click.backward {ClickClust}

Backward search for equivalent states

Description

Runs backward search to detect blocks of equivalent states.

Usage

click.backward(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 backward 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.

Value

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.

See Also

forward.search, click.EM

Examples

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)
B <- click.read(A$S)


# BACKWARD SEARCH

click.backward(X = B$X, K = 2)