# Imputations

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

Missing data can be difficult to handle, especially in the context of unsupervised learning. In a supervised setting, multiply imputed datasets can be used to generate pooled estimates of model coefficients.

A somewhat analogous process is demonstrated in the code below. Here, we pretend we’ve generated two different imputations of the data, `dl_imp1` and `dl_imp2`. The mock code below happens to use the base, unimputed data twice for simplicity.

Separate cluster solutions are generated for the two sets of imputed data, which then have their corresponding solutions data frames stacked together and appended with an `imputation` column that indicates which imputed dataset was used to generate that particular cluster solution.

Moving through the rest of the meta clustering pipeline, the influence of the imputation on meta clustering structure or on separation of other features in the data can be easily visualized in the `meta_cluster_heatmap` function through the use of `ComplexHeatmap` annotations.

    library(metasnf)

    # First imputed dataset
    dl_imp1 <- data_list(
        list(subc_v, "subcortical_volume", "neuroimaging", "continuous"),
        list(income, "household_income", "demographics", "continuous"),
        list(pubertal, "pubertal_status", "demographics", "continuous"),
        list(anxiety, "anxiety", "behaviour", "ordinal"),
        list(depress, "depressed", "behaviour", "ordinal"),
        uid = "unique_id"
    )

    # Second imputed dataset
    dl_imp2 <- data_list(
        list(subc_v, "subcortical_volume", "neuroimaging", "continuous"),
        list(income, "household_income", "demographics", "continuous"),
        list(pubertal, "pubertal_status", "demographics", "continuous"),
        list(anxiety, "anxiety", "behaviour", "ordinal"),
        list(depress, "depressed", "behaviour", "ordinal"),
        uid = "unique_id"
    )

    set.seed(42)
    sc <- snf_config(
        dl = dl_imp1,
        n_solutions = 10,
        min_k = 20,
        max_k = 50
    )

    # Generation of 20 cluster solutions
    sol_df_imp1 <- batch_snf(dl_imp1, sc)
    sol_df_imp2 <- batch_snf(dl_imp2, sc)

    nrow(sol_df_imp1)
    nrow(sol_df_imp1)

    # Create a stacked solution matrix that stores solutions from both imputations
    # Solutions 1:10 are for imputation 1, 11:20 are for imputation 2
    sol_df <- rbind(sol_df_imp1, sol_df_imp2, reset_indices = TRUE)

    sol_df

    # Calculate pairwise similarities across all solutions
    # (Including across imputations)
    sol_aris <- calc_aris(sol_df)

    meta_cluster_order <- get_matrix_order(sol_aris)

    # Base heatmap for identifying meta clusters
    ari_hm <- meta_cluster_heatmap(
        sol_aris,
        order = meta_cluster_order
    )

    # Identify meta cluster boundaries
    shiny_annotator(ari_hm)

    split_vec <- c(7, 13)

    ari_mc_hm <- meta_cluster_heatmap(
        sol_aris,
        order = meta_cluster_order,
        split_vector = split_vec
    )

    # Calculate how features are distributed across solutions
    ext_sol_df_imp1 <- extend_solutions(
        sol_df,
        target_dl = dl_imp1
    )

Unfortunately, you will need to commit to one imputation of the data list to actually generate p-values. You could, however, try `extend_solutions` for multiple combinations of imputed data lists to account for this.

    annotation_data <- as.data.frame(ext_sol_df_imp1, keep_attributes = TRUE)
    annotation_data$"imputation" <- c(rep("imp_1", 10), rep("imp_2", 10))

    # Visualize influence of imputation on meta clustering results
    annotated_ari_hm <- meta_cluster_heatmap(
        sol_aris,
        order = meta_cluster_order,
        split_vector = split_vec,
        data = annotation_data,
        top_hm = list(
            "Depression p-value" = "cbcl_depress_r_pval",
            "Anxiety p-value" = "cbcl_anxiety_r_pval"
        ),
        left_hm = list(
            "Imputation" = "imputation"
        ),
        annotation_colours = list(
            "Depression p-value" = colour_scale(
                annotation_data$"cbcl_depress_r_pval",
                min_colour = "purple",
                max_colour = "black"
            ),
            "Anxiety p-value" = colour_scale(
                annotation_data$"cbcl_anxiety_r_pval",
                min_colour = "green",
                max_colour = "black"
            ),
            "Imputation" = c(
                "imp_1" = "orange",
                "imp_2" = "blue"
            )
        )
    )