
    width = 330,
    height = 300,
    res = 100
)

The clustering solutions are along the rows and columns of the above figure, and the cells at the intersection between two solutions show how similar (big ARI) those solutions are to each other. The diagonals should always be red, representing the maximum value of 1, as they show the similarity between any clustering solution and itself. Complete-linkage, Euclidean-distance based hierarchical clustering is being applied to these solutions to obtain the row ordering. This is also the default approach used by the ComplexHeatmap package, the backbone of all heatmap functions in metasnf.

This heatmap is integral to understanding what meta clusters exist in your data (given the space of parameters you explored in the settings matrix). We will later see how to further customize this heatmap to add in rich information about how each plotted cluster solution differs on various measures of quality, different clustering settings, and different levels of separation on input and out-of-model measures.

First, we’ll divide the heatmap into meta clusters by visual inspection. The indices of our meta cluster boundaries can be passed into the adjusted_rand_index_heatmap function as the split_vector parameter. You can determine this vector through trial and error or by using the shiny_annotator function (a wrapper around functionality from the InteractiveComplexHeatmap package).

shiny_annotator(ari_hm)

A demonstration of the shiny app can be seen here: Meta Cluster Identification

Note that while the shiny app is running, your R console will be unresponsive.

Clicking on cell boundaries and tracking the row/column indices (printed to the R console as well as displayed in the app) can get us results looking something like this:

split_vec <- c(2, 5, 12, 17)

ari_mc_hm <- adjusted_rand_index_heatmap(
    solutions_matrix_aris,
    order = meta_cluster_order,
    split_vector = split_vec
)

save_heatmap(
    heatmap = ari_mc_hm,
    path = "./ari_mc_hm.png",
    width = 330,
    height = 300,
    res = 100
)

At this point, we have our meta clusters but are not yet sure of how they differ in terms of their structure across our input and out-of-model features.

Characterizing cluster solutions

Calculating associations between cluster solutions and initial data

We start by running the extend_solutions function, which will calculate p-values representing the strength of the association between cluster membership (treated as a categorical feature) and any feature present in a provided data list and/or target_list.

extend_solutions also adds summary p-value measures (min, mean, and max) of any features present in the target list.

# Only looking at our out-of-model p-values
extended_solutions_matrix <- extend_solutions(
    solutions_matrix,
    target_list = target_list
)

# What columns have been added?
old_cols <- colnames(extended_solutions_matrix) %in% colnames(solutions_matrix)
new_cols <- !old_cols

head(extended_solutions_matrix[, new_cols])
#>   cbcl_anxiety_r_pval cbcl_depress_r_pval  min_pval mean_pval  max_pval
#> 1           0.7344315           0.7263495 0.7263495 0.7303905 0.7344315
#> 2           0.6644469           0.3238038 0.3238038 0.4941253 0.6644469
#> 3           0.3961268           0.6817113 0.3961268 0.5389191 0.6817113
#> 4           0.4843825           0.7564136 0.4843825 0.6203981 0.7564136
#> 5           0.2256718           0.7895325 0.2256718 0.5076021 0.7895325
#> 6           0.2566391           0.1324778 0.1324778 0.1945585 0.2566391

# Re-running to calculate the p-value for every single input and out-of-model
# feature:
extended_solutions_matrix <- extend_solutions(
    solutions_matrix,
    data_list = data_list,
    target_list = target_list
)

Functionally, the only difference between the data_list and target_list arguments are that the target_list features will also be a part of those summary measures.

# Also would work, but without any summary p-values
extended_solutions_matrix <- extend_solutions(
    solutions_matrix,
    data_list = c(data_list, target_list)
)

# Also would work, but now every feature would be part of the summaries
extended_solutions_matrix <- extend_solutions(
    solutions_matrix,
    target_list = c(data_list, target_list)
)

The summary p-value measures can be suppressed by setting calculate_summaries = FALSE.

Visualizing feature associations with meta clustering results

This extended_solutions_matrix we created can be passed into the adjusted_rand_index_heatmap function to easily visualize the level of separation on each of our features for each of our cluster solutions.

annotated_ari_hm <- adjusted_rand_index_heatmap(
    solutions_matrix_aris,
    order = meta_cluster_order,
    split_vector = split_vec,
    data = extended_solutions_matrix,
    top_hm = list(
        "Depression p-value" = "cbcl_depress_r_pval",
        "Anxiety p-value" = "cbcl_anxiety_r_pval",
        "Overall outcomes p-value" = "mean_pval"
    ),
    bottom_bar = list(
        "Number of Clusters" = "nclust"
    ),
    annotation_colours = list(
        "Depression p-value" = colour_scale(
            extended_solutions_matrix$"cbcl_depress_r_pval",
            min_colour = "purple",
            max_colour = "black"
        ),
        "Anxiety p-value" = colour_scale(
            extended_solutions_matrix$"cbcl_anxiety_r_pval",
            min_colour = "green",
            max_colour = "black"
        ),
        "Overall outcomes p-value" = colour_scale(
            extended_solutions_matrix$"mean_pval",
            min_colour = "lightblue",
            max_colour = "black"
        )
    )
)

save_heatmap(
    heatmap = annotated_ari_hm,
    path = "./annotated_ari_hm.png",
    width = 700,
    height = 500,
    res = 100
)

The adjusted_rand_index_heatmap function wraps around a more generic similarity_matrix_heatmap function in this package, which itself is a wrapper around ComplexHeatmap::Heatmap(). Consequently, anything that can be done in the ComplexHeatmap package can be done here. This also makes the documentation for the ComplexHeatmap package one of the best places to learn more about what can be done for these heatmaps.

The data for the annotations don’t necessarily need to come from functions in metasnf either. If you wanted to, for example, highlight the solutions where two very specific observations happened to cluster together, you could easily add that in as another annotation:

extended_solutions_matrix2 <- extended_solutions_matrix |>
    dplyr::mutate(
        key_subjects_cluster_together = dplyr::case_when(
            subject_NDAR_INVLF3TNDUZ == subject_NDAR_INVLDQH8ATK ~ TRUE,
            TRUE ~ FALSE
        )
    )

annotated_ari_hm2 <- adjusted_rand_index_heatmap(
    solutions_matrix_aris,
    order = meta_cluster_order,
    split_vector = split_vec,
    data = extended_solutions_matrix2,
    top_hm = list(
        "Depression p-value" = "cbcl_depress_r_pval",
        "Anxiety p-value" = "cbcl_anxiety_r_pval",
        "Key Subjects Clustered Together" = "key_subjects_cluster_together"
    ),
    bottom_bar = list(
        "Number of Clusters" = "nclust"
    ),
    annotation_colours = list(
        "Depression p-value" = colour_scale(
            extended_solutions_matrix$"cbcl_depress_r_pval",
            min_colour = "purple",
            max_colour = "black"
        ),
        "Anxiety p-value" = colour_scale(
            extended_solutions_matrix$"cbcl_anxiety_r_pval",
            min_colour = "purple",
            max_colour = "black"
        ),
        "Key Subjects Clustered Together" = c(
            "TRUE" = "blue",
            "FALSE" = "black"
        )
    )
)

save_heatmap(
    heatmap = annotated_ari_hm2,
    path = "./annotated_ari_hm2.png",
    width = 700,
    height = 500,
    res = 100
)

Characterizing individual solutions representative of each meta cluster

Now that we’ve visually delineated our meta clusters, we can get a quick summary of what sort of separation exists across our input and held out features by taking a closer look at one representative cluster solution from each meta cluster.

This can be achieved by the get_representative_solutions function, which extracts one cluster solution per meta cluster based on having the highest average ARI with the other solutions in that meta cluster.

rep_solutions <- get_representative_solutions(
    solutions_matrix_aris,
    split_vector = split_vec,
    order = meta_cluster_order,
    extended_solutions_matrix
)

mc_manhattan <- mc_manhattan_plot(
    rep_solutions,
    data_list = data_list,
    target_list = target_list,
    hide_x_labels = TRUE,
    point_size = 2,
    text_size = 12,
    threshold = 0.05,
    neg_log_pval_thresh = 5
)

ggplot2::ggsave(
    "mc_manhattan.png",
    mc_manhattan,
    height = 4,
    width = 8,
    dpi = 100
)

neg_log_pval_thresh sets a threshold for the negative log of the p-values to be displayed. At a value of 5, any p-value that is smaller than 1e-5 will be truncated to 1e-5.

The plot as it is is a bit unwieldy plot given how many neuroimaging ROIs are present. Let’s take out the cortical thickness and surface area measures to make the plot a little clearer.

We’ll also be able to read some feature measures more clearly when we dial the number of features plotted back a bit, as well.

rep_solutions_no_cort <- dplyr::select(
    rep_solutions,
    -dplyr::contains("mrisdp")
)

mc_manhattan2 <- mc_manhattan_plot(
    rep_solutions_no_cort,
    data_list = data_list,
    target_list = target_list,
    point_size = 4,
    threshold = 0.01,
    text_size = 12,
    domain_colours = c(
        "neuroimaging" = "cadetblue",
        "demographics" = "purple",
        "behaviour" = "firebrick"
    )
)
mc_manhattan2

ggplot2::ggsave(
    "mc_manhattan2.png",
    mc_manhattan2,
    height = 8,
    width = 12,
    dpi = 100
)

Note that the Manhattan plot automatically uses a vertical line to separate features in the data_list argument from those in the target_list. Vertical boundaries can be controlled with the xints parameter.

Relating results to metasnf hyperparameters

If you see something interesting in your heatmap, you may be curious to know how that corresponds to the settings that were in your settings matrix.

You could certainly stack on each setting to the ARI heatmap as annotations, but that may be a bit cumbersome given how many settings there are. Another option is to start by taking a first look at entire settings_matrix, sorted by the meta cluster results, through the settings_matrix_heatmap function.

sm_hm <- settings_matrix_heatmap(
    settings_matrix,
    order = meta_cluster_order
)

save_heatmap(
    heatmap = sm_hm,
    path = "./settings_matrix_heatmap_ordered.png",
    width = 400,
    height = 500,
    res = 75
)

This heatmap rescales all the columns in the settings_matrix to have a maximum value of 1. The purpose of re-ordering the settings matrix in this way is to see if any associations exist between certain settings values and pairwise cluster solution similarities. If there are any particular important settings, you can simply add them into your adjusted rand index heatmap annotations. Recall that the solutions_matrix (and, by extension, the extended_solutions_matrix) is an extension of the settings matrix, so no further data manipulation is needed to add a setting as a heatmap annotation.

Give it a try with the code below:

annotated_ari_hm3 <- adjusted_rand_index_heatmap(
    solutions_matrix_aris,
    order = meta_cluster_order,
    split_vector = c(11, 14),
    data = extended_solutions_matrix,
    top_hm = list(
        "Depression p-value" = "cbcl_depress_r_pval",
        "Anxiety p-value" = "cbcl_anxiety_r_pval",
        "Key Subjects Clustered Together" = "key_subjects_cluster_together"
    ),
    left_hm = list(
        "Clustering Algorithm" = "clust_alg" # from the original settings
    ),
    bottom_bar = list(
        "Number of Clusters" = "nclust" # also from the original settings
    ),
    annotation_colours = list(
        "Depression p-value" = colour_scale(
            extended_solutions_matrix$"cbcl_depress_r_pval",
            min_colour = "purple",
            max_colour = "black"
        ),
        "Anxiety p-value" = colour_scale(
            extended_solutions_matrix$"cbcl_anxiety_r_pval",
            min_colour = "purple",
            max_colour = "black"
        ),
        "Key Subjects Clustered Together" = c(
            "TRUE" = "blue",
            "FALSE" = "black"
        )
    )
)

Quality measures

Quality metrics are another useful heuristic for the goodness of a cluster that don’t require any contextualization of results in the domain they may be used in. metasnf enables measures of silhouette scores, Dunn indices, and Davies-Bouldin indices. To calculate these values, we’ll need not only the cluster results but also the final fused network (the similarity matrices produced by SNF) that the clusters came from. These similarity matrices can be collected from the batch_snf using the return_similarity_matrices parameter:

batch_snf_results <- batch_snf(
    data_list,
    settings_matrix,
    return_similarity_matrices = TRUE
)

solutions_matrix <- batch_snf_results$"solutions_matrix"
similarity_matrices <- batch_snf_results$"similarity_matrices"

This time, the output of batch_snf is a list. The first element of the list is a single solutions_matrix, like what we usually get. The second element is yet another list containing one final fused network (AKA similarity matrix / similarity matrix) per SNF run. Using those two lists, we can calculate the above mentioned quality metrics:

silhouette_scores <- calculate_silhouettes(
    solutions_matrix,
    similarity_matrices
)

dunn_indices <- calculate_dunn_indices(
    solutions_matrix,
    similarity_matrices
)

db_indices <- calculate_db_indices(
    solutions_matrix,
    similarity_matrices
)

The first function is a wrapper around cluster::silhouette while the second and third come from the clv package. clv isn’t set as a mandatory part of the installation, so you’ll ned to install it yourself to calculate these two metrics.

The original documentation on these functions can be helpful for interpreting and working with them:

1. cluster::silhouette documentation
2. clv::clv.Dunn documentation
3. clv::clv.Davies.Bouldin documentation

Stability measures

metasnf offers tools to evaluate two different measures of stability:

1. Pairwise adjusted Rand indices (across resamplings of the clustering, on average, how similar was every pair of solutions according to the adjusted Rand index?)
2. Fraction clustered together (what is the average fraction of times that observations who clustered together in the full results clustered together in resampled results?)

You can learn more about running stability calculations in the stability and coclustering vignette.

Evaluating separation across “target features” of importance

If you can specify a metric or objective function that may tell you how useful a clustering solution will be for your purposes in advance, that makes the cluster selection process much less arbitrary.

There are many ways to go about doing this, but this package offers one way through a target_list. The target_list contains dataframes what we can examine our clustering results over through linear regression (continuous data), ordinal regression (ordinal data), or the Chi-squared test (categorical data).

Just like when generating the initial data_list, we need to specify the name of the column in the provided dataframes that is originally being used to uniquely identify the different observations from each other with the uid parameter.

We will next extend our solutions_matrix with p-values from regressing the target_list features onto our generated clusters.

extended_solutions_matrix <- extend_solutions(solutions_matrix, target_list)

colnames(extended_solutions_matrix)[1:25]
#>  [1] "row_id"                    "alpha"                    
#>  [3] "k"                         "t"                        
#>  [5] "snf_scheme"                "clust_alg"                
#>  [7] "cont_dist"                 "disc_dist"                
#>  [9] "ord_dist"                  "cat_dist"                 
#> [11] "mix_dist"                  "inc_cortical_thickness"   
#> [13] "inc_cortical_surface_area" "inc_subcortical_volume"   
#> [15] "inc_household_income"      "inc_pubertal_status"      
#> [17] "nclust"                    "subject_NDAR_INV0567T2Y9" 
#> [19] "subject_NDAR_INV0J4PYA5F"  "subject_NDAR_INV10OMKVLE" 
#> [21] "subject_NDAR_INV15FPCW4O"  "subject_NDAR_INV19NB4RJK" 
#> [23] "subject_NDAR_INV1HLGR738"  "subject_NDAR_INV1KR0EZFU" 
#> [25] "subject_NDAR_INV1L3Y9EOP"

# Looking at the newly added columns
head(no_subs(extended_solutions_matrix))
#>   row_id alpha  k  t snf_scheme clust_alg cont_dist disc_dist ord_dist cat_dist
#> 1      1   0.5 29 20          2         1         1         1        1        1
#> 2      2   0.4 26 20          1         1         1         1        1        1
#> 3      3   0.3 44 20          2         2         1         1        1        1
#> 4      4   0.3 43 20          1         1         1         1        1        1
#> 5      5   0.5 29 20          2         2         1         1        1        1
#> 6      6   0.4 26 20          2         1         1         1        1        1
#>   mix_dist inc_cortical_thickness inc_cortical_surface_area
#> 1        1                      1                         0
#> 2        1                      1                         1
#> 3        1                      1                         0
#> 4        1                      1                         1
#> 5        1                      1                         1
#> 6        1                      1                         1
#>   inc_subcortical_volume inc_household_income inc_pubertal_status nclust
#> 1                      1                    0                   1      5
#> 2                      1                    1                   1      3
#> 3                      0                    1                   1      9
#> 4                      0                    1                   1      2
#> 5                      1                    1                   1      8
#> 6                      1                    1                   1      2
#>   cbcl_anxiety_r_pval cbcl_depress_r_pval  min_pval mean_pval  max_pval
#> 1           0.7344315           0.7263495 0.7263495 0.7303905 0.7344315
#> 2           0.6644469           0.3238038 0.3238038 0.4941253 0.6644469
#> 3           0.3961268           0.6817113 0.3961268 0.5389191 0.6817113
#> 4           0.4843825           0.7564136 0.4843825 0.6203981 0.7564136
#> 5           0.2256718           0.7895325 0.2256718 0.5076021 0.7895325
#> 6           0.2566391           0.1324778 0.1324778 0.1945585 0.2566391

If you just want the p-values:

target_pvals <- get_pvals(extended_solutions_matrix)

head(target_pvals)
#>   row_id cbcl_anxiety_r_pval cbcl_depress_r_pval  min_pval mean_pval  max_pval
#> 1      1           0.7344315           0.7263495 0.7263495 0.7303905 0.7344315
#> 2      2           0.6644469           0.3238038 0.3238038 0.4941253 0.6644469
#> 3      3           0.3961268           0.6817113 0.3961268 0.5389191 0.6817113
#> 4      4           0.4843825           0.7564136 0.4843825 0.6203981 0.7564136
#> 5      5           0.2256718           0.7895325 0.2256718 0.5076021 0.7895325
#> 6      6           0.2566391           0.1324778 0.1324778 0.1945585 0.2566391

There is a heatmap for visualizing this too:

pval_hm <- pval_heatmap(target_pvals, order = meta_cluster_order)

save_heatmap(
    heatmap = pval_hm,
    path = "./pval_heatmap_ordered.png",
    width = 400,
    height = 500,
    res = 100
)

These p-values hold no real meaning for the traditional hypothesis-testing context, but they are reasonable proxies of the magnitude of the effect size / separation of the clusters across the features in question. Here, they are just a tool to find clustering solutions that are well-separated according to the outcome measures you’ve specified. Finding a cluster solution like this is similar to a supervised learning approach, but where the optimization method is just random sampling. The risk for overfitting your data with this approach is considerable, so make sure you have some rigorous external validation before reporting your findings.

We recommend using label propagation (provided by the SNFtool package in the groupPredict function) for validation: take the top clustering solutions found in some training data, assign predicted clusters to some held out test subjects, and then characterize those test subjects to see how well the clustering solution seemed to have worked.

Validating results with label propagation

Here’s a quick step through of the complete procedure, from the beginning, with label propagation to validate our findings.

The metasnf package comes equipped with a function to do the training/testing split for you :)

# All the subjects present in all dataframes with no NAs
all_subjects <- data_list[[1]]$"data"$"subjectkey"

# Remove the "subject_" prefix to allow merges with the original data
all_subjects <- gsub("subject_", "", all_subjects)

# Dataframe assigning 80% of subjects to train and 20% to test
assigned_splits <- train_test_assign(train_frac = 0.8, subjects = all_subjects)

# Pulling the training and testing subjects specifically
train_subs <- assigned_splits$"train"
test_subs <- assigned_splits$"test"

# Partition a training set
train_cort_t <- cort_t[cort_t$"unique_id" %in% train_subs, ]
train_cort_sa <- cort_sa[cort_sa$"unique_id" %in% train_subs, ]
train_subc_v <- subc_v[subc_v$"unique_id" %in% train_subs, ]
train_income <- income[income$"unique_id" %in% train_subs, ]
train_pubertal <- pubertal[pubertal$"unique_id" %in% train_subs, ]
train_anxiety <- anxiety[anxiety$"unique_id" %in% train_subs, ]
train_depress <- depress[depress$"unique_id" %in% train_subs, ]

# Partition a test set
test_cort_t <- cort_t[cort_t$"unique_id" %in% test_subs, ]
test_cort_sa <- cort_sa[cort_sa$"unique_id" %in% test_subs, ]
test_subc_v <- subc_v[subc_v$"unique_id" %in% test_subs, ]
test_income <- income[income$"unique_id" %in% test_subs, ]
test_pubertal <- pubertal[pubertal$"unique_id" %in% test_subs, ]
test_anxiety <- anxiety[anxiety$"unique_id" %in% test_subs, ]
test_depress <- depress[depress$"unique_id" %in% test_subs, ]

# A data list with just training subjects
train_data_list <- generate_data_list(
    list(train_cort_t, "cortical_thickness", "neuroimaging", "continuous"),
    list(train_cort_sa, "cortical_sa", "neuroimaging", "continuous"),
    list(train_subc_v, "subcortical_volume", "neuroimaging", "continuous"),
    list(train_income, "household_income", "demographics", "continuous"),
    list(train_pubertal, "pubertal_status", "demographics", "continuous"),
    uid = "unique_id"
)

# A data list with training and testing subjects
full_data_list <- generate_data_list(
    list(cort_t, "cortical_thickness", "neuroimaging", "continuous"),
    list(cort_sa, "cortical_surface_area", "neuroimaging", "continuous"),
    list(subc_v, "subcortical_volume", "neuroimaging", "continuous"),
    list(income, "household_income", "demographics", "continuous"),
    list(pubertal, "pubertal_status", "demographics", "continuous"),
    uid = "unique_id"
)

# Construct the target lists
train_target_list <- generate_data_list(
    list(train_anxiety, "anxiety", "behaviour", "ordinal"),
    list(train_depress, "depressed", "behaviour", "ordinal"),
    uid = "unique_id"
)

# Find a clustering solution in your training data
set.seed(42)
settings_matrix <- generate_settings_matrix(
    train_data_list,
    nrow = 5,
    min_k = 10,
    max_k = 30
)

train_solutions_matrix <- batch_snf(
    train_data_list,
    settings_matrix
)

extended_solutions_matrix <- extend_solutions(
    train_solutions_matrix,
    train_target_list
)

extended_solutions_matrix |> colnames()
#>  [1] "row_id"                   "alpha"                   
#>  [3] "k"                        "t"                       
#>  [5] "snf_scheme"               "clust_alg"               
#>  [7] "cont_dist"                "disc_dist"               
#>  [9] "ord_dist"                 "cat_dist"                
#> [11] "mix_dist"                 "inc_cortical_thickness"  
#> [13] "inc_cortical_sa"          "inc_subcortical_volume"  
#> [15] "inc_household_income"     "inc_pubertal_status"     
#> [17] "nclust"                   "subject_NDAR_INV0567T2Y9"
#> [19] "subject_NDAR_INV0J4PYA5F" "subject_NDAR_INV10OMKVLE"
#> [21] "subject_NDAR_INV15FPCW4O" "subject_NDAR_INV19NB4RJK"
#> [23] "subject_NDAR_INV1HLGR738" "subject_NDAR_INV1KR0EZFU"
#> [25] "subject_NDAR_INV1L3Y9EOP" "subject_NDAR_INV1ZHRDJ6B"
#> [27] "subject_NDAR_INV2PK6C85M" "subject_NDAR_INV2XO1PHCT"
#> [29] "subject_NDAR_INV3CU5Y9BZ" "subject_NDAR_INV3MBSY16V"
#> [31] "subject_NDAR_INV3N0QFDLO" "subject_NDAR_INV3Y027GVK"
#> [33] "subject_NDAR_INV40Z7GVYJ" "subject_NDAR_INV49UPOXHJ"
#> [35] "subject_NDAR_INV4N5XGZE8" "subject_NDAR_INV4OWRB536"
#> [37] "subject_NDAR_INV4X80QUZY" "subject_NDAR_INV50JL2RXP"
#> [39] "subject_NDAR_INV5BRNFYQC" "subject_NDAR_INV6RVH5KZS"
#> [41] "subject_NDAR_INV6WBQCY2I" "subject_NDAR_INV752EFAQ0"
#> [43] "subject_NDAR_INV7QO93CJH" "subject_NDAR_INV84G9ONXP"
#> [45] "subject_NDAR_INV8EHP6W1U" "subject_NDAR_INV8MJFUKIW"
#> [47] "subject_NDAR_INV8WGK6ECZ" "subject_NDAR_INV94AKNGMJ"
#> [49] "subject_NDAR_INV9GAZYV8Q" "subject_NDAR_INV9IREH05N"
#> [51] "subject_NDAR_INV9KC3GVMU" "subject_NDAR_INV9NFKZ82A"
#> [53] "subject_NDAR_INV9S1BMDE5" "subject_NDAR_INVA68OU0YK"
#> [55] "subject_NDAR_INVADCYZ38B" "subject_NDAR_INVAYM8WTIN"
#> [57] "subject_NDAR_INVB8O4LAQV" "subject_NDAR_INVBAP80W1R"
#> [59] "subject_NDAR_INVBTRW1NUK" "subject_NDAR_INVCIXE0496"
#> [61] "subject_NDAR_INVCYBSZD0N" "subject_NDAR_INVD37Z9N61"
#> [63] "subject_NDAR_INVD61ZUBC7" "subject_NDAR_INVEQ1OBNSM"
#> [65] "subject_NDAR_INVEVBDLSTM" "subject_NDAR_INVEY0FMJDI"
#> [67] "subject_NDAR_INVFLU0YINE" "subject_NDAR_INVFNZPWMSI"
#> [69] "subject_NDAR_INVFY76P8AJ" "subject_NDAR_INVG3T0PXW6"
#> [71] "subject_NDAR_INVG8BRLSO9" "subject_NDAR_INVH1KV76BQ"
#> [73] "subject_NDAR_INVH3P4T8C2" "subject_NDAR_INVH4FZC2XB"
#> [75] "subject_NDAR_INVH8QN7WLT" "subject_NDAR_INVHERPS382"
#> [77] "subject_NDAR_INVHM3XS68O" "subject_NDAR_INVI1RKT9MX"
#> [79] "subject_NDAR_INVIZFV08RU" "subject_NDAR_INVJ574KX6A"
#> [81] "subject_NDAR_INVK3FL5CP2" "subject_NDAR_INVKB0CYO1H"
#> [83] "subject_NDAR_INVKHWS26UN" "subject_NDAR_INVKTUMPLXY"
#> [85] "subject_NDAR_INVL4NIUZYF" "subject_NDAR_INVLF3TNDUZ"
#> [87] "subject_NDAR_INVLI58ERQC" "subject_NDAR_INVLIQRM8KC"
#> [89] "subject_NDAR_INVLXDP1SWT" "subject_NDAR_INVMBOZVEA4"
#> [91] "subject_NDAR_INVMIWOSHJN" "cbcl_anxiety_r_pval"     
#> [93] "cbcl_depress_r_pval"      "min_pval"                
#> [95] "mean_pval"                "max_pval"

# The fifth row had the lowest minimum p-value across our outcomes
lowest_min_pval <- min(extended_solutions_matrix$"min_pval")
which(extended_solutions_matrix$"min_pval" == lowest_min_pval)
#> [1] 1

# Keep track of your top solution
top_row <- extended_solutions_matrix[4, ]

# Use the solutions matrix from the training subjects and the data list from
# the training and testing subjects to propagate labels to the test subjects
propagated_labels <- lp_solutions_matrix(top_row, full_data_list)

head(propagated_labels)
#>                 subjectkey group 4
#> 1 subject_NDAR_INV0567T2Y9 train 1
#> 2 subject_NDAR_INV0J4PYA5F train 1
#> 3 subject_NDAR_INV10OMKVLE train 2
#> 4 subject_NDAR_INV15FPCW4O train 1
#> 5 subject_NDAR_INV19NB4RJK train 2
#> 6 subject_NDAR_INV1HLGR738 train 1
tail(propagated_labels)
#>                  subjectkey group 4
#> 82 subject_NDAR_INVG5CI7XK4  test 1
#> 83 subject_NDAR_INVGDBYXWV4  test 1
#> 84 subject_NDAR_INVHEUWA52I  test 2
#> 85 subject_NDAR_INVK9ULDQA2  test 1
#> 86 subject_NDAR_INVKYH529RD  test 1
#> 87 subject_NDAR_INVLDQH8ATK  test 2

You could, if you wanted, see how all of your clustering solutions propagate to the test set, but that would mean reusing your test set and removing the protection against overfitting conferred by this procedure.

propagated_labels_all <- lp_solutions_matrix(
    extended_solutions_matrix,
    full_data_list
)

head(propagated_labels_all)
#>                 subjectkey group 1 2 3 4  5
#> 1 subject_NDAR_INV0567T2Y9 train 1 1 5 1 10
#> 2 subject_NDAR_INV0J4PYA5F train 2 1 5 1  3
#> 3 subject_NDAR_INV10OMKVLE train 1 1 3 2  5
#> 4 subject_NDAR_INV15FPCW4O train 1 1 4 1  4
#> 5 subject_NDAR_INV19NB4RJK train 1 1 8 2  9
#> 6 subject_NDAR_INV1HLGR738 train 1 2 8 1  9
tail(propagated_labels_all)
#>                  subjectkey group 1 2 3 4 5
#> 82 subject_NDAR_INVG5CI7XK4  test 1 1 2 1 2
#> 83 subject_NDAR_INVGDBYXWV4  test 1 1 4 1 4
#> 84 subject_NDAR_INVHEUWA52I  test 2 1 1 2 1
#> 85 subject_NDAR_INVK9ULDQA2  test 1 1 1 1 1
#> 86 subject_NDAR_INVKYH529RD  test 1 1 7 1 7
#> 87 subject_NDAR_INVLDQH8ATK  test 1 1 6 2 8

That’s all!

If you have any questions, comments, suggestions, bugs, etc. feel free to post an issue at https://github.com/BRANCHlab/metasnf.

References

Caruana, Rich, Mohamed Elhawary, Nam Nguyen, and Casey Smith. 2006. “Meta Clustering.” In Sixth International Conference on Data Mining (ICDM’06), 107–18. https://doi.org/10.1109/ICDM.2006.103.

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.