# Downhill Riding (DR) Procedure Downhill riding procedure for selecting optimal tuning parameters in clustering algorithms, using an (in)stability probe. ```r DR(X, method, minPts = 3, theta = 0.9, B = 500, lb = -30, ub = 10) ``` ## Arguments - `X`: an $n\times k$ matrix where columns are $k$ objects to be clustered, and each object contains n observations (objects could be a set of time series). - `method`: the clustering method to be used -- currently either TRUST if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="Ciampi_etal_2010",package="funtimes",cached_env=.Rdpack.currefs) or DBSCAN if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="Ester_etal_1996",package="funtimes",cached_env=.Rdpack.currefs) . If the method is `DBSCAN`, then set `MinPts` and optimal $\epsilon$ is selected using DR. If the method is `TRUST`, then set `theta`, and optimal $\delta$ is selected using DR. - `minPts`: the minimum number of samples in an $\epsilon$-neighborhood of a point to be considered as a core point. The `minPts` is to be used only with the `DBSCAN` method. The default value is 3. - `theta`: connectivity parameter $\theta \in (0,1)$, which is to be used only with the `TRUST` method. The default value is 0.9. - `B`: number of random splits in calculating the Average Cluster Deviation (ACD). The default value is 500. - `lb, ub`: endpoints for a range of search for the optimal parameter. ## Returns A list containing the following components: - **P_opt**: the value of the optimal parameter. If the method is `DBSCAN`, then `P_opt` is optimal $\epsilon$. If the method is `TRUST`, then `P_opt` is optimal $\delta$. - **ACD_matrix**: a matrix that returns `ACD` for different values of a tuning parameter. If the method is `DBSCAN`, then the tuning parameter is $\epsilon$. If the method is `TRUST`, then the tuning parameter is $\delta$. ## Details Parameters `lb,ub` are endpoints for the search for the optimal parameter. The parameter candidates are calculated in a way such that $P:= 1.1^x , x \in {lb,lb+0.5,lb+1.0,...,ub}$. Although the default range of search is sufficiently wide, in some cases `lb,ub` can be further extended if a warning message is given. For more discussion on properties of the considered clustering algorithms and the DR procedure see if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="Huang_etal_2016;textual",package="funtimes",cached_env=.Rdpack.currefs) and if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="Huang_etal_2018_riding;textual",package="funtimes",cached_env=.Rdpack.currefs) . ## Examples ```r ## Not run: ## example 1 ## use iris data to test DR procedure data(iris) require(clue) # calculate NMI to compare the clustering result with the ground truth require(scatterplot3d) Data <- scale(iris[,-5]) ground_truth_label <- iris[,5] # perform DR procedure to select optimal eps for DBSCAN # and save it in variable eps_opt eps_opt <- DR(t(Data), method="DBSCAN", minPts = 5)$P_opt # apply DBSCAN with the optimal eps on iris data # and save the clustering result in variable res res <- dbscan(Data, eps = eps_opt, minPts =5)$cluster # calculate NMI to compare the clustering result with the ground truth label clue::cl_agreement(as.cl_partition(ground_truth_label), as.cl_partition(as.numeric(res)), method = "NMI") # visualize the clustering result and compare it with the ground truth result # 3D visualization of clustering result using variables Sepal.Width, Sepal.Length, # and Petal.Length scatterplot3d(Data[,-4],color = res) # 3D visualization of ground truth result using variables Sepal.Width, Sepal.Length, # and Petal.Length scatterplot3d(Data[,-4],color = as.numeric(ground_truth_label)) ## example 2 ## use synthetic time series data to test DR procedure require(funtimes) require(clue) require(zoo) # simulate 16 time series for 4 clusters, each cluster contains 4 time series set.seed(114) samp_Ind <- sample(12,replace=F) time_points <- 30 X <- matrix(0,nrow=time_points,ncol = 12) cluster1 <- sapply(1:4,function(x) arima.sim(list(order = c(1, 0, 0), ar = c(0.2)), n = time_points, mean = 0, sd = 1)) cluster2 <- sapply(1:4,function(x) arima.sim(list(order = c(2 ,0, 0), ar = c(0.1, -0.2)), n = time_points, mean = 2, sd = 1)) cluster3 <- sapply(1:4,function(x) arima.sim(list(order = c(1, 0, 1), ar = c(0.3), ma = c(0.1)), n = time_points, mean = 6, sd = 1)) X[,samp_Ind[1:4]] <- t(round(cluster1, 4)) X[,samp_Ind[5:8]] <- t(round(cluster2, 4)) X[,samp_Ind[9:12]] <- t(round(cluster3, 4)) # create ground truth label of the synthetic data ground_truth_label = matrix(1, nrow = 12, ncol = 1) for(k in 1:3){ ground_truth_label[samp_Ind[(4*k - 4 + 1):(4*k)]] = k } # perform DR procedure to select optimal delta for TRUST # and save it in variable delta_opt delta_opt <- DR(X, method = "TRUST")$P_opt # apply TRUST with the optimal delta on the synthetic data # and save the clustering result in variable res res <- CSlideCluster(X, Delta = delta_opt, Theta = 0.9) # calculate NMI to compare the clustering result with the ground truth label clue::cl_agreement(as.cl_partition(as.numeric(ground_truth_label)), as.cl_partition(as.numeric(res)), method = "NMI") # visualize the clustering result and compare it with the ground truth result # visualization of the clustering result obtained by TRUST plot.zoo(X, type = "l", plot.type = "single", col = res, xlab = "Time index", ylab = "") # visualization of the ground truth result plot.zoo(X, type = "l", plot.type = "single", col = ground_truth_label, xlab = "Time index", ylab = "") ## End(Not run) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `BICC`, `dbscan` ## Author(s) Xin Huang, Yulia R. Gel

DR function