1.1 Load environment

Libraries used to create and generate this report:

• R : R version 4.3.3 (2024-02-29)
• rmarkdown : 2.21
• knitr : 1.42
• rmdformats : 1.0.4
• bookdown : 0.34
• kableExtra : 1.3.4

1.2 Load libraries

Libraries used to analyse data:

library("SNFtool")
library("pheatmap")
library("igraph")

• SNFtool: 2.3.1
• pheatmap: 1.0.12
• igraph: 1.4.2

Libraries used to load data:

library("MOFAdata")
library("data.table")
library("mixOmics")
library("WallomicsData")

• MOFAdata: 1.16.1
• data.table: 1.14.8
• mixOmics: 6.24.0
• WallomicsData: 1.0

1.3 Visualization using Cytoscape

Cytoscape is used for visualization. Figures were generated using the Cytoscape v3.9.1 and several Cytoscape apps:

• yFiles Layout Algorithm: 1.1.3
• LegendCreator: 1.1.6

3.1 Metagenomic dataset from Tara Ocean project

To retrieve data: files are available in /shared/projects/tp_etbii_2024_165650/Networks/TaraOcean_mibiomics directory path in the IFB server.

• dataset:

  • TARAoceans_proNOGS.cvs
  • TARAoceans_proPhylo.csv

• metadata:

  • TARAoceans_metadata.csv

Samples come from eight oceans around the world (SPO: South Pacific Ocean, NAO: North Atlantic Ocean, IO: Indian Ocean, RS: Red Sea, MS: Mediterranean Sea, NPO: North Pacific Ocean, SO: Southern Ocean, SAO: South Atlantic Ocean).

Samples can come from different layers with different temperatures:

• SRF: Surface Water Layer (0-5 meters)
• DCM: Deep Chlorophyll Maximum (peak of chlorophyll, 0-600 meters)
• MIX: Subsurface epipelagic Mixed Layer
• MES(O): Mesopelagic zone (from 500/1000 meters)

In a previous analysis (Sunagawa et al., 2015), they identified a stratification mostly driven by the temperature rather than geography or other environmental factors.

We have two types of data:

• orthologous genes: the relative abundance of groups of orthologous genes (OGs)
• phylogenetic profil: counts of S16 rRNA

Does an integrative analysis of these two data types retrieve the stratification driver by the layers? Does it also find a geographical clustering?

Data are coming from: MiBiOmics gitlab.

3.2 Breast cancer dataset from The Cancer Genome Atlas

To retrieve data:

• dataset: using data("breast.TCGA") from the mixOmics R package

  • breast.TCGA$data.train$mirna
  • breast.TCGA$data.train$mrna
  • breast.TCGA$data.train$protein

• metadata: using data("breast.TCGA") from the mixOmics R package

  • breast.TCGA$data.train$subtype

Human breast cancer is a heterogeneous disease. Breast tumors can be classified into several subtypes (PAM50 classification), according to the mRNA expression level (Sorlie et al., 2001). In this dataset, we have three subtypes:

• Basal: considered more aggressive than LumA
• Her2: tend to grow faster than LumA and can have a worse prognosis, but are usually successfully treated
• LumA: tend to grow more slowly than other cancers, be lower grade, and have a good prognosis

We have three types of data:

• mRNA: mRNA expression level
• miRNA: microRNA expression level
• protein: protein abundance

Does an integrative analysis of these three data types retrieve the classification of the breast cancer? Or find another classification?

Data are coming from the mixOmics R package. The full data can be downloaded here.

3.3 Chronic Lymphocytic Leukaemia (CLL) dataset

To retrieve data:

• dataset: using data("CLL_data") from the MOFAdata R package

  • CLL_data_t$Drugs
  • CLL_data_t$Methylation
  • CLL_data_t$mRNA
  • CLL_data_t$Mutations

• metadata: file is available in /shared/projects/tp_etbii_2024_165650/Networks/CLL directory path in the IFB server.

  • sample_metadata.txt

The Chronic Lymphocytic Leukaemia (CLL) is type of blood and bone marrow cancer. The full data are explained in Dietrich et al., 2018 and available here.

We have four types of data:

• mRNA: transcriptom expression level
• methylation: DNA methylation assays
• drug: drug response measurements
• mutation: sommatic mutation status

3.4 Tomato plant dataset

To retrieve data: files are available in /shared/projects/tp_etbii_2024_165650/Networks/Tomato directory path in the IFB server.

• dataset:

  • mrna.tsv
  • prots.tsv

• metadata:

  • samples_metadata.tsv

In order to study the protein turnover in developing tomato fruit (Solanum lycopersicum) in Belouah et al., two omics data types were collected:

• transcript data: gene abundance
• protein data: protein abundance

Each data type was collected in nine different developmental stages: GR1, GR2, GR3, GR4, GR5, GR6, GR7, GR8 and GR9. For each developmental stages, we have three replicates.

Does an integrative analysis of these data types retrieve the different developmental stages?

Data are coming from Belouah et al., 2019.

3.5 Arabidopsis thaliana

To retrieve data:

• dataset: using data("X") from the WallomicsData R package

  • Phenomics_Rosettes
  • Transcriptomics_Rosettes_CW
  • Proteomics_Rosettes_CW
  • …

• metadata: using data("X") from the WallomicsData R package also

  • Altitude_Cluster
  • Ecotype
  • …

In order to study the cell wall plasticity of Arabidopsis thaliana plants, exposed to different temperature growth conditions, four omics data types were collected :

• phenomics data: 5 phenotype variables measured
• metabolomics: identification and quantification of the seven cell wall monosaccharides
• cell wall proteomics: counts of cell wall proteins
• transcriptomics: counts of transcripts

Each data type was collected for

• 2 organs, rosettes and stems with three replicates.
• 2 temperatures, 15°C an d 22°C
• 5 ecotypes, Roch, Grip, Hern and Hosp growing at different altitudes in the Pyrénées and Col from low altitude in Poland
• 3 genetic clusters

To see all the available data, have a look to the manual.

Data are explained in Duruflé et al., 2019, 2020 and 2021.

4.1 In summary

The preprocessing step is the most important part of the analysis. Data need to be prepared correctly in order to extract relevant information and produce a correct and pertinent interpretation of the results.

Data preprocessing could be summarized by four main steps:

1. Prepare the data (e.g. remove outliers, correct bacth effect etc…)
2. Remove and/or impute missing data
   • remove features/samples if more than 20% of missing data
   • impute missing data (e.g. using K-nearest neighbor method (KNN))
3. Normalize the data according to the data type
4. Scale (mean = 0 and standard deviation = 1)

Figure 4.1: Distribution examples expected after preprocessing

The data must conform to a specific matrix shape:

• samples (e.g. samples, organisms …) in rows
• features (e.g. genes, proteins …) in columns

4.2 Read and prepare the data

For this tutorial, we assume that the data have been already prepared: outliers are already removed and there is no batch effect.

tara_nog <- read.table(file = "../00_Data/TaraOcean_mibiomics/TARAoceans_proNOGS.csv", sep = ",", head = TRUE, row.names = 1)
tara_nog[c(1:5), c(1:5)]

##              NOG317682    NOG135470 NOG85325    NOG285859    NOG147792
## TARA_109_SRF         0 2.390962e-05        0 4.663604e-08 1.800215e-07
## TARA_149_MES         0 4.339824e-06        0 5.182915e-07 4.190123e-06
## TARA_110_MES         0 1.348252e-05        0 6.000043e-07 2.218342e-07
## TARA_102_MES         0 6.380711e-06        0 3.816016e-07 0.000000e+00
## TARA_142_SRF         0 9.484144e-06        0 6.437103e-08 1.132431e-06

4.3 Missing data

In the SNF paper, authors recommend to filter out samples with more than 20% of missing data in a certain data type. They also recommend to filter out features with more than 20% of missing data across samples. Then, they impute the remaining missing data using K nearest neighbors (KNN) imputation.

In this tutorial, we decide to remove samples with at least one missing data. To remove samples with missing data, we propose the following NARemoving() function. Input parameters are:

• data: the data type
• margin: a vector giving the subscripts which the function will be applied over (e.g. 1 indicates rows and 2 indicates columns)
• threshold: threshold above which samples/features are deleted

NARemoving <- function(data, margin, threshold){
    #' NA removing
    #'
    #' Calculate percentage of na
    #' Remove na from rows (margin = 1) or column (margin = 2)
    #' 
    #' @param data data.frame.
    #' @param margin int. 1 = row and 2 = column
    #' @param threshold int. Number of missing data accepted
    #'  
    #' @return Return data.frame with a specific number of na by row/column

  data_na <- apply(data, MARGIN = margin, FUN = function(v){sum(is.na(v)) / length(v) * 100})
  # print(table(data_na))
  toRemove <- split(names(data_na[data_na > threshold]), " ")[[1]]
  if(margin == 1){
    data_withoutNa <- data[!(row.names(data) %in% toRemove),]
    print(paste0("Remove ", as.character(length(toRemove)), " samples."))
  }
  if(margin == 2){
    data_withoutNa <- data[,!(colnames(data) %in% toRemove)]
    print(paste0("Remove ", as.character(length(toRemove)), " features"))
  }
  return(data_withoutNa)
}

For instance, the CLL drug data contain missing data (sample H024).

CLL_data_t$Drugs[c(1:5), c(1:5)]

##         D_001_1    D_001_2   D_001_3   D_001_4   D_001_5
## H045 0.02363938 0.04623274 0.3187471 0.8237027 0.8962777
## H109 0.07359900 0.10623002 0.2732891 0.7171379 0.8850003
## H024         NA         NA        NA        NA        NA
## H056 0.05813930 0.09022028 0.2322145 0.7225736 0.7957497
## H079 0.02042077 0.04750543 0.3638962 0.8073907 0.8794886

To remove samples with missing data in drug data, we use the following command line:

• data = CLL_data_t$Drugs: remove the samples with missing data in the drug data
• margin = 1: samples are in rows, so we want to apply the function on the rows
• threshold = 0: we remove samples with at least one missing data

CLL_drug <- NARemoving(data = CLL_data_t$Drugs, margin = 1, threshold = 0)

## [1] "Remove 16 samples."

The H024 sample is not anymore in the CLL drug data.

CLL_drug[c(1:5), c(1:5)]

##         D_001_1    D_001_2   D_001_3   D_001_4   D_001_5
## H045 0.02363938 0.04623274 0.3187471 0.8237027 0.8962777
## H109 0.07359900 0.10623002 0.2732891 0.7171379 0.8850003
## H056 0.05813930 0.09022028 0.2322145 0.7225736 0.7957497
## H079 0.02042077 0.04750543 0.3638962 0.8073907 0.8794886
## H164 0.02962725 0.08054628 0.4725991 0.8179143 0.8927961

We repeat this step for each data type. Then, we filter out samples that are not present in all data type.

sampleNames <- Reduce(intersect, list(rownames(CLL_drug), rownames(CLL_mrna)))
CLL_drug <- CLL_drug[rownames(CLL_drug) %in% sampleNames,]
CLL_mrna <- CLL_mrna[rownames(CLL_mrna) %in% sampleNames,]

These functions could help you: is.na(), lapply(), table() and view().

4.4 Normalization and scaling

4.4.2 Scaling

Each feature (column) needs to have the mean equals to zero and the standard deviation equals to one. For that, the SNF package provides the function standardNormalization().

In the Figure 4.2, you can see the data distribution for the breast cancer miRNA data before (on the left) and after (on the right) scaling. After scaling, the data distribution should be normal.

hist(as.matrix(tcga_mirna), nclass = 100, main = "Breast cancer miRNA data", xlab = "values")
hist(as.matrix(tcga_mirna_scaled), nclass = 100, main = "Breast cancer miRNA scaled data", xlab = "values")

Figure 4.2: Breast cancer miRNA data distribution before (left) and after (right) scaling.

Practice:

1. Check if your samples are in rows and your features in columns.
2. Scale your data with standardNormalization().
3. Plot the data distribution before and after scaling for each data type.
4. What can you say about these distribution plots?

These functions could help you: hist(), as.matrix().

5.1 In summary

In this section, we create a sample network for each type of data, based on the similarity between samples. The main steps are (Figure 5.1):

1. Compute the distance between each pair of samples (distance matrix D).
2. Transform distances (from distance matrix D) into weights (into similarity matrix W) using distance with nearest neighbors.
3. Create the corresponding similarity network (G).

Figure 5.1: Similarity network creation overview. Data type 1 is in the first row, represented with the green matrices. Data type 2 is in the last row, represented with the purple matrices.

The similarity network is a sample network. It is defined as a network G with nodes (or vertices) called V and connections (or edges) called E. The connections between samples are weighted. Weights come from the similarity matrix.

We can define the similarity network G like this:

• V: Nodes are samples
• E: Edges are connections between samples
• W: Edge weights are the similarity (or weight) between samples

5.2 Distance calculation

First, we calculate the distance between each pair of samples for each data type using the preprocessed data. The distance method used needs to be adapted to the feature type (e.g. continuous, discrete).

In the SNF paper (Wang et al.), authors suggest to use:

• distance (e.g. euclidean) or correlation (e.g. pearson) for continuous features
• chi-squared distance for discrete features
• agreement based measure for binary features

In the SNF R package, the dist2() function performs a squared Euclidean distances between samples.

These functions could help you: as.matrix(), dim(), nrow() and ncol().

5.3 Similarity calculation

The distance matrix D is then transformed into the similarity matrix W. Distances are converted to weights using the scaled exponential similarity kernel (µ) and average distances between samples and their nearest neighbors (ε):

\[ W = exp(-\frac{D^2}{µ\varepsilon})\] In other words, distances are converted to weights according the distance with the nearest neighbors of each sample pair.

The SNF R package proposes the affinityMatrix() to calculate this similarity matrix. In this case, affinity and similarity are equivalent. This function needs three parameters:

• diff: distance matrix D
• K: number of nearest neighbors (between 10 and 30)
• sigma: hyperparameter or variance (between 0.3 and 0.8)

The K neighbors is used to set the similarities outside of the neighborhood to zero. The sigma parameter allows scaling exponential similarity kernel, which is used to calculated the similarity.

Then, you can visualized the similarity matrix using the pheatmap() function. This function creates an heatmap of samples. By default samples are clustered using hierarchical clustering. For a better visualization, we recommend to:

• remove labels with show_rownames = FALSE and show_colnames = FALSE
• give metadata to the parameter annotation
• apply a log 10 transformation to the similarity matrix (log(x, 10))

6.1 In summary

Previously, we created a similarity matrix W and its corresponding similarity network G for each data type (Figure 6.1).

Figure 6.1: In the previous step, we create a similarity matrix that contains weights for each data type. We also created the corresponding similarity network.

Now, we integrate these similarity matrices (in the Figure 6.1 there are two data types). For that, we use an iterative fusion method. The number of iteration T, needs to be defined.

First, two matrices are created from the similarity matrix of each data type:

• the P matrix: this matrix, also called status matrix, contains normalized weights (come from the similarity matrix W).
• the S matrix: this matrix is the kernel matrix. It contains information about the nearest neighbors.

The P matrix carries the full information about the similarity of each samples to all others.

The S matrix carries the similarity to the K most similar samples for each sample (i.e. topology). The similarities between non-neighboring nodes are set to zero because authors assume that local similarities (high weights) are more reliable than the remote ones.

Then, the P matrix of each data type is iteratively updated with information from P matrices of the other data type, making them more similar at each step. In the Figure 6.2, you have an example with two data type. It’s a bit more complex with more data type (see the paper if you are interested in).

Figure 6.2: Example of the fusion method applied to two data types. Each data type is represented using a color: data type 1 in green and data type 2 in purple.

Finally after T iterations, the P matrices of each data type are merged together to create the final fused similarity matrix, and the corresponding fused similarity network.

Then, you can visualize the fused similarity network using Cytoscape.

6.2 Create the fused similarity matrix

First, we have to define the number of iteration called T. It should be between 10 and 20 (recommended by the authors).

Then, to perform the fusion, SNF R package proposes the SNF() function. You have to provide:

• the list of similarity matrices of each data type
• the number of nearest neighbors K (same as previously)
• the number of iteration T

These functions could help you: list(), length().

6.3 Visualize the fused similarity network

write.table(as_data_frame(W_net), "CLL_W_edgeList.txt", quote = FALSE, col.names = TRUE, row.names = FALSE, sep = "\t")

6.3.2 Visualize using Cytoscape

To create a network using Cytoscape, use the following steps:

6.3.2.1 Import files

Figure 6.3: Step 1 - Import files

• Import Network from File: *_W_edgeList.txt and define:
  • column 1 as Source node
  • column 2 as Target node
  • column 3 as Edge attributes
• Import Table from File: *_metadata.txt (Import Data as Node Table Columns)

6.3.2.2 Network style

Figure 6.4: Step 2 - Change the network style

In the Style tab:

• Fill Color
  • select a column from the metadata. Here it’s growth_stage from the tomato dataset
  • you can automatically fill the color by right click on Mapping Type tab
• Shape = Ellipse
• Lock node width and height

6.3.2.3 Network layout

Apply your favorite layout. For this step, we recommend to try at least yFiles Organic Layout.

7.1 In summary

In Cytoscape, you see that the fused similarity network is fully connected. Indeed, each sample is connected to all other samples. Remember, connections between samples are weighted: this weight represents the similarity between samples. A high weight value means a strong similarity between two samples whereas a low weight value means a weak similarity between two samples.

For a better visualization, we can select a threshold to decide which connections to keep, based on this weight value.

How to choose the good threshold? It’s an open question. There are some possibilities:

• choose an arbitrary threshold (e.g. nearest neighbors)
• choose a threshold based on basic metrics (e.g. median, quantiles)
• choose a threshold using methods based on network topology
• …

7.2 Select an arbitrary threshold

In this example, we select a threshold based on the weight distribution of the fused similarity network.

First, we extract edges from the network object. Indeed, the network object doesn’t contains duplicate edges, neither self loops unlike the corresponding fused similarity matrix W.

For instance, we extract weight values from the Tara Ocean fused similarity network. This network contains 9591 connections in total.

weights <- edge.attributes(tara_W_net)$weight

Then, we display the corresponding weight histogram in the Figure 7.1 (left). You can see a large number of small weight values. We can remove values between 0 and 0.01 where the majority of the small values seem to be. With the 0.01 threshold, 777 connections are kept.

In the Figure 7.1 (right), we log-transform weights. The weight distribution is binomial and we would like to cut the distribution into two parts. With the threshold 0.001 (log(0.001, 10) = -3), 6440 connections are kept.

## Raw weights
hist(weights, nclass = 100, main = "Fused similarity network weight distribution", xlab = "weights")
abline(v = 0.01, col = "red", lwd = 3)
## log10 weights
hist(log(weights, 10), nclass = 100, main = "Fused similarity network weight distribution", xlab = "log10(weights)")
abline(v = -3.1, col = "red", lwd = 3)

Figure 7.1: Weight distribution of the fused similarity network. On the left the weight distribution of the fused similarity network. On the right the log-transformed weight distribution of the fused similarity network.

7.3 Select the threshold using quantiles

As example for this part, we select the median and the third quantile values as thresholds. We calculate the median and the third quantile of the weight values.

W_median <- median(x = weights)
W_q75 <- quantile(x = weights, 0.75)

The weight distribution and the log-transformed weight distribution are displayed in the Figure 7.2, respectively left and right.

## Raw weights
hist(weights, nclass = 100, main = "Fused similarity network weight distribution", xlab = "weights")
abline(v = W_median, col = "blue", lwd = 3)
text(W_median, 2000, pos = 4, "Median", col = "blue", cex = 1)
## log10 weights
hist(log(weights, 10), nclass = 100, main = "Fused similarity network weight distribution", xlab = "log10(weights)")
abline(v = log(W_median, 10), col = "blue", lwd = 3)
text(log(W_median, 10), 400, pos = 2, "Median", col = "blue", cex = 1)
abline(v = log(W_q75, 10), col = "purple", lwd = 3)
text(log(W_q75, 10), 350, pos = 4, "quantile 75%", col = "purple", cex = 1)

Figure 7.2: Weight distribution of the fused similarity network. On the left the weight distribution of the fused similarity network. On the right the log-transformed weight distribution of the fused similarity network.

The median is the value that splits data into two groups with the same number of data. With this value (0.002143), we selected 4795 connections.

The values above the third quantile value (0.0041194) are in the top of 25% highest weights. We selected 2398 connections.

7.4 Threshold based on network topology

In the Zahoranszky-Kohalmi et al. paper, authors propose a method to determine the best threshold according to the topology of the network. This method calculates the Average Clustering Coefficient (ACC) for a whole network. The ACC represents a global parameter that characterizes the overall network topology.

As an Elbow approach, an ACC value is calculated for a range of thresholds. The obtained values are displayed and we choose the threshold that seems the best!

## CC calculation function
CCCalculation <- function(node, graph){
    #' Clustering Coefficient (CC) calculation
    #'
    #' Calculate the Clustering Coefficient (CC) for each node in a network
    #' 
    #' @param node str.
    #' @param graph igraph. Network object (e.g. the fused network object)
    #'  
    #' @return Return the corresponding CC value
    
  degNode <- degree(graph = graph, v = node, loops = FALSE)
  if(degNode > 1){
    neighborNames <- neighbors(graph = graph, v = node)
    graph_s <- subgraph(graph = graph, vids = neighborNames)
    neighborNb <- sum(degree(graph_s, loops = FALSE))
    CC <- neighborNb / (degNode * (degNode-1))
  }else{CC <- 0}
  return(CC)
}

## ACC calculation function
ACCCalculation <- function(graph){
    #' Average Clustering Coefficient (ACC) calculation
    #'
    #' It average the Clustering Coefficient (CC) of a network
    #' 
    #' @param graph igraph. Network object (e.g. the fused network object)
    #'  
    #' @return Return the corresponding ACC value
    
  nodes <- V(graph)
  ACC <- do.call(sum, lapply(nodes, CCCalculation, graph)) / length(nodes)
  return(ACC)
}

summary(weights)

##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## 5.696e-05 4.389e-04 2.143e-03 3.623e-03 4.119e-03 1.414e-01

thresholds <- seq(0, 0.1, 0.0005)

7.4.3 Calculate the ACC values

Calculate the ACC values for each selected threshold.

ACC_W <- do.call(rbind, lapply(thresholds, function(t, net){
  net_sub <- subgraph.edges(net, E(net)[weight >= t])
  df <- data.frame("ACC" = ACCCalculation(net_sub), "thresholds" = t, "EN" = length(E(net_sub)))
  return(df)
}, tara_W_net))

The ACC values are displayed in the Figure 7.3 (left). The number of network edges for each threshold is displayed in the Figure 7.3 (right).

plot(x = ACC_W$thresholds, y = ACC_W$ACC, xlab = "thresholds", ylab = "ACC", main = "ACC calculation of the Fused network W", type = "o")
points(x = ACC_W$thresholds[1], y = ACC_W$ACC[1], col = "red", pch = 16, cex = 1.2)
points(x = ACC_W$thresholds[21], y = ACC_W$ACC[21], col = "pink", pch = 16, cex = 1.2)
points(x = ACC_W$thresholds[29], y = ACC_W$ACC[29], col = "purple", pch = 16, cex = 1.2)
abline(v = ACC_W$thresholds[29], col = "purple")
text(ACC_W$thresholds[29], 0.7, pos = 4, paste0("Threshold = ",  ACC_W$thresholds[29]), col = "purple")
text(ACC_W$thresholds[29], 0.6, pos = 4, paste0("ACCmax = ",  round(ACC_W$ACC[29], 2)), col = "purple")
plot(x = ACC_W$thresholds, y = ACC_W$EN, xlab = "thresholds", ylab = "number of edges", main = "EN of the Fused network W", type = "o")
abline(v = ACC_W$thresholds[29], col = "purple")
text(ACC_W$thresholds[29], 2800, pos = 4, paste0("Threshold = ",  ACC_W$thresholds[29]), col = "purple")
text(ACC_W$thresholds[29], 2000, pos = 4, paste0("ACCmax = ",  round(ACC_W$ACC[29], 2)), col = "purple")
text(ACC_W$thresholds[29], 1200, pos = 4, paste0("EN = ",  ACC_W[29, "EN"]), col = "purple")

Figure 7.3: Left: Average Clustering Coeeficient (ACC) values for each threshold - Right: Number of edges on network for each threshold

On the Figure 7.3 you can see a peak that stands out in comparison with the others.

• Red dot: no filter, every sample is connected to each other
• Pink dot: the smallest value before the peak
• Purple dot: the local maxima of ACC (we want this one)

Advantages	Drawbacks
1. Take account of the topology of the network	1. Might be time consuming
	2. Interpretation (need to be used to this method)
	3. Sometimes, no peak …

7.5 Visualize this threshold in Cytoscape

The fused similarity network is already imported in Cytoscape. You already changed the network style and the network layout. If it is not, you can go to the previous Cytoscape section.

We have a fully connected network. To select edges based on their weights, use the following steps:

7.5.1 Filter column

Figure 7.4: Filter edge weight using the determined threshold.

In the Filter tab:

• Add a new condition
• Select Column Filter
• Choose the Edge: weight column name
• Put your threshold in the range

7.5.2 Create a new network visualization

Figure 7.5: Create new network visualization according the determined threshold

• Select All Nodes
• Create a New Network from Selected Nodes, Selected Edges
• Apply your favorite layer on this new network

7.6 Practice

Now, it’s your turn to find the best threshold!!

Keep in mind that you can change this threshold in Cytoscape anytime.

8.1 Clustering

In the SNF paper, authors propose a clustering method called spectralClustering(). This function takes in input three parameters:

• affinity: fused similarity matrix W
• K: number of clusters we want
• type: the variants of spectral clustering to use (default 3)

Samples are clustered together according to their similarity. The number of clusters needs to be defined. Obviously, this cluster number can be chosen using an Elbow approach, which would be less arbitrary.

First, define the number of clusters. Here, we define four clusters.

C <- 4

Then, perform the clustering. Results are stored into the group variable.

group <- data.frame(Groups = spectralClustering(tara_W, C)) 
row.names(group) <- colnames(tara_W)

Next, merge the clustering results with the metadata.

dataGroups <- merge(metadata, group, by = 0) 
head(dataGroups)

##      Row.names ocean depth Groups
## 1 TARA_004_DCM   NAO   DCM      1
## 2 TARA_004_SRF   NAO   SRF      1
## 3 TARA_007_DCM    MS   DCM      1
## 4 TARA_007_SRF    MS   SRF      1
## 5 TARA_009_DCM    MS   DCM      1
## 6 TARA_009_SRF    MS   SRF      1

Finally, save the merged data into a file.

write.table(dataGroups, "TARAOcean_4clusters.txt", quote = FALSE, col.names = TRUE, row.names = FALSE, sep = "\t") 

You might merge clustering results to create on result file using merge() function.

8.2 Visualization on Cytoscape

As a reminder:

1. How to import files and change network visualization style, see section 6.3.2
2. How to apply a threshold on edges, see section 7.5.2

You already loaded the fused similarity network in Cytoscape. And you also removed the weak edges. To visualize the clustering results follow the steps:

Figure 8.1: Import table to the Network Collection.

• Import Table from File: *_clusters.txt to the Network Collection (information will be add to every network in the collection)
• Color the nodes according to their cluster
• Create the corresponding legend using the Legend Panel tab
  • First, Scan Network
  • Then, modify the title and the subtitle
  • Finally, Refresh Legend
• To move legend elements, click on the T icon

Figure 8.2: Create a legend using the Legend Panel.

This is a network visualization example for each dataset:

Figure 8.3: Example of fused similarity network visualization using Cytoscape for each dataset.

9.1 Normalization and distance calculation

At the beginning of the hands-on, we assumed that data have been already well normalized. We also used only the euclidean distance, whatever the types of data.

It could be interesting to try different normalization and distance calculation to choose the most-adapted preprocessing of the data.

For instance, the two main adapted normalization methods for the Tara Ocean data are:

• Centered log ratio method (CLR)
• Total sum-scaling (TSS)

Moreover, other distance distances exist and are more appropriate for ecological data than Euclidean distance:

• Bray-Curtis distance
• Hellinger distance

These functions could help you: distance(), tss() or clr(). They are available in the ecodist, hilldiv and compositions packages.