# A Simple Example

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

In this vignette, we will show how `metasnf` can be used for a very simple SNF workflow.

This simple workflow is the example of SNF provided in the original SNFtool package. You can find the example by loading the SNFtool package and then viewing the documentation for the main SNF function by running `?SNF`.

## The original SNF example

### 1. Load the package

    library(SNFtool)

### 2. Set SNF hyperparameters

Three hyperparameters are introduced in this example: K, alpha (also referred to as sigma or eta in different documentations), and T. You can learn more about the significance of these hyperparameters in the original SNF paper (see references).

    K <- 20
    alpha <- 0.5
    T <- 20

### 3. Load the data

The SNFtool package provides two mock data frames titled Data1 and Data2 for this example. Data1 contains gene expression values of two genes for 200 patients. Data2 similarly contains methylation data for two genes for those same 200 patients.

    data(Data1)
    data(Data2)

Here’s what the mock data looks like:

    library(ComplexHeatmap)

    # gene expression data
    gene_expression_hm <- Heatmap(
        as.matrix(Data1),
        cluster_rows = FALSE,
        cluster_columns = FALSE,
        show_row_names = FALSE,
        show_column_names = FALSE,
        heatmap_legend_param = list(
            title = "Gene Expression"
        )
    )

    gene_expression_hm

Heatmap of gene expression values.

    # methylation data
    methylation_hm <- Heatmap(
        as.matrix(Data2),
        cluster_rows = FALSE,
        cluster_columns = FALSE,
        show_row_names = FALSE,
        show_column_names = FALSE,
        heatmap_legend_param = list(
            title = "Methylation"
        )
    )

    methylation_hm

Heatmap of methylation values.

The “ground truth” of how this data was generated was that patients 1 to 100 were drawn from one distribution and patients 101 to 200 were drawn from another. We don’t have access to that kind of knowledge in real data, but we do here.

    true_label <- c(matrix(1, 100, 1), matrix(2, 100, 1))

### 4. Generate similarity matrices for each data source

We consider the two gene expression features in Data1 to contain information from one broader gene expression source and the two methylation features in Data2 to contain information from a broader methylation source.

The next step is to determine, for each of the sources we have, how similar all of our patients are to each other.

This is done by first determining how dissimilar the patients are to each other for each source, and then converting that dissimilarity information into similarity information.

To calculate dissimilarity, we’ll use Euclidean distance.

    distance_matrix_1 <- as.matrix(dist(Data1, method = "euclidean"))
    distance_matrix_2 <- as.matrix(dist(Data2, method = "euclidean"))

Then, we can use the `affinityMatrix` function provided by SNFtool to convert those distance matrices into similarity matrices.

    similarity_matrix_1 <- affinityMatrix(distance_matrix_1, K, alpha)
    similarity_matrix_2 <- affinityMatrix(distance_matrix_2, K, alpha)

Those similarity matrices can be passed into the `SNF` function to integrate them into a single similarity matrix that describes how similar the patients are to each other across both the gene expression and methylation data.

### 5. Integrate similarity matrices with SNF

    fused_network <- SNF(list(similarity_matrix_1, similarity_matrix_2), K, T)

### 6. Find clusters in the integrated matrix

If we think there are 2 clusters in the data, we can use spectral clustering to find 2 clusters in the fused network.

    number_of_clusters <- 2
    assigned_clusters <- spectralClustering(fused_network, number_of_clusters)

Sure enough, we are able to obtain the correct cluster label for all patients.

    all(true_label == assigned_clusters)
    #> [1] TRUE

## The same example using metasnf

The purpose of `metasnf` is primarily to aid users explore a wide possible range of solutions. Recreating the example provided with the original `SNF` function will be an extremely restricted usage of the package, but will reveal, broadly, how `metasnf` works.

### 1. Load the package

    library(metasnf)

### 2. Store the data in a data list

Data used for clustering will be stored in a `data_list` class object. The data list is made by passing each data frame into the `data_list()` function, alongside information about the name of the data frame, the broader source (referred to in this package as a “domain”) of information that data frame comes from, and the type of features that are stored inside that data frame (can be continuous, discrete, ordinal, categorical, or mixed). The `data_list()` function also requires you to specify which column contains information about the ID of the patients. In this case, that information isn’t there, so we’ll have to add it ourselves. The added IDs span from 101 onwards (rather than from 1 onwards) purely for convenience: automatic sorting of patient names won’t result in patient 199 being placed before patient 2.

    # Add "patient_id" column to each data frame
    Data1$"patient_id" <- 101:(nrow(Data1) + 100)
    Data2$"patient_id" <- 101:(nrow(Data2) + 100)

    my_dl <- data_list(
        list(
            data = Data1,
            name = "genes_1_and_2_exp",
            domain = "gene_expression",
            type = "continuous"
        ),
        list(
            data = Data2,
            name = "genes_1_and_2_meth",
            domain = "gene_methylation",
            type = "continuous"
        ),
        uid = "patient_id"
    )

The entries are lists which contain the following elements:

1. The data frame
2. A user-determined name for the data frame (character)
3. A user-determined name for the domain of information the data frame is representative of (character)
4. The type of feature stored in the data frame (character; options are continuous, discrete, ordinal, categorical, and mixed)

Finally, there’s an argument for the `uid` (the column name that currently uniquely identifies all the observations in your data).

In the process of formatting the provided data frames, this function:

- Converts the UID of the data into “uid”
- Prefixing the UID values with the string “uid_” to help with cluster result characterization
- Removes all observations that contain any missing values
- Removes all observations that are not present in all data frames
- Arranges the observations in all data frames by their UID

To avoid losing a considerable amount of data during data list generation, consider using imputation first. The `mice` package in R is helpful for this.

Also note that you do not need to name out every element explicitly; as long as you provide the objects within each list in the correct order (data, name, domain, type), you’ll get the correct result:

    # Compactly:
    my_dl <- 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"
    )

### 3. Store all the settings of the desired SNF runs in an SNF config

The SNF config is an object storing all the information required to convert the raw data into a final cluster solution. It is composed of multiple parts, including a settings data frame which tracks one set of SNF hyperparameters per row, a weights matrix which tracks one set of all the feature weights per row, a distance functions list which stores all the functions that will be uesd to convert raw data into a intermediate distance matrices, and a clustering algorithms list which stores all the functions that will be used to convert final SNF-fused networks into cluster solutions. By varying the elements in the SNF config, we can access a broader space of possible solutions and hopefully get closer to something that will be as useful as possible for our context.

In this case, we’re going to create only a single cluster solution using the same process outlined in the original SNFtool example above.

A full explanation of all the parameters in the `snf_config()` function can be found at the SNF config vignette.

    sc <- snf_config(
        dl = my_dl,
        n_solutions = 1,
        alpha_values = 0.5,
        k_values = 20,
        t_values = 20,
        dropout_dist = "none",
        possible_snf_schemes = 1
    )
    #> ℹ No distance functions specified. Using defaults.
    #> ℹ No clustering functions specified. Using defaults.

    sc
    #> Settings Data Frame:
    #>                         1
    #> SNF hyperparameters:
    #> alpha                 0.5
    #> k                      20
    #> t                      20
    #> SNF scheme:
    #>                         1
    #> Clustering functions:
    #>                         2
    #> Distance functions:
    #> CNT                     1
    #> DSC                     1
    #> ORD                     1
    #> CAT                     1
    #> MIX                     1
    #> Component dropout:
    #> genes_1_and_2_exp       ✔
    #> genes_1_and_2_meth      ✔
    #> Distance Functions List:
    #> Continuous (1):
    #> [1] euclidean_distance
    #> Discrete (1):
    #> [1] euclidean_distance
    #> Ordinal (1):
    #> [1] euclidean_distance
    #> Categorical (1):
    #> [1] gower_distance
    #> Mixed (1):
    #> [1] gower_distance
    #> Clustering Functions List:
    #> [1] spectral_eigen
    #> [2] spectral_rot
    #> Weights Matrix:
    #> Weights defined for 1 cluster solutions.
    #> $ V1  1
    #> $ V2  1
    #> $ V3  1
    #> $ V4  1

We can more clearly examine the settings data frame within the config as follows:

    as.data.frame(sc$"settings_df")
    #>   solution alpha  k  t snf_scheme clust_alg cnt_dist dsc_dist ord_dist cat_dist
    #> 1        1   0.5 20 20          1         2        1        1        1        1
    #>   mix_dist inc_genes_1_and_2_exp inc_genes_1_and_2_meth
    #> 1        1                     1                      1

The columns in this `settings_df`-class object account for the following:

- solution: A way to keep track of the different rows
- alpha, k, t: The hyperparameters seen above
- snf_scheme: Which “scheme” will be used to transform the inputs into a final fused network. We’ll discuss this in more detail in the next vignette.
- clust_alg: Which clustering function from the `clust_fns_list` will be applied to the final fused network. By default, the `clust_fns_list` has index 1 referencing spectral clustering paired with the eigen-gap heuristic determining the number of clusters, while index 2 references spectral clustering paired with the rotation cost heuristic instead.
- Columns ending in “dist”: Which distance metric function from the `dist_fns_list` should be used. By default, the `dist_fns_list` has index 1 referencing simple Euclidean distance for continuous, discrete, and ordinal data, and Gower’s distance for categorical and mixed data.
- Columns starting with “inc”: Component dropout - whether or not the corresponding data frame will be included for this round of SNF.

More detailed descriptions on all of these columns can also be found in the the SNF config vignette.

### 4. Run SNF

The `batch_snf` function will use all of the hyperparameters and functions stored in the SNF config to the create cluster solutions from the `data_list`.

    sol_df <- batch_snf(dl = my_dl, sc = sc)

    sol_df
    #> 1 cluster solution of 200 observations:
    #> solution nclust mc uid_101 uid_102 uid_103 uid_104 uid_105 uid_106 uid_107
    #>        1      2  .       1       1       1       1       1       1       1
    #> 193 observations not shown.
    #> Use `print(n = ...)` to change the number of rows printed.
    #> Use `t()` to view compact cluster solution format.

The solutions data frame (`solutions_df` class object) is a data frame that contains one cluster solution per row. essentially an augmented , where new columns have been added for each included patient. On each row, those new columns show what cluster that patient ended up in.

A friendlier format of the clustering results can be obtained:

    cluster_solution <- t(sol_df)

    cluster_solution
    #> 1 cluster solution of 200 observations:
    #>     uid      s1
    #> uid_101       1
    #> uid_102       1
    #> uid_103       1
    #> uid_104       1
    #> uid_105       1
    #> uid_106       1
    #> uid_107       1
    #> uid_108       1
    #> uid_109       1
    #> uid_110       1
    #> 190 observations not shown.

These cluster results are exactly the same as in the original SNF example:

    all.equal(cluster_solution$"s1", true_label)
    #> [1] TRUE

Running `batch_snf` with the `return_sim_mats` parameter set to `TRUE` will let us also take a look at the final fused networks from SNF rather than just the results of applying spectral clustering to those networks:

    sol_df <- batch_snf(
        dl = my_dl,
        sc,
        return_sim_mats = TRUE
    )

    # The first (and only, in this case) final fused network
    similarity_matrix <- sim_mats_list(sol_df)[[1]]

The fused network obtained through this approach is also the same as the one obtained in the original example:

    max(similarity_matrix - fused_network)
    #> [1] 0

And now we’ve completed a basic example of using this package. The subsequent vignettes provide guidance on how you can leverage the SNF config to access a wide range of clustering solutions from your data, how you can use other tools in this package to pick a best solution for your purposes, and how to validate the generalizability of your results.

Go give the less simple example a try!

## 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.