NIMAA-vignette

1.1 Plot the original data:

Function plotInput() will print the incidence matrix plot of input data, and return that matrix.

NB: To keep the size of vignette small enough for CRAN rules, we won’t output the interactive figure here.

beatAML_incidence_matrix <- plotInput(
  x = beatAML_data, # original data with 3 columns
  index_nominal = c(2,1), # the first two columns are nominal data
  index_numeric = 3,  # the third column inumeric data
  print_skim = FALSE, # if you want to check the skim output, set this as TRUE(Default)
  plot_weight = TRUE, # when plotting the figure, show the weights
  verbose = FALSE # NOT save the figures to local folder
  )

beatAML dataset as incidence matrix

1.2 Plot the bipartite graph of the original data:

Since we have got the incidence matrix, then we can easily use it to form a bipartite graph, in this part we have two different ways to visualize the bipartite graph, static or interactive

graph <- plotBipartite(inc_mat = beatAML_incidence_matrix,vertex.label.display = T)

# show the igraph graph object
graph
#> IGRAPH ad6c4b9 UNWB 650 47636 -- 
#> + attr: name (v/c), type (v/l), shape (v/c), color (v/c), weight (e/n)
#> + edges from ad6c4b9 (vertex names):
#>  [1] Alisertib (MLN8237)      --11-00261 Barasertib (AZD1152-HQPA)--11-00261
#>  [3] Bortezomib (Velcade)     --11-00261 Canertinib (CI-1033)     --11-00261
#>  [5] Crenolanib               --11-00261 CYT387                   --11-00261
#>  [7] Dasatinib                --11-00261 Doramapimod (BIRB 796)   --11-00261
#>  [9] Dovitinib (CHIR-258)     --11-00261 Erlotinib                --11-00261
#> [11] Flavopiridol             --11-00261 GDC-0941                 --11-00261
#> [13] Gefitinib                --11-00261 Go6976                   --11-00261
#> [15] GW-2580                  --11-00261 Idelalisib               --11-00261
#> + ... omitted several edges

plotBipartiteInteractive(inc_mat = beatAML_incidence_matrix)

1.3 Analysis of the network(graph)

analysis_reuslt <- analyseNetwork(graph)

2.1 Extract the sub-matrices without missing data

Here we extract two sub-matrices of the beatAML_incidence_matrix

sub_matrices <- extractSubMatrix(
  x = beatAML_incidence_matrix,
  shape = c("Square", "Rectangular_element_max"), # the shapes wanted
  row.vars = "patient_id",
  col.vars = "inhibitor",
  plot_weight = TRUE,
  verbose = FALSE,
  print_skim = TRUE # just to reduce the length of vignette
  )

We can see that there is an output called binmatnest2.temperature, this is the nestedness measure of the matrix, if the input is a highly nested (nestedness temperature is less than 1). We suggest that divide the data into different parts.

Row-wise arrangement

Column-wise arrangement

3.1 Do clustering based on sub-matrices

First we can do clustering on one part (patient_id), to find the clusters.

cls <- findCluster(
  sub_matrices$Rectangular_element_max,
  dim = 1,
  method = "all", # clustering mehod
  normalization = TRUE, # normalize the input matrix
  rm_weak_edges = TRUE, # remove the weak edges in graph
  rm_method = 'delete', # removing method is deleting the edges
  threshold = 'median', # edges with weights under the median of all edges' weight are weak edges
  set_remaining_to_1 = TRUE, # set the weights of remaining edges to 1
  )

In addition, if there is an input of external features (prior knowledge), the function will also compare the clustering results obtained with external features regard similarity.

For example, let’s generate some random features for patient_id part, here are the samples:

Then we can do clustering again on one part (patient_id) to see the difference.

cls <- findCluster(
  sub_matrices$Rectangular_element_max,
  dim = 1,
  method = "all", # clustering mehod
  normalization = TRUE, # normalize the input matrix
  rm_weak_edges = TRUE, # remove the weak edges in graph
  rm_method = 'delete', # removing method is deleting the edges
  threshold = 'median', # edges with weights under the median of all edges' weight are weak edges
  set_remaining_to_1 = TRUE, # set the weights of remaining edges to 1
  extra_feature =external_feature # ADD A EXTRA FEATURE REFRRENCE HERE!
  )

Some new indices are included (jaccard_similarity, corrected), which showing the similarity between the different clustering results and the reference feature.

We can do clustering on the other part (inhibitors), just need to change the dim to 2.

cls2 <- findCluster(
  sub_matrices$Rectangular_element_max, # the same sub-matrix
  dim = 2 # set to 2 to use the other part of graph
  )

4.1 plotCluster

plotCluster() will output an interactive network figure, in which nodes belonging to the same group will be given the same color, and nodes belonging to different groups will have different colors.

plotCluster(graph=cls2$graph,cluster = cls2$louvain)

4.2 Visualize the clusters in sankey figure format

We use the sankey graph to represent the bipartite graph. The difference is that we group the nodes that belong to the same part and the same group in the two parts as ‘summary’ nodes, and output an interactive figure.

visualClusterInBipartite(
  data = beatAML_data,
  community_left = cls$leading_eigen,
  community_right = cls2$fast_greedy,
  name_left = 'patient_id',
  name_right = 'inhibitor')

Interactive plot for function visualClusterInBipartite()

4.3 Score clusters

When we get a cluster, we can score it, which mainly uses the fpc package, and secondly we will calculate the coverage, which is an indicator obtained from Almeida, Hélio, et al. “Is there a best quality metric for graph clusters?.”, which is a clustering is given as the fraction of the weight of all intra-cluster edges with respect to the total weight of all edges in the whole graph.

scoreCluster(community = cls2$infomap,
             graph = cls2$graph,
             distance_matrix = cls2$distance_matrix)

4.4 Validate clusters

validateCluster() will calculate the similarity of the given clustering result and the reference feature, that is, corrected.rand and jaccard_similarity

validateCluster(dist_mat = cls$distance_matrix,
                extra_feature = external_feature,
                community = cls$leading_eigen)

5.1 impute missing data

The imputeMissingValue() function can impute the missing values in the matrix, we only need to select which methods are needed. The result will be a list, each element is a matrix with no missing values.

it will perform a variety of numerical imputation according to the user’s input, and return all the data that does not contain any missing data, a list of matrices.

• ‘median’ will replace the missing values with the median of each rows(observations)

• ‘knn’ is the method in package

• ‘als’ and ‘svd’ are methods from package

• ‘CA’, ‘PCA’ and ‘FAMD’ are from package

• others are from the famous package.

imputations <- imputeMissingValue(
  inc_mat = beatAML_incidence_matrix,
  method = c('svd','median','als','CA')
  )
# show the result format
names(imputations)
#> [1] "median" "svd"    "als"    "CA"

5.2 Validate imputation

validateImputation() will calculate the

1. Jaccard similarity

2. Dice similarity coefficient

3. Rand index

4. Minkowski (inversed)

5. Fowlkes–Mallows index

between each imputation and the reference community, then plot the ranking, user can find which imputation method is relatively better.

validation_of_imputation <- validateImputation(
  imputation = imputations,
  refer_community = cls$fast_greedy,
  clustering_args = cls$clustering_args
  )