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‎ConMod.m

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function [ modulesfinal ] = ConMod( multiNetworks, N, K, lambda, xita, maxIter )
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% The implement of ConMod method for identifying conserved functional
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% modules in multiple networks
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%
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% INPUT:
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% multiNetworks: a cell contains multiple networks, each is
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% presented by a sparse matrix or a full matrix with N nodes
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% N: the number of all nodes
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% K: the number of hidden factors
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% lambda: a vector containing the parameters for balancing the relative
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% weight among different views
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% xita: the parameter for selecting nodes
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% maxIter: the maximum number of iterations for multi-view NMF
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%
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% OUTPUT:
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% modulesfinal: a cell contains the final conserved modules
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%
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% Peizhuo Wang ([email protected])
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%% parameters
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%% Calculting the feature matrices
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disp('Calculating the strengh matrix and the uniformity matrix...')
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[Strength, Distribution] = featureNets(multiNetworks, N);
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%% Obtaining the candidate modules by multi-view NMF
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disp('Obtaining candidate modules by multi-view NMF...')
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disp(['K=', num2str(K)])
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X = {Strength, Distribution};
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[ H, Hc, objValue ] = multiViewNMF( X, K, lambda, maxIter );
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%% Selecting nodes from the consensus factors
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modulesfinal = moduleNodesSelection( Hc, xita );
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end
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‎README.md

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‎README.txt

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===============================================
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ConMod: Identifying conserved functional modules in multiple networks
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===============================================
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#----------------------The main function---------------------------
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ConMod.m % The implement of ConMod method
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>> [ modulesfinal ] = ConMod( multiNetworks, N, K, lambda, xita, maxIter )
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% INPUT:
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% multiNetworks: a cell contains multiple networks, each is presented by a sparse matrix or a full matrix with N nodes
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% N: the number of all nodes
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% K: the number of hidden factors
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% lambda: a vector containing the parameters for balancing the relative
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% weight among different views
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% xita: the parameter for selecting nodes
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% maxIter: the maximum number of iterations for multi-view NMF
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%
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% OUTPUT:
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% modulesfinal: a cell contains the final conserved modules
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---------------The code for generating the synthetic datasets---------
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syn_dataset_common.m % Conserved modules have the same size and are common to a given set of networks
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syn_dataset_overlap.m % Conserved modules are present only in a subset of networks and they are the overlapping parts of specific modules across different networks
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--------------The code for evaluation measures-------------
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evaluation.m % Compute the performance measures (TPR, FPR, Accuracy and MCC)
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------------------------------------------------------------------
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If any questions, please contact [email protected].

‎SNMF.m

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function [ H,objj ] = SNMF(X, K, H_init, maxIter, epsilon)
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% Symmetric Non-Negtive Matrix Factorization
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% INPUT:
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% X: the adjacency matrix of a network
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% K: the number of hidden factors
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% maxIter: the maximal number of iterations for alternating minimization
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% epsilon: the convergence parameter
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%
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% OUTPUT:
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% H: the factor matirx
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% objj: the value of objective function
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%
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% Peizhuo Wang ([email protected])
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%% Normalize the network
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X = X/sqrt(trace(X'*X));
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%% Initializaiton
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N = size(X,1);
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if isempty(H_init)
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H = rand(N,K);
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else
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H = H_init;
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end
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H = H/sqrt(trace(H'*H));
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obj_old = norm(X - H*H', 'fro')^2;
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beta = 0.5;
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objj = obj_old;
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%% Alternating update
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for iter = 1:maxIter
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temp_1 = X*H;
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temp_2 = (H')*H;
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temp_2 = H*temp_2;
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H = H.*(1 - beta + beta*(temp_1./(temp_2+eps)));
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obj = norm(X - H*H', 'fro')^2;
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Delta = obj_old - obj;
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obj_old = obj;
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objj = [objj, obj];
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if Delta < epsilon
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break;
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end
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end
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end

‎SNMFforView.m

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function [ H ] = SNMFforView(X, Hc, H, lambda, maxIter, epsilon)
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% Multi-View Non-negative symmetric Matrix Factorization for each view
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%
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% INPUT:
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% X: the adjacency matrix of a network
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% Hc: initialization for consensus factor matrix
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% H: initialization for factor matrix of each view
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% lambda: a vector containing the parameters for balancing the relative
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% weight among different views
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% MaxIter: the maximal number of iterations for alternating minimization
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% epsilon: the convergence parameter
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%
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% OUTPUT:
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% H: the factor matrix
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%
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% Peizhuo Wang ([email protected])
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obj_old = norm(X - H*H', 'fro')^2 + lambda*norm(H - Hc, 'fro')^2;
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% Fixing Hc, minimize objective function over H
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for iter = 1:maxIter
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% Update rule
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temp_1 = 2*X*H + lambda*Hc;
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temp_2 = 2*H*(H'*H) + lambda*H;
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H = H.*(temp_1./(temp_2+eps));
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% Objective function
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obj_body = norm(X - H*H', 'fro')^2;
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obj_consensus = norm(H - Hc, 'fro')^2;
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obj = obj_body + lambda*obj_consensus;
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Delta = obj_old - obj;
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obj_old = obj;
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if Delta < epsilon
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break;
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end
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end
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end

‎evaluation.m

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function [ TPR, FPR, Accuracy, MCC ] = evaluation(C_preticted, C_reference, N)
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% Compute the performance measures (TPR, FPR, Accuracy and MCC)
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%
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% INPUT:
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% C_preticted: a cell containing the preticted cluster results
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% C_reference: a cell containing the ground truth
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% N: total number of items
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% OUTPUT:
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% TPR: the True Positive Rate
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% FPR: the False Positive Rate
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% Accuracy:
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% MCC: the Matthews Correlation Coefficient
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% I: Confusion Matrix
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%
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% Peizhuo Wang ([email protected])
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%% Confusion matrix
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K_preticted = length(C_preticted);
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K_reference = length(C_reference);
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Ncount_P = 0;
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Ncount_R = 0;
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c_num = zeros(K_preticted+1, K_reference+1);
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C = cell(K_preticted, K_reference);
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for i = 1:K_preticted
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Ncount_P = Ncount_P + length(C_preticted{i});
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theRef_nonoverlap = [];
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for j = 1:K_reference
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C{i, j} = intersect(C_preticted{i}, C_reference{j});
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c_num(i, j) = length(C{i, j});
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if (i == 1)
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Ncount_R = Ncount_R + length(C_reference{j});
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end
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theRef_nonoverlap = union(theRef_nonoverlap, C{i, j});
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end
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c_num(i, j+1) = length(C_preticted{i}) - length(theRef_nonoverlap); % Background noise nodes
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end
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for j = 1:K_reference
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thePre_nonoverlap = [];
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for i = 1:K_preticted
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thePre_nonoverlap = union(thePre_nonoverlap, C{i, j});
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end
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c_num(i+1, j) = length(C_reference{j}) - length(thePre_nonoverlap); % Lost reference nodes
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end
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%% TP, FP, FN, TN for nodes pairs
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TP = sum(sum(c_num(1:K_preticted, 1:K_reference).*(c_num(1:K_preticted, 1:K_reference)-1)/2));
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FP = 0;
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for j = 1:K_reference
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tempC = c_num(1:K_preticted, (j+1):(K_reference+1));
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FP = FP + sum(c_num(1:K_preticted,j).*sum(tempC, 2));
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end
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FN = 0;
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for i = 1:K_preticted
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tempC = c_num((i+1):(K_preticted+1), 1:K_reference);
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FN = FN + sum(c_num(i,1:K_reference).*sum(tempC, 1));
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end
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TN = N*(N-1)/2 - (TP+FN+FP);
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I = [TP, FP; FN, TN];
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%% TPR, FPR, MCC
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TPR = TP/(TP+FN);
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FPR = FP/(FP+TN);
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Accuracy = (TP+TN)/(TP+FP+TN+FN);
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MCC = (TP*TN-FP*FN)/sqrt((TP+FP)*(TP+FN)*(TN+FP)*(TN+FN));
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end

‎featureNets.m

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function [ Strength, Participation ] = featureNets( multiNetworks, N )
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% Compute two feature metrices from multiple networks
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%
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% INPUT:
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% multiNetworks : a cell contains multiple networks, each is
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% presented by a sparse matrix or a full matrix
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% with N nodes
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% N : the number of all nodes
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%
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% OUTPUT:
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% Strength : N x N matrix for Connection Strength
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% Participation : N x N matrix for Participation Coefficient
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%
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% Peizhuo Wang ([email protected])
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network_count = length(multiNetworks);
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[n, m] = size(multiNetworks{1});
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Strength = zeros(N);
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temp = zeros(N);
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A = zeros(N);
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if (m <= 3) % Sparse matrix format
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for k = 1:network_count
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theMatrix = multiNetworks{k};
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[edge_count, col_count] = size(theMatrix);
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weight_max = 1;
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weight_min = 0;
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if (col_count == 3)
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weight_max = max(multiNetworks{k}(:,3));
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end
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for e = 1:edge_count
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ii = theMatrix(e, 1);
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jj = theMatrix(e, 2);
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if (col_count == 3) % weighted network
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weight = abs(theMatrix(e, 3));
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else
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weight = 1; % unweighted network
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end
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Strength(ii, jj) = Strength(ii ,jj) + weight;
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Strength(jj, ii) = Strength(ii, jj);
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weight_1 = (weight - weight_min) / (weight_max-weight_min);
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weight_2 = 1/(1+exp(log(9999)-2*log(9999)*weight_1));
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if (weight_1 <= 0.3)
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weight_2 = 0;
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end
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A(ii, jj) = A(ii, jj) + weight_2;
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A(jj, ii) = A(ii, jj);
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temp(ii, jj) = temp(ii, jj) + weight_2^2;
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temp(jj, ii) = temp(ii, jj);
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end
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end
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elseif (m == n) % Full matrix format
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N = n;
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for k = 1:network_count
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% The edge weight is transformed using a logistic function, such that for the
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% element less than 0.3, we make it close to 0; for the element more than
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% 0.6, we make it close to 1.
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weight_max = max(max(multiNetworks{k}));
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weight_min = 0;
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matrix_weight_1 = (multiNetworks{k} - ones(N)*weight_min) ./ (weight_max-weight_min);
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matrix_weight_2 = 1./(1+exp(log(9999)-2*log(9999)*matrix_weight_1));
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matrix_weight_2(matrix_weight_1 <= 0.3) = 0;
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A = A + matrix_weight_2;
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temp = temp + matrix_weight_2.^2;
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Strength = Strength + multiNetworks{k};
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end
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end
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Participation = (network_count/(network_count-1)) * (1-(temp./(A.^2)));
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Participation(isinf(Participation)) = 0;
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Participation(isnan(Participation)) = 0;
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Participation = Participation - diag(diag(Participation));
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Strength = A./network_count;
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Strength = Strength - diag(diag(Strength));
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end

‎main_run.m

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clear
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clc
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%% Load multi-network data sets
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disp('Processing the networks...')
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% I: Load data from files
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% nets = importdata('./networklist.txt');
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% T = length(nets);
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% multiNetworks = cell(T, 1);
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% for i = 1:T
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% disp(['network: ', num2str(i)])
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% multiNetworks{i} = load(['./', nets{i}]);
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% end
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% realLabels = importdata('./labels.txt');
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% II: Automatically generated synthetic datasets
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%[multiNetworks, realLabels] = syn_dataset_common(0.5, false); % common type
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[multiNetworks, realLabels, lables_specific] = syn_dataset_overlap(0.3, false); % overlap type
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num_Nodes = 500;
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%% One-step finding conserved functional modules
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tic
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K = 5;
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lambda = [0.01, 0.05];
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xita = 2;
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maxIter = 50;
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modules = ConMod( multiNetworks, num_Nodes, K, lambda, xita, maxIter );
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runtime = toc;
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disp(['Done. Running time: ', num2str(runtime), ' sec.'])
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%% Step-by-step finding conserved functional modules
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% Calculting the feature networks
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% tic
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% disp('Calculating the strengh matrix and the uniformity matrix...')
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% [Strength, Participation] = featureNets(multiNetworks, num_Nodes);
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%
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% % Obtaining the candidate modules by multi-view NMF
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% disp('Obtaining candidate modules by multi-view NMF...')
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% K = 5;
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% disp(['K=', num2str(K)])
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% X = {Strength, Participation};
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% lambda = [0.01, 0.05];
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% [ H, Hc, objValue ] = multiViewNMF( X, K, lambda, 50 );
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%
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% % Selecting nodes from the consensus factors
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% xita = 1.5;
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% modules_final = modulesTruing( Hc, xita );
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% runtime = toc;
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% disp(['Running time: ', num2str(runtime), ' sec.'])
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%% Module validation
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% disp('Validation...')
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% [ pvalues_modulePerNet, FDR2 ] = significantModules(modules_Merged, multiNetworks, num_Nodes);
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% disp('Done.')
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%% Clustering performance
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[ TPR, FPR, Accuracy, MCC] = evaluation(modules, realLabels, num_Nodes);

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