Package 'ClickClust' reference manual

Title:	Model-Based Clustering of Categorical Sequences
Description:	Clustering categorical sequences by means of finite mixtures with Markov model components is the main utility of ClickClust. The package also allows detecting blocks of equivalent states by forward and backward state selection procedures.
Authors:	Volodymyr Melnykov [aut, cre], Rouben Rostamian [ctb, cph] (memory allocation in c)
Maintainer:	Volodymyr Melnykov <[email protected]>
License:	GPL (>= 2)
Version:	1.1.6
Built:	2024-12-01 08:28:04 UTC
Source:	CRAN

Model-based clustering of categorical sequences

Description

The package runs finite mixture modeling and model-based clustering for categorical sequences

Details

Function 'click.EM' runs the EM algorithm for finite mixture models with Markov model components.

Author(s)

Volodymyr Melnykov

Maintainer: Volodymyr Melnykov <[email protected]>

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.

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


# EM ALGORITHM

click.EM(X = C$X, K = 2)


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)


# EM ALGORITHM

click.EM(X = C$X, K = 2)

Dataset: result of backward state selection

Description

These data demonstrate the result of the backward state selection procedure obtained for the dataset "C".

Usage

data(utilityB3)data(utilityB3)

Details

Results of the backward state selection procedure assuming three components are provided for the dataset "C".

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.

Examples


data(utilityB3)

dev.new(width = 11, height = 11)
click.plot(X = C$X, id = B3$id, colors = c("lightyellow", "red", "darkred"), col.levels = 10)

data(utilityB3)

dev.new(width = 11, height = 11)
click.plot(X = C$X, id = B3$id, colors = c("lightyellow", "red", "darkred"), col.levels = 10)

Dataset: simulated dataset

Description

This dataset is used to run the backward state selection procedure (results in "B3").

Usage

data(utilityB3)data(utilityB3)

Details

Original dataset used to illustrate the utility of backward selection.

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.

Examples


data(utilityB3)

dev.new(width = 11, height = 11)
click.plot(X = C$X, id = B3$id, colors = c("lightyellow", "red", "darkred"), col.levels = 10)

data(utilityB3)

dev.new(width = 11, height = 11)
click.plot(X = C$X, id = B3$id, colors = c("lightyellow", "red", "darkred"), col.levels = 10)

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)
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.

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)

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)

EM algorithm for mixtures of Markov models

Description

Runs the EM algorithm for finite mixture models with Markov model components.

Usage

click.EM(X, y = NULL, K, eps = 1e-10, r = 100, iter = 5, min.beta = 1e-3,
  min.gamma = 1e-3, scale.const = 1)
click.EM(X, y = NULL, K, eps = 1e-10, r = 100, iter = 5, min.beta = 1e-3,
  min.gamma = 1e-3, scale.const = 1)

Arguments

`X`	dataset array (p x p x n)
`y`	vector of initial states (length n)
`K`	number of mixture components
`eps`	tolerance level
`r`	number of restarts for initialization
`iter`	number of iterations for each short EM run
`min.beta`	lower bound for initial state probabilities
`min.gamma`	lower bound for transition probabilities
`scale.const`	scaling constant for avoiding numerical issues

Details

Runs the EM algorithm for finite mixture models with first order Markov model components. The function returns estimated mixing proportions 'alpha' and transition probabilty matrices 'gamma'. If initial states 'y' are not provided, initial state probabilities 'beta' are not estimated and assumed to be equal to 1 / p. In this case, the total number of estimated parameters is given by M = K - 1 + K * p * (p - 1). Otherwise, initial state probabilities 'beta' are also estimated and the total number of parameters is M = K - 1 + K * (p - 1) + K * p * (p - 1). 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)
`id`	classification vector (length n)
`alpha`	vector of mixing proportions (length K)
`beta`	matrix of initial state probabilities (K x p)
`gamma`	array of transition probabilities (p x p x K)
`logl`	log likelihood value
`BIC`	Bayesian Information Criterion

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.

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


# EM ALGORITHM (without initial state probabilities)

N2 <- click.EM(X = C$X, K = 2)
N2$BIC


# EM ALGORITHM (with initial state probabilities)

M2 <- click.EM(X = C$X, y = C$y, K = 2)
M2$BIC

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)


# EM ALGORITHM (without initial state probabilities)

N2 <- click.EM(X = C$X, K = 2)
N2$BIC


# EM ALGORITHM (with initial state probabilities)

M2 <- click.EM(X = C$X, y = C$y, K = 2)
M2$BIC

Forward search for equivalent states

Description

Runs forward search to detect blocks of equivalent states.

Usage

click.forward(X, K, eps = 1e-10, r = 100, iter = 5, bic = TRUE,
  min.gamma = 1e-3, scale.const = 1.0, silent = FALSE)
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.

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)

Author(s)

Melnykov, V.

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.

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


# FORWARD SEARCH

click.forward(X = C$X, K = 2)

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)

Plot of the obtained clustering solution

Description

Constructs a click-plot for the clustering solution.

Usage

click.plot(X, y = NULL, file = NULL, id, states = NULL, marg = 1,
  font.cex = 2, font.col = "black", cell.cex = 1, cell.lwd = 1.3,
  cell.col = "black", sep.lwd = 1.3, sep.col = "black",
  obs.lwd = NULL, colors = c("lightcyan", "pink", "darkred"),
  col.levels = 8, legend = TRUE, leg.cex = 1.3, top.srt = 0,
  frame = TRUE)
click.plot(X, y = NULL, file = NULL, id, states = NULL, marg = 1,
  font.cex = 2, font.col = "black", cell.cex = 1, cell.lwd = 1.3,
  cell.col = "black", sep.lwd = 1.3, sep.col = "black",
  obs.lwd = NULL, colors = c("lightcyan", "pink", "darkred"),
  col.levels = 8, legend = TRUE, leg.cex = 1.3, top.srt = 0,
  frame = TRUE)

Arguments

`X`	dataset array (p x p x n)
`y`	vector of initial states (length n)
`file`	name of the output pdf-file
`id`	classification vector (length n)
`states`	vector of state labels (length p)
`marg`	plot margin value (for the left and top)
`font.cex`	magnification of labels
`font.col`	color of labels
`cell.cex`	magnification of cells
`cell.lwd`	width of cell frames
`cell.col`	color of cell frames
`sep.lwd`	width of separator lines
`sep.col`	color of separator lines
`obs.lwd`	width of observation lines
`colors`	edge colors for interpolation
`col.levels`	number of colors obtained by interpolation
`legend`	legend of color hues
`leg.cex`	magnification of legend labels
`top.srt`	rotation of state names in the top
`frame`	frame around the plot

Details

Constructs a click-plot for the provided clustering solution. Click-plot is a graphical display representing relative transition frequencies for the partitioning specified via the parameter 'id'. If the parameter 'file' is specified, the constructed plot will be saved in the pdf-file with the name 'file'. If the width of observation lines 'obs.lwd' is not specified, median colors will be used for all cell segments.

Author(s)

Melnykov, V.

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.

Examples


set.seed(123)

n.seq <- 200

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)


# EM ALGORITHM

M2 <- click.EM(X = C$X, y = C$y, K = 2)


# CONSTRUCT CLICK-PLOT

click.plot(X = C$X, y = C$y, file = NULL, id = M2$id)

set.seed(123)

n.seq <- 200

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)


# EM ALGORITHM

M2 <- click.EM(X = C$X, y = C$y, K = 2)


# CONSTRUCT CLICK-PLOT

click.plot(X = C$X, y = C$y, file = NULL, id = M2$id)

Prediction of future state visits

Description

Calculates the transition probability matrix associated with the M-step transition.

Usage

click.predict(M = 1, gamma, pr = NULL)
click.predict(M = 1, gamma, pr = NULL)

Arguments

`M`	number of transition steps (M = 1 by default)
`gamma`	array of transition probabilities (p x p x K)
`pr`	vector of probabilities associated with components (length K)

Details

Returns a transition probability matrix associated with the M-step transition. If the vector pr is not specified, all components are assumed equally likely.

Author(s)

Melnykov, V.

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.

Examples


set.seed(123)

n.seq <- 200

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)


# EM ALGORITHM

M2 <- click.EM(X = C$X, y = C$y, K = 2)


# Assuming component probabilities given by mixing proportions, predict the next state 

click.predict(M = 1, gamma = M2$gamma, pr = M2$alpha)

# For the last location in the first sequence, predict the three-step transition
# location, given corresponding posterior probabilities

click.predict(M = 3, gamma = M2$gamma, pr = M2$z[1,])[A$S[[1]][length(A$S[[1]])],]

set.seed(123)

n.seq <- 200

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)


# EM ALGORITHM

M2 <- click.EM(X = C$X, y = C$y, K = 2)


# Assuming component probabilities given by mixing proportions, predict the next state 

click.predict(M = 1, gamma = M2$gamma, pr = M2$alpha)

# For the last location in the first sequence, predict the three-step transition
# location, given corresponding posterior probabilities

click.predict(M = 3, gamma = M2$gamma, pr = M2$z[1,])[A$S[[1]][length(A$S[[1]])],]

Reading sequences of visited states

Description

Prepares sequences of visited states for running the EM algorithm.

Usage

click.read(S)
click.read(S)

Arguments

`S`	list of numeric sequences

Details

Prepares sequences of visited states for running the EM algorithm by means of the click.EM() function.

Value

`X`	dataset array (p x p x n) (p - # of states, n - # of sequences)
`y`	vector of initial states (length n)

Author(s)

Melnykov, V.

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.

Examples


set.seed(123)

n.seq <- 20

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$S)
C$X
C$y

set.seed(123)

n.seq <- 20

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$S)
C$X
C$y

Simulating sequences of visited states

Description

Simulates sequences of visited states.

Usage

click.sim(n, int = c(5, 100), alpha, beta = NULL, gamma)
click.sim(n, int = c(5, 100), alpha, beta = NULL, gamma)

Arguments

`n`	number of sequences
`int`	interval defining the lower and upper bounds for the length of sequences
`alpha`	vector of mixing proportions (length K)
`beta`	matrix of initial state probabilities (K x p)
`gamma`	array of K p x p transition probability matrices (p x p x K)

Details

Simulates 'n' sequences of visited states according to the following mixture model parameters: 'alpha' - mixing proportions, 'beta' - initial state probabilities, 'gamma' - transition probability matrices. If the matrix 'beta' is not provided, all initial states are assumed to be equal to 1 / p.

Value

`S`	list of simulated sequences
`id`	true classification of simulated sequences

Author(s)

Melnykov, V.

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.

Examples



# SPECIFY MODEL PARAMETERS

set.seed(123)

n.seq <- 20

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)
A


# SPECIFY MODEL PARAMETERS

set.seed(123)

n.seq <- 20

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)
A

Variance-covariance matrix estimation

Description

Estimates the variance-covariance matrix for model parameter estimates.

Usage

click.var(X, y = NULL, alpha, beta = NULL, gamma, z)
click.var(X, y = NULL, alpha, beta = NULL, gamma, z)

Arguments

`X`	dataset array (p x p x n)
`y`	vector of initial states (length n)
`alpha`	vector of mixing proportions (length K)
`beta`	matrix of initial state probabilities (K x p)
`gamma`	array of transition probabilities (p x p x K)
`z`	matrix of posterior probabilities (n x K)

Details

Returns an estimated variance-covariance matrix for model parameter estimates.

Author(s)

Melnykov, V.

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.

Examples


set.seed(123)

n.seq <- 200

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)


# EM ALGORITHM

M2 <- click.EM(X = C$X, y = C$y, K = 2)


# VARIANCE ESTIMATION

V <- click.var(X = C$X, y = C$y, alpha = M2$alpha, beta = M2$beta,
               gamma = M2$gamma, z = M2$z)

# 95% confidence intervals for all model parameters

Estimate <- c(M2$alpha[-K], as.vector(t(M2$beta[,-p])),
              as.vector(apply(M2$gamma[,-p,], 3, t)))

Lower <- Estimate - qnorm(0.975) * sqrt(diag(V))
Upper <- Estimate + qnorm(0.975) * sqrt(diag(V))

cbind(Estimate, Lower, Upper)

set.seed(123)

n.seq <- 200

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)


# EM ALGORITHM

M2 <- click.EM(X = C$X, y = C$y, K = 2)


# VARIANCE ESTIMATION

V <- click.var(X = C$X, y = C$y, alpha = M2$alpha, beta = M2$beta,
               gamma = M2$gamma, z = M2$z)

# 95% confidence intervals for all model parameters

Estimate <- c(M2$alpha[-K], as.vector(t(M2$beta[,-p])),
              as.vector(apply(M2$gamma[,-p,], 3, t)))

Lower <- Estimate - qnorm(0.975) * sqrt(diag(V))
Upper <- Estimate + qnorm(0.975) * sqrt(diag(V))

cbind(Estimate, Lower, Upper)

Dataset: msnbc323

Description

A portion of the msnbc dataset containing 323 clickstream sequences. This version of the original dataset (David Heckerman) was used in Melnykov (2014).
There are 17 states representing the following categories:
1: frontpage
2: news
3: tech
4: local
5: opinion
6: on-air
7: misc
8: weather
9: msn-news
10: health
11: living
12: business
13: msn-sports
14: sports
15: summary
16: bbs
17: travel

Usage

data(msnbc323)data(msnbc323)

Format

List of 323 numeric vectors representing categorical sequences.

Source

Melnykov, V. (2014)

References

Cadez, I., Heckerman, D., Meek, C., Smyth, P., White, S. (2003) Model-based clustering and visualization of navigation patterns on a web site, Data Mining and Knowledge Discovery, 399-424.

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.

Functions for Printing or Summarizing Objects

Description

EM and search classes for printing and summarizing objects.

Usage

## S3 method for class 'EM'
print(x, ...)
## S3 method for class 'EM'
summary(object, ...)
## S3 method for class 'search'
print(x, ...)
## S3 method for class 'search'
summary(object, ...)
## S3 method for class 'EM'
print(x, ...)
## S3 method for class 'EM'
summary(object, ...)
## S3 method for class 'search'
print(x, ...)
## S3 method for class 'search'
summary(object, ...)

Arguments

`x`	an object with the 'EM' (or 'search') class attributes.
`object`	an object with the 'EM' (or 'search') class attributes.
`...`	other possible options.

Details

Some useful functions for printing and summarizing results.

Author(s)

Melnykov, V.

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.

Illustrative dataset: sequences of five states

Description

The data represents the synthetic dataset used as an illustrative example in the Journal of Statistical Software paper discussing the use of the package.
There are 5 states denoted as A, B, C, D, and E. Categorical sequences have lengths varying from 10 to 50.

Usage

data(synth)data(synth)

Format

$data contains a vector of 250 strings representing categorical sequences; $id is the original classification vector.

Source

Melnykov, V. (2015)

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.

Examples


data(synth)
head(synth$data)

# FUNCTION THAT REPLACES CHARACTER STATES WITH NUMERIC VALUES
repl.levs <- function(x, ch.lev){
	for (j in 1:length(ch.lev)) x <- gsub(ch.levs[j], j, x)
	return(x)
}

# DETECT ALL STATES IN THE DATASET
d <- paste(synth$data, collapse = " ")
d <- strsplit(d, " ")[[1]]
ch.levs <- levels(as.factor(d))

# CONVERT DATA TO THE FORM USED BY click.read()
S <- strsplit(synth$data, " ")
S <- sapply(S, repl.levs, ch.levs)
S <- sapply(S, as.numeric)
head(S)

data(synth)
head(synth$data)

# FUNCTION THAT REPLACES CHARACTER STATES WITH NUMERIC VALUES
repl.levs <- function(x, ch.lev){
	for (j in 1:length(ch.lev)) x <- gsub(ch.levs[j], j, x)
	return(x)
}

# DETECT ALL STATES IN THE DATASET
d <- paste(synth$data, collapse = " ")
d <- strsplit(d, " ")[[1]]
ch.levs <- levels(as.factor(d))

# CONVERT DATA TO THE FORM USED BY click.read()
S <- strsplit(synth$data, " ")
S <- sapply(S, repl.levs, ch.levs)
S <- sapply(S, as.numeric)
head(S)

Package 'ClickClust'

Help Index

Model-based clustering of categorical sequences

Description

Details

Author(s)

References

Examples

Dataset: result of backward state selection

Description

Usage

Details

References

See Also

Examples

Dataset: simulated dataset

Description

Usage

Details

References

See Also

Examples

Backward search for equivalent states

Description

Usage

Arguments

Details

Value

References

See Also

Examples

EM algorithm for mixtures of Markov models

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Forward search for equivalent states

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Plot of the obtained clustering solution

Description

Usage

Arguments

Details

Author(s)

References

See Also

Examples

Prediction of future state visits

Description

Usage

Arguments

Details

Author(s)

References

See Also

Examples

Reading sequences of visited states

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Simulating sequences of visited states

Description