# Perform Up-and-Down Search Optimization The `upAndDownSearch` function performs an up-and-down search (increasing and lowering the number of clusters) on a given dataset, starting from an initial partition and fitness value. The function assumes that the higher fitness value is better. Experimental! The `stochBlockForUDS` is just a wrapper to `stochBlock` function to be used within `upAndDownSearch` function. ```r upAndDownSearch( data, initPart, initFit, optimFun, nRep = 100, minPmove = 0.2, pFitSumTreshMoveBest = 5, ... ) stochBlockForUDS(data, initPart, ...) ``` ## Arguments - `data`: A data object (e.g., data frame or matrix) on which the search is performed. - `initPart`: Initial partition or configuration to start the search from. It can be a vector for simple datasets and a list of vectors for temporal or linked networks - `initFit`: Initial fitness value associated with the initial partition. - `optimFun`: A function used for optimization. A function must accept a data and a initial partition and return a list with an element `part` holding the final partition and an element `fit` fitness value. - `nRep`: Integer. The number of repetitions for the search algorithm. Defaults to 100. - `minPmove`: Numeric. The minimum probability of moving to a new partition when the fitness does not improve. Defaults to 0.2. - `pFitSumTreshMoveBest`: Numeric. The threshold for the sum of 1 - probabilities of moving to a new partition before reverting to the best partition. Defaults to 5. - `...`: Additional paramters to optimFun. ## Returns A list with the following components: - **data**: The input data. - **finalPart**: The final partition obtained. - **finalFit**: The final fitness value after the search. - **searchHistory**: A list containing the history of partitions and fitness values during the search. - **callUsed**: The call used to invoke the function, capturing the parameters passed. - **initial.param**: A list of initial parameters used in the function call withiut the data. ## Examples ```r # Create a synthetic network matrix set.seed(2022) library(blockmodeling) k<-2 # number of blocks to generate blockSizes<-rep(20,k) IM<-matrix(c(0.8,.4,0.2,0.8), nrow=2) clu<-rep(1:k, times=blockSizes) n<-length(clu) M<-matrix(rbinom(n*n,1,IM[clu,clu]),ncol=n, nrow=n) initClu<-rep(1, times=n) initFit<-ICLStochBlock(M, initClu) # Initial fitness value # Using up-and-down search to optimise the partition res<-upAndDownSearch(data=M,initPart=initClu, initFit=initFit, optimFun=stochBlockForUDS, nRep=10) plotMat(res$data, clu=res$bestPart) # Have a look at the optimised parition print(res$bestFit) # Print the final fitness value # Create a synthetic linked-network matrix set.seed(2022) library(blockmodeling) IM<-matrix(c(0.9,.5,0.1,0.8), nrow=2) clu<-rep(1:2, each=20) # Partition to generate n<-length(clu) nClu<-length(unique(clu)) # Number of clusters to generate M1<-matrix(rbinom(n^2,1,IM[clu,clu]),ncol=n, nrow=n) # First network M2<-matrix(rbinom(n^2,1,IM[clu,clu]),ncol=n, nrow=n) # Second network M12<-diag(n) # Linking network nn<-c(n,n) k<-c(2,2) Ml<-matrix(0, nrow=sum(nn),ncol=sum(nn)) Ml[1:n,1:n]<-M1 Ml[n+1:n,n+1:n]<-M2 Ml[n+1:n, 1:n]<-M12 plotMat(Ml) # Linked network clu1<-rep(1, n) clu2<-rep(2, n) initClu<-list(clu1, clu2) initFit<-ICLStochBlock(Ml, initClu) # Initial fitness value # Using up-and-down search to optimise the partition res<-upAndDownSearch(data=Ml,initPart=initClu, initFit=initFit, optimFun=stochBlockForUDS, nRep=10) plotMat(res$data, clu=res$bestPart) # Have a look at the optimised parition print(res$bestFit) # Print the final fitness value ```

upAndDownSearch function