# Forward search for equivalent states Runs forward search to detect blocks of equivalent states. ```r click.forward(X, K, eps = 1e-10, r = 100, iter = 5, bic = TRUE, min.gamma = 1e-3, scale.const = 1.0, silent = FALSE) ``` ## Arguments - `X`: dataset array (p x p x n) - `K`: number of mixture components - `eps`: tolerance level - `r`: number of restarts for initialization - `iter`: number of iterations for each short EM run - `bic`: flag indicating whether BIC or AIC is used - `min.gamma`: lower bound for transition probabilities - `scale.const`: scaling constant for avoiding numerical issues - `silent`: output control ## Details Runs forward search to detect blocks of equivalent states. States i and j are called equivalent if their behavior expressed in terms of transition probabilities is identical, i.e., the probabilities of leaving i and j to visit another state h are the same as well as the probabilities of coming to i and j from another state h are the same; this condition should hold for all mixture components. Notation: p - number of states, n - sample size, K - number of mixture components, d - number of equivalence blocks. ## Returns - **z**: matrix of posterior probabilities (n x K) - **alpha**: vector of mixing proportions (length K) - **gamma**: array of transition probabilities (d x d x K) - **states**: detected equivalence blocks (length p) - **logl**: log likelihood value - **BIC**: Bayesian Information Criterion - **AIC**: Akaike Information Criterion - **id**: classification vector (length n) ## References Melnykov, V. (2016) Model-Based Biclustering of Clickstream Data, Computational Statistics and Data Analysis, 93, 31-45. Melnykov, V. (2016) ClickClust: An R Package for Model-Based Clustering of Categorical Sequences, Journal of Statistical Software, 74, 1-34. ## Author(s) Melnykov, V. ## See Also backward.search, click.EM ## Examples ```r set.seed(123) n.seq <- 50 p <- 5 K <- 2 mix.prop <- c(0.3, 0.7) TP1 <- matrix(c(0.20, 0.10, 0.15, 0.15, 0.40, 0.20, 0.20, 0.20, 0.20, 0.20, 0.15, 0.10, 0.20, 0.20, 0.35, 0.15, 0.10, 0.20, 0.20, 0.35, 0.30, 0.30, 0.10, 0.10, 0.20), byrow = TRUE, ncol = p) TP2 <- matrix(c(0.15, 0.15, 0.20, 0.20, 0.30, 0.20, 0.10, 0.30, 0.30, 0.10, 0.25, 0.20, 0.15, 0.15, 0.25, 0.25, 0.20, 0.15, 0.15, 0.25, 0.10, 0.30, 0.20, 0.20, 0.20), byrow = TRUE, ncol = p) TP <- array(rep(NA, p * p * K), c(p, p, K)) TP[,,1] <- TP1 TP[,,2] <- TP2 # DATA SIMULATION A <- click.sim(n = n.seq, int = c(10, 50), alpha = mix.prop, gamma = TP) C <- click.read(A$S) # FORWARD SEARCH click.forward(X = C$X, K = 2) ```

ForwardSearch function