# BIC-Based Spatio-Temporal Clustering Apply the algorithm of unsupervised spatio-temporal clustering, TRUST if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="Ciampi_etal_2010",package="funtimes",cached_env=.Rdpack.currefs) , with automatic selection of its tuning parameters `Delta` and `Epsilon` based on Bayesian information criterion, BIC if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="Schaeffer_etal_2016_trust",package="funtimes",cached_env=.Rdpack.currefs) . ```r BICC(X, Alpha = NULL, Beta = NULL, Theta = 0.8, p, w, s) ``` ## Arguments - `X`: a matrix of time series observed within a slide (time series in columns). - `Alpha`: lower limit of the time-series domain, passed to `CSlideCluster`. - `Beta`: upper limit of the time-series domain passed to `CSlideCluster`. - `Theta`: connectivity parameter passed to `CSlideCluster`. - `p`: number of layers (time-series observations) in each slide. - `w`: number of slides in each window. - `s`: step to shift a window, calculated in the number of slides. The recommended values are 1 (overlapping windows) or equal to `w` (non-overlapping windows). ## Returns A list with the following elements: - **delta.opt**: optimal value for the clustering parameter `Delta`. - **epsilon.opt**: optimal value for the clustering parameter `Epsilon`. - **clusters**: vector of length `ncol(X)` with cluster labels. - **IC**: values of the information criterion (BIC) for each considered combination of `Delta` (rows) and `Epsilon` (columns). - **delta.all**: vector of considered values for `Delta`. - **epsilon.all**: vector of considered values for `Epsilon`. ## Details This is the upper-level function for time series clustering. It exploits the functions `CWindowCluster` and `CSlideCluster` to cluster time series based on closeness and homogeneity measures. Clustering is performed multiple times with a range of equidistant values for the parameters `Delta` and `Epsilon`, then optimal parameters `Delta` and `Epsilon` along with the corresponding clustering results are shown if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="@see@Schaeffer_etal_2016_trust, for more details",package="funtimes",cached_env=.Rdpack.currefs) . The total length of time series (number of levels, i.e., `nrow(X)`) should be divisible by `p`. ## Examples ```r # Fix seed for reproducible simulations: set.seed(1) ##### Example 1 # Similar to Schaeffer et al. (2016), simulate 3 years of monthly data #for 10 locations and apply clustering: # 1.1 Simulation T <- 36 #total months N <- 10 #locations phi <- c(0.5) #parameter of autoregression burn <- 300 #burn-in period for simulations X <- sapply(1:N, function(x) arima.sim(n = T + burn, list(order = c(length(phi), 0, 0), ar = phi)))[(burn + 1):(T + burn),] colnames(X) <- paste("TS", c(1:dim(X)[2]), sep = "") # 1.2 Clustering # Assume that information arrives in year-long slides or data chunks p <- 12 #number of time layers (months) in a slide # Let the upper level of clustering (window) be the whole period of 3 years, so w <- 3 #number of slides in a window s <- w #step to shift a window, but it does not matter much here as we have only one window of data tmp <- BICC(X, p = p, w = w, s = s) # 1.3 Evaluate clustering # In these simulations, it is known that all time series belong to one class, #since they were all simulated the same way: classes <- rep(1, 10) # Use the information on the classes to calculate clustering purity: purity(classes, tmp$clusters[1,]) ##### Example 2 # 2.1 Modify time series and update classes accordingly: # Add a mean shift to a half of the time series: X2 <- X X2[, 1:(N/2)] <- X2[, 1:(N/2)] + 3 classes2 <- rep(c(1, 2), each = N/2) # 2.2 Re-apply clustering procedure and evaluate clustering purity: tmp2 <- BICC(X2, p = p, w = w, s = s) tmp2$clusters purity(classes2, tmp2$clusters[1,]) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `CSlideCluster`, `CWindowCluster`, `purity` ## Author(s) Ethan Schaeffer, Vyacheslav Lyubchich

BICC function