Package 'clickstream'

Title: Analyzes Clickstreams Based on Markov Chains
Description: A set of tools to read, analyze and write lists of click sequences on websites (i.e., clickstream). A click can be represented by a number, character or string. Clickstreams can be modeled as zero- (only computes occurrence probabilities), first- or higher-order Markov chains.
Authors: Michael Scholz, Theo van Kraay
Maintainer: Michael Scholz <[email protected]>
License: GPL-2
Version: 1.3.3
Built: 2024-12-26 06:42:58 UTC
Source: CRAN

Help Index

Analyzes Clickstreams Based on Markov Chains

Description

This package allows modeling clickstreams with Markov chains. It supports to model clickstreams as zero-order, first-order or higher-order Markov chains.

Details

Package: clickstream
Type: Package
Version: 1.3.3
Date: 2023-09-27
License: GPL-2
Depends: R (>= 3.0), methods

Author(s)

Michael Scholz [email protected]

Theo van Kraay [email protected]

References

Scholz, M. (2016) R Package clickstream: Analyzing Clickstream Data with Markov Chains, Journal of Statistical Software, 74, 4, pages 1–17 .

Ching, W.-K.and Huang, X. and Ng, M.K. and Siu, T.-K. (2013) Markov Chains – Models, Algorithms and Applications, 2nd edition, New York: Springer-Verlag.

Examples

# fitting a simple Markov chain and predicting the next click
clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
mc <- fitMarkovChain(cls)
startPattern <- new("Pattern", sequence = c("h", "c"))
predict(mc, startPattern)
plot(mc)

Concatenates two Pattern objects

Description

Concatenates two Pattern objects

Usage

## S4 method for signature 'Pattern,Pattern'
e1 + e2

Arguments

e1

First pattern
e2

Second pattern

Methods

list("signature(e1 = \"Pattern\", e2 = \"Pattern\")")

Concatenates two Pattern objects.

Author(s)

Michael Scholz [email protected]

Returns All Absorbing States

Description

Returns All Absorbing States

Usage

absorbingStates(object)

Arguments

object

An instance of the MarkovChain-class

Methods

list("signature(object = \"MarkovChain\")")

Returns the names of all states that never have a successor in a clickstream (i.e. that are absorbing).

Author(s)

Michael Scholz [email protected]

Coerces a Clickstream Object to a ClickClust Object

Description

Coerces a Clickstream object to a ClickClust object.

Usage

as.ClickClust(clickstreamList)

Arguments

clickstreamList

A list of clickstreams.

Value

A list consisting of a dataset X and a vector of initial states y

Author(s)

Michael Scholz [email protected]

See Also

frequencies

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
X <- as.ClickClust(cls)

Converts a character vector or a character list into a clickstream list.

Description

Converts a character vector or a character list into a clickstream list. Note that non-alphanumeric characters will be removed.

Usage

as.clickstreams(obj, sep = ",", header = TRUE)

Arguments

obj

The character vector or character list which will be converted into a clickstream list. Each line of the vector must represent exactly one click stream.
sep

The character separating clicks (default is “,”).
header

A logical flag indicating whether the first entry of each entry in the character vector is the name of the clickstream.

Value

A list of clickstreams. Each element is a vector of characters representing the clicks. The name of each list element is either extracted from the character vector or a unique number.

Author(s)

Michael Scholz [email protected]

See Also

print.Clickstreams, randomClickstreams

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
print(cls)

Coerces a Clickstream Object to a Transactions Object

Description

Coerces a Clickstream object to a transactions object.

Usage

as.moltenTransactions(clickstreamList)

Arguments

clickstreamList

A list of clickstreams.

Value

An instance of the old class transactions

Author(s)

Michael Scholz [email protected]

See Also

frequencies

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
trans <- as.moltenTransactions(cls)

Coerces a Clickstream Object to a Transactions Object

Description

Coerces a Clickstream object to a transactions object.

Usage

as.transactions(clickstreamList)

Arguments

clickstreamList

A list of clickstreams.

Value

An instance of the class transactions

Author(s)

Michael Scholz [email protected]

See Also

frequencies

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
trans <- as.transactions(cls)

Calculates the chi-square statistic

Description

Calculates the chi-Square statistic, p-value, and degrees of freedom, for the first-order transition matrix of a MarkovChain object compared with observed state changes.

Usage

chiSquareTest(cls, mc)

Arguments

cls

The clickstream object.
mc

The Markov chain against which to compare the clickstream data. Please note that the first-order transition matrix is used for performing the chi-square test.

Author(s)

Theo van Kraay [email protected]

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
                 "User2,i,c,i,c,c,c,d",
                 "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
                 "User4,c,c,p,c,d")

csf <- tempfile()
writeLines(clickstreams, csf)
cls <- readClickstreams(csf, header = TRUE)
unlink(csf)

mc <- fitMarkovChain(cls)
chiSquareTest(cls, mc)

Performs K-Means Clustering on a List of Clickstreams

Description

Performs k-means clustering on a list of clickstreams. For each clickstream a transition matrix of a given order is computed. These transition matrices are used as input for performing k-means clustering.

Usage

clusterClickstreams(clickstreamList, order = 0, centers, ...)

Arguments

clickstreamList

A list of clickstreams for which the cluster analysis is performed.
order

The order of the transition matrices used as input for clustering (default is 0; 0 and 1 are possible).
centers

The number of clusters.
...

Additional parameters for k-means clustering (see kmeans).

Value

This method returns a ClickstreamClusters object (S3-class). It is a list with the following components:

clusters

The resulting list of Clickstreams objects.
centers

A matrix of cluster centres.

states

Vector of states
totss

The total sum of squares.

withinss

Vector of within-cluster sum of squares, one component per cluster.

tot.withinss

Total within-cluster sum of squares, i.e., sum(withinss).

betweenss

The between-cluster sum of squares, i.e., totss - tot.withinss.

Author(s)

Michael Scholz [email protected]

See Also

print.ClickstreamClusters, summary.ClickstreamClusters

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
clusters <- clusterClickstreams(cls, order = 0, centers = 2)
print(clusters)

Class EvaluationResult

Description

Class EvaluationResult

Objects from the Class

Objects can be created by calls of the form new("EvaluationResult", ...). This S4 class describes EvaluationResult objects.

Author(s)

Michael Scholz [email protected]

See Also

mcEvaluate

Examples

# show EvaluationResult definition
showClass("EvaluationResult")

Fits a List of Clickstreams to a Markov Chain

Description

This function fits a list of clickstreams to a Markov chain. Zero-order, first-order as well as higher-order Markov chains are supported. For estimating higher-order Markov chains this function solves the following linear or quadratic programming problem:

min⁡∣∣∑i=1kX−λiQiX∣∣\min ||\sum_{i=1}^k X-\lambda_i Q_iX||

s.t.\mathrm{s.t.}

∑i=1kλi=1\sum_{i=1}^k \lambda_i = 1

λi≥0\lambda_i \ge 0

The distribution of states is given as XX. λi\lambda_i is the lag parameter for lag ii and QiQ_i the transition matrix.

Usage

fitMarkovChain(clickstreamList, order = 1, verbose = TRUE, control = list())

Arguments

clickstreamList

A list of clickstreams for which a Markov chain is fitted.
order

(Optional) The order of the Markov chain that is fitted from the clickstreams. Per default, Markov chains with order=1 are fitted. It is also possible to fit zero-order Markov chains (order=0) and higher-order Markov chains.
verbose

(Optional) An optimal logical variable to indicate whether warnings and infos should be printed.
control

(Optional) The control list of optimization parameters. Parameter optimizer specifies the type of solver used to solve the given optimization problem. Possible values are "linear" (default) and "quadratic". Parameter use.lpSolve determines whether lpSolve or linprog is used as linear solver.

Details

For solving the quadratic programming problem of higher-order Markov chains, an augmented Lagrange multiplier method from the package Rsolnp is used.

Value

Returns a MarkovChain object.

Note

At least half of the clickstreams need to consist of as many clicks as the order of the Markov chain that should be fitted.

Author(s)

Michael Scholz [email protected]

References

This method implements the parameter estimation method presented in Ching, W.-K. et al.: Markov Chains – Models, Algorithms and Applications, 2nd edition, Springer, 2013.

See Also

MarkovChain, Rsolnp

Examples

# fitting a simple Markov chain
clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
mc <- fitMarkovChain(cls)
show(mc)

Generates a list of markov chains from a given set of clusters

Description

The purpose of this function is to generate pre-computed markov chain objects from clusters of clickstreams.

Usage

fitMarkovChains(clusters, order = 1)

Arguments

clusters

The clusters from which to generate markov chain objects.
order

The order for the markov chain.

Author(s)

Theo van Kraay [email protected]

Examples

training <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
              "User2,i,c,i,c,c,c,d",
              "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
              "User4,c,c,p,c,d")

test <- c("User1,h,c,c,p,p,h,c,p,p,c,p,p,o",
          "User2,i,c,i,c,c,c,d",
          "User4,c,c,c,c,d")

trainingCLS <- as.clickstreams(training, header = TRUE)
testCLS <- as.clickstreams(test, header = TRUE)

clusters <- clusterClickstreams(trainingCLS, centers = 2)
markovchains <- fitMarkovChains(clusters, order = 1)

Generates a Data Frame of State Frequencies for All Clickstreams in a List of Clickstreams

Description

Generates a data frame of state frequencies for all clickstreams in a list of clickstreams.

Usage

frequencies(clickstreamList)

Arguments

clickstreamList

A list of clickstreams.

Value

A data frame containing state frequencies for each clickstream.

Author(s)

Michael Scholz [email protected]

See Also

transactions

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
frequencyDF <- frequencies(cls)

Generates an optimal set of clusters for a clickstream object based on consensus clustering.

Description

This is an experimental function for a consensus clustering algorithm based on targeting a range of average next state probabilities derived when fitting each cluster to a markov chain.

Usage

getConsensusClusters(
  trainingCLS,
  testCLS,
  maxIterations = 5,
  optimalProbMean = 0.5,
  range = 0.3,
  centresMin = 2,
  clusterCentresRange = 0,
  order = 1,
  takeHighest = FALSE,
  verbose = FALSE
)

Arguments

trainingCLS

Clickstream object with training data (this should be the data used to build the markov chain object).
testCLS

Clickstream object with test data.
maxIterations

Number of times to iterate (repeat) through the k-means clustering.
optimalProbMean

The target average probability of each next page click prediction in a 1st order markov chain.
range

The range above the optimal probability to target.
centresMin

The minimum cluster centres to evaluate.
clusterCentresRange

the additional cluster centres to evaluate.
order

The order for markov chains that will be used to evaluate each cluster.
takeHighest

Determines whether to default to the highest mean next click probability, or error if the target is not reached after the given number of k-means iterations.
verbose

Should this function report extra information on progress?

Author(s)

Theo van Kraay [email protected]

Examples

training <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
              "User2,i,c,i,c,c,c,d",
              "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
              "User4,h,c,c,p,p,c,p,p,p,i,p,o",
              "User5,i,h,c,c,p,p,c,p,c,d",
              "User6,i,h,c,c,p,p,c,p,c,o",
              "User7,i,h,c,c,p,p,c,p,c,d",
              "User8,i,h,c,c,p,p,c,p,c,d,o")

test <- c(
    "User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
    "User2,i,c,i,c,c,c,d",
    "User3,h,i,c,i,c,p,c,c,p,c,c,i,d"
)

trainingCLS <- as.clickstreams(training, header = TRUE)
testCLS <- as.clickstreams(test, header = TRUE)

clusters <- getConsensusClusters(trainingCLS, testCLS, maxIterations=5, 
                         optimalProbMean=0.40, range = 0.70, centresMin = 2, 
                         clusterCentresRange = 0, order = 1, takeHighest = FALSE, 
                         verbose = FALSE)
markovchains <- fitMarkovChains(clusters)
startPattern <- new("Pattern", sequence = c("i", "h", "c", "p"))
mc <- getOptimalMarkovChain(startPattern, markovchains, clusters)
predict(mc, startPattern)

Generates an optimal set of clusters for a clickstream based on consensus clustering and with parallel computation

Description

This is an experimental function for a consensus clustering algorithm based on targeting a range of average next state probabilities derived when fitting each cluster to a markov chain. This function parallelizes k-means and fitToMarkovChain operations across computer cores, and depends on the parallel package to function.

Usage

getConsensusClustersParallel(
  trainingCLS,
  testCLS,
  maxIterations = 5,
  optimalProbMean = 0.5,
  range = 0.3,
  centresMin = 2,
  clusterCentresRange = 0,
  order = 1,
  cores = 2,
  takeHighest = FALSE,
  verbose = FALSE
)

Arguments

trainingCLS

Clickstream object with training data (this should be the data used to build the markov chain object).
testCLS

Clickstream object with test data.
maxIterations

Number of times to iterate (repeat) through the k-means clustering.
optimalProbMean

The target average probability of each next page click prediction in a 1st order markov chain.
range

The range above the optimal probability to target.
centresMin

The minimum cluster centres to evaluate.
clusterCentresRange

the additional cluster centres to evaluate.
order

The order for markov chains that will be used to evaluate each cluster.
cores

Number of cores used for clustering.
takeHighest

Determines whether to default to the highest mean next click probability, or error if the target is not reached after the given number of k-means iterations.
verbose

Should this function report extra information on progress?

Author(s)

Theo van Kraay [email protected]

Examples

training <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
              "User2,i,c,i,c,c,c,d",
              "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
              "User4,h,c,c,p,p,c,p,p,p,i,p,o",
              "User5,i,h,c,c,p,p,c,p,c,d",
              "User6,i,h,c,c,p,p,c,p,c,o",
              "User7,i,h,c,c,p,p,c,p,c,d",
              "User8,i,h,c,c,p,p,c,p,c,d,o")

test <- c(
    "User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
    "User2,i,c,i,c,c,c,d",
    "User3,h,i,c,i,c,p,c,c,p,c,c,i,d"
)

trainingCLS <- as.clickstreams(training, header = TRUE)
testCLS <- as.clickstreams(test, header = TRUE)

clusters <- getConsensusClustersParallel(trainingCLS, testCLS, maxIterations=3, 
                                 optimalProbMean=0.40, range = 0.70, centresMin = 2, 
                                 clusterCentresRange = 0, order = 1, cores = 1,
                                 takeHighest = FALSE, verbose = FALSE)
markovchains <- fitMarkovChains(clusters)
startPattern <- new("Pattern", sequence = c("i", "h", "c", "p"))
mc <- getOptimalMarkovChain(startPattern, markovchains, clusters)
predict(mc, startPattern)

Generates the optimal markov chains from a list of markov chains and corresponding clusters

Description

The purpose of this function is to predict from a pattern using pre-computed markov chains and corresponding clusters. The markov chain corresponding with the cluster that is the best fit to the prediction value is used.

Usage

getOptimalMarkovChain(startPattern, markovchains, clusters)

Arguments

startPattern

The pattern object to be used.
markovchains

The pre-computed markov chains generated from a set of clusters.
clusters

The corresponding clusters (should be in the corresponding order as the markov chains).

Author(s)

Theo van Kraay [email protected]

Examples

training <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
              "User2,i,c,i,c,c,c,d",
              "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
              "User4,c,c,p,c,d")

test <- c("User1,h,c,c,p,p,h,c,p,p,c,p,p,o",
          "User2,i,c,i,c,c,c,d",
          "User4,c,c,c,c,d")

trainingCLS <- as.clickstreams(training, header = TRUE)
testCLS <- as.clickstreams(test, header = TRUE)

clusters <- clusterClickstreams(trainingCLS, centers = 2)
markovchains <- fitMarkovChains(clusters, order = 1)
startPattern <- new("Pattern", sequence = c("c")) 
mc <- getOptimalMarkovChain(startPattern, markovchains, clusters)
predict(mc, startPattern)

Plots a Heatmap

Description

Plots a Heatmap

Usage

hmPlot(
  object,
  order = 1,
  absorptionProbability = FALSE,
  title = NA,
  lowColor = "yellow",
  highColor = "red",
  flip = FALSE
)

Arguments

object

The MarkovChain for which a heatmap is plotted.
order

Order of the transition matrix that should be plotted. Default is 1.
absorptionProbability

Should the heatmap show absorption probabilities? Default is FALSE.
title

Title of the heatmap.
lowColor

Color for the lowest transition probability of 0. Default is "yellow".
highColor

Color for the highest transition probability of 1. Default is "red".
flip

Flip to horizontal plot. Default is FALSE.

Methods

list("signature(object = \"MarkovChain\")")

Plots a heatmap for a specified transition matrix or the absorption probability matrix of a given MarkovChain object.

Author(s)

Michael Scholz [email protected]

See Also

fitMarkovChain

Examples

# fitting a simple Markov chain and plotting a heat map
clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
mc <- fitMarkovChain(cls)
hmPlot(mc)

Creates a new Pattern object

Description

Creates a new Pattern object

Usage

## S4 method for signature 'Pattern'
initialize(.Object, sequence, probability, absorbingProbabilities, ...)

Arguments

.Object

Pattern (name of the class)
sequence

Click sequence
probability

Probability for the click sequence
absorbingProbabilities

Probabilities that the sequence will finally end in one of the absorbing states
...

Further arguments for the CallNextMethod function

Methods

list("signature(sequence = \"character\", probability = \"numeric\", absorbingProbabilities = \"numeric"))

Creates a new Pattern object.

Author(s)

Michael Scholz [email protected]

Class MarkovChain

Description

Class MarkovChain

Objects from the Class

Objects can be created by calls of the form new("MarkovChain", ...). This S4 class describes MarkovChain objects.

Author(s)

Michael Scholz [email protected]

See Also

fitMarkovChain

Examples

# show MarkovChain definition
showClass("MarkovChain")

# fit a simple Markov chain from a list of click streams
clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
mc <- fitMarkovChain(cls)
show(mc)

Evaluates the number of occurrences of predicted next clicks

Description

Evaluates the number of occurrences of predicted next clicks vs. total number of starting pattern occurrences in a given clickstream. The predicted next click can be a markov chain of any order.

Usage

mcEvaluate(mc, startPattern, testCLS)

Arguments

mc

a markovchain object (this should have been built from a set of training data)
startPattern

the starting pattern we want to predict next click on, and evaluate observed occurrences in test data.
testCLS

clickstream object with test data

Author(s)

Theo van Kraay [email protected]

Examples

training <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
              "User2,i,c,i,c,c,c,d",
              "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
              "User4,c,c,p,c,d")

test <- c("User1,h,h,h,h,c,c,p,p,h,c,p,p,c,p,p,o",
          "User2,i,c,i,c,c,c,d",
          "User4,c,c,c,c,d,c,c,c,c")

csf <- tempfile()
writeLines(training, csf)
trainingCLS <- readClickstreams(csf, header = TRUE)
unlink(csf)

csf <- tempfile()
writeLines(test, csf)
testCLS <- readClickstreams(csf, header = TRUE)
unlink(csf)

mc <- fitMarkovChain(trainingCLS, order = 1)
startPattern <- new("Pattern", sequence = c("c","c")) 
res <- mcEvaluate(mc, startPattern, testCLS)
res

Evaluates all next page clicks in a clickstream training data set against a test data

Description

Evaluates all next page clicks in a clickstream training data set against a test data. Handles higher order by cycling through every possible pattern permutation. Produces a report of observed and expected values in a matrix.

Usage

mcEvaluateAll(
  mc,
  trainingCLS,
  testCLS,
  includeChiSquare = TRUE,
  returnChiSquareOnly = FALSE
)

Arguments

mc

A markovchain object that corresponds to a list of clusters.
trainingCLS

Clickstream object with training data (this should be the data used to build the markov chain object).
testCLS

Clickstream object with test data.
includeChiSquare

Should the result include the chi-square value?
returnChiSquareOnly

Should the result only consist of the chi-square value?

Author(s)

Theo van Kraay [email protected]

See Also

mcEvaluate

Examples

training <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p",
              "User2,i,c,i,c,c,c,d")

test <- c("User1,h,c,c,p,c,h,c,d,p,c,d,p",
             "User2,i,c,i,p,c,c,d")

csf <- tempfile()
writeLines(training, csf)
trainingCLS <- readClickstreams(csf, header = TRUE)
unlink(csf)

csf <- tempfile()
writeLines(test, csf)
testCLS <- readClickstreams(csf, header = TRUE)
unlink(csf)

mc <- fitMarkovChain(trainingCLS, order = 2)
mcEvaluateAll(mc, trainingCLS, testCLS)

Evaluates all next page clicks in a clickstream training data set against a test data

Description

Evaluates all next page clicks in a clickstream training data set against a test data on the basis of a set of pre-computed Markov chains and corresponding clusters. Handles higher order by cycling through every possible pattern permutation. Produces and produces a report of observed and expected values in a matrix

Usage

mcEvaluateAllClusters(
  markovchains,
  clusters,
  testCLS,
  trainingCLS,
  includeChiSquare = TRUE,
  returnChiSquareOnly = FALSE
)

Arguments

markovchains

A list of MarkovChain-objects.
clusters

The list of clusters.
testCLS

Clickstream object with test data.
trainingCLS

Clickstream object with training data (this should be the data used to build the markov chain object).
includeChiSquare

Should the result include the chi-square value?
returnChiSquareOnly

Should the result only consist of the chi-square value?

Author(s)

Theo van Kraay [email protected]

See Also

mcEvaluateAll

Examples

training <- c("User1,h,c,c,p,c,h,c,h,o,p,p,c,p,p,o",
              "User2,i,c,i,c,c,c,o,o,o,i,d",
              "User3,h,i,c,i,c,o,i,p,c,c,p,c,c,i,d",
              "User4,c,c,p,c,d,o,i,h,o,o")

test <- c("User1,h,c,c,p,p,h,o,i,c,p,p,c,p,p,o",
          "User2,i,c,i,c,c,c,d",
          "User4,c,c,c,c,d")

csf <- tempfile()
writeLines(training, csf)
trainingCLS <- readClickstreams(csf, header = TRUE)
unlink(csf)

csf <- tempfile()
writeLines(test, csf)
testCLS <- readClickstreams(csf, header = TRUE)
unlink(csf)

clusters <- clusterClickstreams(trainingCLS, centers = 2, order = 1)
markovchains <- fitMarkovChains(clusters, order = 2)
mcEvaluateAllClusters(markovchains, clusters, testCLS, trainingCLS)

Class Pattern

Description

This S4 class describes a click pattern consisting of a sequence of clicks and a probability of occurrence.

Objects from the Class

Objects can be created by calls of the form new("Pattern", sequence, probability, ...). This S4 class describes a click pattern consisting of a sequence of clicks and a probability of occurrence.

Author(s)

Michael Scholz [email protected]

See Also

randomClicks

Examples

# show Pattern definition
showClass("Pattern")

# create simple Pattern objects
pattern1 <- new("Pattern", sequence = c("h", "c", "p"))
pattern2 <- new("Pattern", sequence = c("c", "p", "p"), probability = 0.2)
pattern3 <- new("Pattern", sequence = c("h", "p", "p"), probability = 0.35,
        absorbingProbabilities = data.frame(d = 0.6, o = 0.4))

Plots a MarkovChain object

Description

Plots a MarkovChain object

Usage

## S4 method for signature 'MarkovChain'
plot(x, order = 1, digits = 2, minProbability = 0, ...)

Arguments

x

An instance of the MarkovChain-class
order

The order of the transition matrix that should be plotted
digits

The number of digits of the transition probabilities
minProbability

Only transitions with a probability >= the specified minProbability will be shown
...

Further parameters for the plot-function in package igraph

Methods

list("signature(x = \"MarkovChain\", order = \"numeric\", digits = \"numeric\")")

Plots the transition matrix with order order of a MarkovChain object as graph.

Author(s)

Michael Scholz [email protected]

Predicts the Next Click(s) of a User

Description

Predicts the Next Click(s) of a User

Usage

## S4 method for signature 'MarkovChain'
predict(object, startPattern, dist = 1, ties = "random")

Arguments

object

The MarkovChain used for predicting the next click(s)
startPattern

Starting clicks of a user as Pattern object. A Pattern with an empty sequence is also possible.
dist

(Optional) The number of clicks that should be predicted (default is 1).
ties

(Optional) The strategy for handling ties in predicting the next click. Possible strategies are random (default) and first.

Methods

list("signature(object = \"MarkovChain\")")

This method predicts the next click(s) of a user. The first clicks of a user are given as Pattern object. The next click(s) are predicted based on the transition probabilities in the MarkovChain object. The probability distribution of the next click (n) is estimated as follows:

X(n)=B⋅∑i=1kλiQiX(n−i)X^{(n)}=B \cdot \sum_{i=1}^k \lambda_iQ_iX^{(n-i)}

The distribution of states at time nn is given as XnX^n. The transition matrix for lag ii is given as QiQ_i. λi\lambda_i specifies the lag parameter and BB the absorbing probability matrix.

Author(s)

Michael Scholz [email protected]

See Also

fitMarkovChain

Examples

# fitting a simple Markov chain and predicting the next click
clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
mc <- fitMarkovChain(cls)
startPattern <- new("Pattern", sequence = c("h", "c"))
predict(mc, startPattern)
#
# predict with predefined absorbing probabilities
#
startPattern <- new("Pattern", sequence = c("h", "c"),
        absorbingProbabilities = data.frame(d = 0.2, o = 0.8))
predict(mc, startPattern)

Predicts the Cluster for a Given Pattern Object

Description

Predicts the cluster for a given Pattern object. Potential clusters need to be identified with the method clusterClickstreams before predicting the cluster.

Usage

## S3 method for class 'ClickstreamClusters'
predict(object, pattern, ...)

Arguments

object

A ClickstreamClusters object containing the clusters. ClickstreamClusters represent the result of a cluster analysis on a list of clickstreams (see clusterClickstreams).
pattern

Sequence of a user's initial clicks as Pattern object.
...

Ignored parameters.

Value

Returns the index of the clusters to which the given Pattern object most probably belongs to.

Author(s)

Michael Scholz [email protected]

See Also

clusterClickstreams, print.ClickstreamClusters

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
clusters <- clusterClickstreams(cls, order = 0, centers = 2)
pattern <- new("Pattern", sequence = c("h", "c"))
predict(clusters, pattern)

Prints a ClickstreamClusters Object

Description

Prints a ClickstreamClusters object. A ClickstreamClusters object represents the result of a cluster analysis on a list of clickstreams (see clusterClickstreams).

Usage

## S3 method for class 'ClickstreamClusters'
print(x, ...)

Arguments

x

A ClickstreamClusters object (see clusterClickstreams).
...

Ignored parameters.

Author(s)

Michael Scholz [email protected]

See Also

clusterClickstreams, summary.ClickstreamClusters

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
clusters <- clusterClickstreams(cls, order = 0, centers = 2)
print(clusters)

Prints a Clickstreams Object

Description

Prints a Clickstreams object

Usage

## S3 method for class 'Clickstreams'
print(x, ...)

Arguments

x

A list of clickstreams.
...

Ignored parameters.

Author(s)

Michael Scholz [email protected]

See Also

readClickstreams, randomClickstreams

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
print(cls)

Prints the Summary of a MarkovChain Object

Description

Prints the summary of a MarkovChain object.

Usage

## S3 method for class 'MarkovChainSummary'
print(x, ...)

Arguments

x

A MarkovChainSummary object generated with the function summary
...

Ignored parameters.

Author(s)

Michael Scholz [email protected]

See Also

summary

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
mc <- fitMarkovChain(cls)
print(summary(mc))

Generates a Sequence of Clicks

Description

Generates a Sequence of Clicks

Usage

randomClicks(object, startPattern, dist)

Arguments

object

The MarkovChain used for generating the next click(s)
startPattern

Pattern containing the first clicks of a user. A Pattern object with an empty sequence is also possible.
dist

(Optional) The number of clicks that should be generated (default is 1).

Methods

list("signature(object = \"MarkovChain\")")

Generates a sequence of clicks by randomly walking through the transition graph of a given MarkovChain object.

Author(s)

Michael Scholz [email protected]

See Also

fitMarkovChain

Examples

# fitting a simple Markov chain and predicting the next click
clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
mc <- fitMarkovChain(cls)
startPattern <- new("Pattern", sequence = c("h", "c"))
predict(mc, startPattern)

Generates a List of Clickstreams

Description

Generates a list of clickstreams by randomly walking through a given transition matrix.

Usage

randomClickstreams(
  states,
  startProbabilities,
  transitionMatrix,
  meanLength,
  n = 100
)

Arguments

states

Names of all possible states.
startProbabilities

Start probabilities for all states.
transitionMatrix

Matrix of transition probabilities.
meanLength

Average length of the click streams.
n

Number of click streams to be generated.

Value

Returns a list of clickstreams.

Author(s)

Michael Scholz [email protected]

See Also

fitMarkovChain, readClickstreams, print.Clickstreams

Examples

# generate a simple list of click streams
states <- c("a", "b", "c")
startProbabilities <- c(0.2, 0.5, 0.3)
transitionMatrix <- matrix(c(0, 0.4, 0.6, 0.3, 0.1, 0.6, 0.2, 0.8, 0), nrow = 3)
cls <- randomClickstreams(states, startProbabilities, transitionMatrix, meanLength = 5, n = 10)
print(cls)

Reads a List of Clickstreams from File

Description

Reads a list of clickstream from a csv-file. Note that non-alphanumeric characters will be removed.

Usage

readClickstreams(file, sep = ",", header = FALSE)

Arguments

file

The name of the file which the clickstreams are to be read from. Each line of the file appears as one click stream. If it does not contain an absolute path, the file name is relative to the current working directory, getwd.
sep

The character separating clicks (default is “,”).
header

A logical flag indicating whether the first entry of each line in the file is the name of the clickstream user.

Value

A list of clickstreams. Each element is a vector of characters representing the clicks. The name of each list element is either the header of a clickstream file or a unique number.

Author(s)

Michael Scholz [email protected]

See Also

print.Clickstreams, randomClickstreams

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
csf <- tempfile()
writeLines(clickstreams, csf)
cls <- readClickstreams(csf, header = TRUE)
unlink(csf)
print(cls)

Shows an EvaluationResult object

Description

Shows an EvaluationResult object

Usage

## S4 method for signature 'EvaluationResult'
show(object)

Arguments

object

An instance of the EvaluationResult-class

Methods

list("signature(object = \"EvaluationResult\")")

Shows an EvaluationResult object.

Author(s)

Michael Scholz [email protected]

Shows a MarkovChain object

Description

Shows a MarkovChain object

Usage

## S4 method for signature 'MarkovChain'
show(object)

Arguments

object

An instance of the MarkovChain-class

Methods

list("signature(object = \"MarkovChain\")")

Shows an MarkovChain object.

Author(s)

Michael Scholz [email protected]

Shows a Pattern object

Description

Shows a Pattern object

Usage

## S4 method for signature 'Pattern'
show(object)

Arguments

object

An instance of the Pattern-class

Methods

list("signature(object = \"Pattern\")")

Shows a Pattern object.

Author(s)

Michael Scholz [email protected]

Returns All States

Description

Returns All States

Usage

states(object)

Arguments

object

An instance of the MarkovChain-class

Methods

list("signature(object = \"MarkovChain\")")

Returns the name of all states of a MarkovChain object.

Author(s)

Michael Scholz [email protected]

Prints the Summary of a MarkovChain Object

Description

Prints the Summary of a MarkovChain Object

Usage

## S4 method for signature 'MarkovChain'
summary(object)

Arguments

object

An instance of the MarkovChain-class

Value

Returns a MarkovChainSummary object.

list("desc")

A short description of the MarkovChain object.
list("observations")

The number of observations from which the MarkovChain has been fitted.
list("k")

The number of estimation parameters.
list("logLikelihood")

The maximal log-likelihood of the MarkovChain estimation.
list("aic")

Akaike's Information Criterion for the MarkovChain object
list("bic")

Bayesian Information Criterion for the MarkovChain object

Methods

list("signature(object = \"MarkovChain\")")

Generates a summary for a given MarkovChain object

Author(s)

Michael Scholz [email protected]

Prints a Summary of a ClickstreamCluster Object

Description

Prints a summary of a ClickstreamCluster object. A ClickstreamClusters object represents the result of a cluster analysis on a list of clickstreams (see clusterClickstreams).

Usage

## S3 method for class 'ClickstreamClusters'
summary(object, ...)

Arguments

object

A ClickstreamClusters object returned by clusterClickstreams.
...

Ignored parameters.

Author(s)

Michael Scholz [email protected]

See Also

clusterClickstreams, print.ClickstreamClusters

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
clusters <- clusterClickstreams(cls, order = 0, centers = 2)
summary(clusters)

Prints a Summary of a Clickstreams Object

Description

Prints a summary of a Clickstreams object.

Usage

## S3 method for class 'Clickstreams'
summary(object, ...)

Arguments

object

A Clickstreams object (see readClickstreams).
...

Ignored parameters.

Author(s)

Michael Scholz [email protected]

See Also

readClickstreams, randomClickstreams

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
summary(cls)

Returns All Transient States

Description

Returns All Transient States

Usage

transientStates(object)

Arguments

object

An instance of the MarkovChain-class

Methods

list("signature(object = \"MarkovChain\")")

Returns the names of all states that have a non-zero probability that a user will never return to them (i.e. that are transient).

Author(s)

Michael Scholz [email protected]

Writes a List of Clickstreams to File

Description

Writes a list of clickstream to a csv-file.

Usage

writeClickstreams(
  clickstreamList,
  file,
  header = TRUE,
  sep = ",",
  quote = TRUE
)

Arguments

clickstreamList

The list of clickstreams to be written.
file

The name of the file which the clickstreams are written to.
header

A logical flag indicating whether the name of each clickstream element should be used as first element.
sep

The character used to separate clicks (default is “,”).
quote

A logical flag indicating whether each element of a clickstream will be surrounded by double quotes (default is TRUE.

Author(s)

Michael Scholz [email protected]

See Also

readClickstreams, clusterClickstreams

Examples

clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
               "User2,i,c,i,c,c,c,d",
               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
               "User4,c,c,p,c,d",
               "User5,h,c,c,p,p,c,p,p,p,i,p,o",
               "User6,i,h,c,c,p,p,c,p,c,d")
cls <- as.clickstreams(clickstreams, header = TRUE)
clusters <- clusterClickstreams(cls, order = 0, centers = 2)
writeClickstreams(cls, file = "clickstreams.csv", header = TRUE, sep = ",")

# Remove the clickstream file
unlink("clickstreams.csv")