Package 'arulesSequences'

Combining Objects

Description

c combines a collection of (timed) sequences or sequence rules into a single object.

Usage

## S4 method for signature 'sequences'
c(x, ..., recursive = FALSE)

## S4 method for signature 'timedsequences'
c(x, ..., recursive = FALSE)

## S4 method for signature 'sequencerules'
c(x, ..., recursive = FALSE)

Arguments

x	an object.
...	(a list of) further objects of the same class as x

.

recursive

a logical value specifying if the function should descend through lists.

Value

For c and unique an object of the same class as x.

Note

Method c is similar to rbind but with the added twist that objects are internally conformed matching their item labels. That is, an object based on the union of item labels is created.

For timed sequences event times are currently conformed as follows: if the union of all labels can be cast to integer the labels are sorted. Otherwise, labels not occurring in x are appended.

The default setting does not allow any object to be of a class other than x, i.e. the objects are not combined into a list.

Author(s)

Christian Buchta

See Also

Class sequences, timedsequences, sequencerules, method match.

Examples

## continue example
example(ruleInduction, package = "arulesSequences")
s <- c(s1, s2)
s
match(unique(s), s1)

## combine rules
r <- c(r2, r2[1:2])
r
match(unique(r), r2)

## combine timed sequences
z <- as(zaki, "timedsequences")
match(z, c(z[1], z[-1]))

---

Mining Associations with cSPADE

Description

Mining frequent sequential patterns with the cSPADE algorithm. This algorithm utilizes temporal joins along with efficient lattice search techniques and provides for timing constraints.

Usage

cspade(data, parameter = NULL, control = NULL, tmpdir = tempdir())

Arguments

data	an object of class transactions with temporal information.
parameter	an object of class SPparameter or a named list with corresponding components.
control	an object of class SPcontrol or a named list with corresponding components.
tmpdir	a non-empty character vector giving the directory name where temporary files are written.

Details

Interfaces the command-line tools for preprocessing and mining frequent sequences with the cSPADE algorithm by M. Zaki via a proper chain of system calls.

The temporal information is taken from components sequenceID (sequence or customer identifier) and eventID (event identifier) of transactionInfo. Note that integer identifiers must be positive and that transactions must be ordered by sequenceID and eventID.

Class information (on sequences or customers) is taken from component classID, if available.

The amount of disk space used by temporary files is reported in verbose mode (see class SPcontrol).

If specified timeout is passed to system2 (see details there and class SPcontrol).

Value

Returns an object of class sequences.

Warning

The implementation of the maxwin constraint in the command-line tools seems to be broken. To avoid confusion it is disabled with a warning.

Note

Temporary files may not be deleted until the end of the R session if the call is interrupted. Use timeouts to avoid this problem.

The current working directory (see getwd) must be writable.

Author(s)

Christian Buchta, Michael Hahsler

References

M. J. Zaki. (2001). SPADE: An Efficient Algorithm for Mining Frequent Sequences. Machine Learning Journal, 42, 31–60.

See Also

Class transactions, sequences, SPparameter, SPcontrol, method ruleInduction, support, function read_baskets.

Examples

## use example data from paper
data(zaki)
## get support bearings
s0 <- cspade(zaki, parameter = list(support = 0,
                                    maxsize = 1, maxlen = 1),
                   control   = list(verbose = TRUE))
as(s0, "data.frame")
## mine frequent sequences
s1 <- cspade(zaki, parameter = list(support = 0.4), 
		   control   = list(verbose = TRUE, tidLists = TRUE))
summary(s1)
as(s1, "data.frame")

##
summary(tidLists(s1))
transactionInfo(tidLists(s1))

## use timing constraint
s2 <- cspade(zaki, parameter = list(support = 0.4, maxgap = 5))
as(s2, "data.frame")

## use classification
t <- zaki
transactionInfo(t)$classID <-
    as.integer(transactionInfo(t)$sequenceID) %% 2 + 1L
s3 <- cspade(t, parameter = list(support = 0.4, maxgap = 5))
as(s3, "data.frame")

## replace timestamps
t <- zaki
transactionInfo(t)$eventID <-
    unlist(tapply(seq(t), transactionInfo(t)$sequenceID,
	function(x) x - min(x) + 1), use.names = FALSE)
as(t, "data.frame")
s4 <- cspade(t, parameter = list(support = 0.4))
s4
identical(as(s1, "data.frame"), as(s4, "data.frame"))

## work around
s5 <- cspade(zaki, parameter = list(support = .25, maxgap = 5))
length(s5)
k <- support(s5, zaki, control   = list(verbose = TRUE,
                       parameter = list(maxwin = 5)))
table(size(s5[k == 0]))

## Not run: 
## use generated data
t <- read_baskets(con  = system.file("misc", "test.txt", package =
				      "arulesSequences"),
		  info = c("sequenceID", "eventID", "SIZE"))
summary(t)
## use low support
s6 <- cspade(t, parameter = list(support = 0.0133), 
		control   = list(verbose = TRUE, timeout = 15))
summary(s6)

## check
k <- support(s6, t, control = list(verbose = TRUE))
table(size(s6), sign(quality(s6)$support -k))

## use low confidence
r6 <- ruleInduction(s6, confidence = .5,
			control    = list(verbose = TRUE))
summary(r6)

## End(Not run)

---

Get/Set Object Information

Description

sequenceInfo gets or sets information on the elements of a collection of sequences

ruleInfo gets or sets information on the elements of a collection of sequence rules.

itemInfo gets or sets information on the set of distinct items associated with a collection of sequences.

timeInfo gets or sets information on the event times of a collection of timed sequences.

Usage

## S4 method for signature 'sequences'
sequenceInfo(object)

## S4 method for signature 'sequences':
sequenceInfo(object) <- value

## S4 method for signature 'sequencerules'
ruleInfo(object)

## S4 method for signature 'sequencerules':
ruleInfo(object) <- value

## S4 method for signature 'sequences'
itemInfo(object)

## S4 method for signature 'sequences':
itemInfo(object) <- value

## S4 method for signature 'timedsequences'
timeInfo(object)

## S4 method for signature 'timedsequences':
timeInfo(object) <- value

Arguments

object	an object.
value	a data frame corresponding with the elements or times of object.

Value

For method sequenceInfo and method ruleInfo a data frame of information on and corresponding with the elements of object.

For method itemInfo a data frame of information on and corresponding with the distinct items of object.

For method timeInfo a data frame of information on and corresponding with the distinct event times of object.

Note

For reasons of efficiency the reference set of distinct itemsets may contain unreferenced elements, i.e. items that do not occur in any sequence.

Unique item identifiers must be provided in column labels.

Unique event time identifiers must be provided in columns labels and eventID. Note that the latter is used for computation of gaps, etc.

Author(s)

Christian Buchta

See Also

Class sequences, timedsequences, sequencerules.

Examples

## continue example
example(ruleInduction, package = "arulesSequences")

## empty
sequenceInfo(s2) <- sequenceInfo(s2)
ruleInfo(r2) <- ruleInfo(r2)

## item info
itemInfo(s2)


## time info
z <- as(zaki, "timedsequences")
timeInfo(z)

---

Display Objects

Description

inspect displays a collection of (timed) sequences or sequence rules and their associated quality measures formatted for online inspection.

labels retrieves the string representations of a collection of (timed) sequences or sequence rules.

itemLabels gets the string representations of the set of distinct items or itemsets (elements) associated with a collection of sequences, or sets item labels.

Usage

## S4 method for signature 'sequences'
inspect(x, setSep = ",", seqStart = "<", seqEnd = ">",
	decode = TRUE)

## S4 method for signature 'timedsequences'
inspect(x, setSep = ",", seqStart = "<", seqEnd = ">", 
	decode = TRUE)

## S4 method for signature 'sequencerules'
inspect(x, setSep = ",", seqStart = "<", seqEnd = ">",
	ruleSep = "=>", decode = TRUE)


## S4 method for signature 'sequences'
labels(object, setSep = ",", seqStart = "<", seqEnd = ">",
       decode = TRUE, ...)

## S4 method for signature 'timedsequences'
labels(object, timeStart = "[", timeEnd = "]", setSep = ",",
       seqStart = "<", seqEnd = ">", decode = TRUE, ...)
       

## S4 method for signature 'sequencerules'
labels(object, setSep = ",", seqStart = "<", seqEnd = ">", 
       ruleSep = " => ", decode = TRUE, ...)

## S4 method for signature 'sequences'
itemLabels(object, itemsets = FALSE, ...)

## S4 method for signature 'sequences, character':
itemLabels(object) <- value

Arguments

x, object	an object.
setSep	a string value specifying the itemset (element) separator.
seqStart	a string value specifying the left sequence delimiter.
seqEnd	a string value specifying the right sequence delimiter.
ruleSep	a string value specifying the separator of the left-hand (antecedent) and the right-hand side (consequent) sequence.
timeStart	a string value specifying the left event time delimiter.
timeEnd	a string value specifying the right event time delimiter.
decode	a logical value specifying if the item indexes should be replaced by item labels.
itemsets	a logical value specifying the type of labels.
...	arguments specifying the markup of itemsets: itemSep = ",", setStart = "{", or setEnd = "\}".
value	a character vector of length the number of items of object.

Value

For method inspect returns x invisibly.

For method labels a character vector corresponding with the elements of x.

For method itemLabels a character vector corresponding with the distinct items or itemsets of object.

Note

For compatibility with package arules the markup of itemsets is not customizable in the inspect methods.

For reasons of efficiency the reference set of distinct itemsets may contain unreferenced elements, e.g. after subsetting.

Author(s)

Christian Buchta

See Also

Class sequences, timedsequences, sequencerules, method subset.

Examples

## continue example
example(ruleInduction, package = "arulesSequences")

## stacked style
inspect(s2)
inspect(s2, setSep = "->", seqStart = "", seqEnd = "")

## economy style
labels(s2, setSep = "->", seqStart = "", seqEnd = "",
	   itemSep = " ", setStart = "", setEnd = "")

## rules
inspect(r2)

## alternate style
labels(r2, ruleSep = " + ")

## itemset labels
itemLabels(s2, itemsets = TRUE)
itemLabels(s2[reduce = TRUE], itemsets = TRUE)

## item labels
itemLabels(s2) <- tolower(itemLabels(s2))
itemLabels(s2)

## timed
z <- as(zaki, "timedsequences") 
labels(z)
inspect(z)

---

Count Items or Itemsets

Description

itemFrequency counts the number of distinct occurrences of items or itemsets (elements) in a collection of sequences. That is, multiple occurrences within a sequence are ignored.

itemTable cross-tabulates the counts an item or itemset occurs in a sequence.

nitems computes the total number of distinct occurrences of items or itemsets in a collection of sequences.

dim retrieves the dimensions of an object of class sequences or timedsequences.

length retrieves the number of elements of a collection of sequences or sequence rules.

Usage

## S4 method for signature 'sequences'
itemFrequency(x, itemsets = FALSE, type = c("absolute", "relative"))

## S4 method for signature 'sequences'
itemTable(x, itemsets = FALSE)

## S4 method for signature 'sequences'
nitems(x, itemsets = FALSE)

## S4 method for signature 'sequences'
dim(x)

## S4 method for signature 'timedsequences'
dim(x)

## S4 method for signature 'sequences'
length(x)

## S4 method for signature 'sequencerules'
length(x)

Arguments

x	an object.
itemsets	a logical value specifying the type of count.
type	a string value specifying the scale of count.

Value

For itemFrequency returns a vector of counts corresponding with the reference set of distinct items or itemsets.

For itemTable returns a table with the rownames corresponding with the reference set of distinct items or itemsets.

For nitems a scalar value.

For dim and class sequences a vector of length three containing the number of sequences and the dimension of the reference set of distinct itemsets. For class timedsequences the fourth element contains the number of distinct event times.

For length a scalar value.

Note

For efficiency reasons, the reference set of distinct itemsets can be larger than the set actually referenced by a collection of sequences. Thus, the counts of some items or itemsets may be zero.

Method nitems is provided for efficiency; method dim for technical information.

For analysis of a set of rules use the accessors lhs or rhs, or coerce to sequences.

Author(s)

Christian Buchta

See Also

Class sequences, timedsequences, method size, subset.

Examples

## continue example
example(cspade)

##
itemFrequency(s2)
itemFrequency(s2, itemsets = TRUE)

##
itemTable(s2)
itemTable(s2, itemsets = TRUE)

##
nitems(s2)
nitems(s2, itemsets = TRUE)

##
length(s2)
dim(s2)

##
z <- as(zaki, "timedsequences")
dim(z)

---

Match Objects

Description

match finds the positions of first matches of a collection of sequences or sequence rules in an object of the same class.

%in% indicates matches of the left in the right operand. If the right operand is a vector of item labels indicates if a sequence contains any of the items given.

%ain% indicates if a sequence contains all the items given as the right operand.

%pin% indicates if a sequence contains any item matching the regular expression given as the right operand.

%ein% indicates if a sequence contains any itemset containing all the items given as the right operand.

duplicated indicates duplicate occurrences of sequences or sequence rules.

Usage

## S4 method for signature 'sequences,sequences'
match(x, table, nomatch = NA_integer_, incomparables = NULL)

## S4 method for signature 'sequencerules,sequencerules'
match(x, table, nomatch = NA_integer_, incomparables = NULL)

## S4 methods for signature 'sequences, character':
x %in%  table
x %ain% table
x %pin% table
x %ein% table

## S4 method for signature 'sequences'
duplicated(x, incomparables = FALSE)

## S4 method for signature 'sequencerules'
duplicated(x, incomparables = FALSE)

Arguments

x	an object.
table	an object (of the same class as x).
nomatch	the value to be returned in the case of no match.
incomparables	not used.

Value

For match returns an integer vector of the same length as x containing the position in table of the first match, or if there is no match the value of nomatch.

For %in%, %ain%, and %pin% returns a logical vector indicating for each element of x if a match was found in the right operand.

For duplicated a logical vector corresponding with the elements of x.

Note

For practical reasons, the item labels given in the right operand must match the item labels associated with x exactly.

Currently, an operator for matching against the labels of a set of sequences is not provided. For example, it could be defined as

"%lin%" <- function(l, r) match(r, labels(l)) > 0

with the caveat of being too general.

FIXME currently matching of timed sequences does not take event times into consideration.

Author(s)

Christian Buchta

See Also

Class sequences, sequencerules, method labels, itemLabels.

Examples

## continue example
example(cspade)

## match
labels(s1[match(s2, s1)])
labels(s1[s1 %in% s2])	    # the same

## match items
labels(s2[s2 %in%  c("B", "F")])
labels(s2[s2 %ain% c("B", "F")])
labels(s2[s2 %pin% "F"])

## match itemsets
labels(s1[s1 %ein% c("F","B")])

---

Read Transaction Data

Description

Read transaction data in basket format (with additional temporal or other information) and create an object of class transactions.

Usage

read_baskets(con, sep = "[ \t]+", info = NULL, iteminfo = NULL,
             encoding = "unknown")

Arguments

con	an object of class connection or file name.
sep	a regular expression specifying how fields are separated in the data file.
info	a character vector specifying the header for columns with additional transaction information.
iteminfo	a data frame specifying (additional) item information.
encoding	a character string indicating the encoding which is passed to readlines (see Encoding)

.

Details

Each line of text represents a transaction where items are separated by a pattern matching the regular expression specified by sep.

Columns with additional information such as customer or time (event) identifiers are required to come before any item identifiers and to be separated by sep, and must be specified by info.

Sequential data are identified by the presence of the column identifiers "sequenceID" (sequence or customer identifier) and "eventID" (time or event identifier) of transactionInfo.

The row names of iteminfo must match the item identifiers present in the data. However, iteminfo need not contain a labels column.

Value

An object of class transactions.

Note

The item labels are sorted in the order they appear first in the data.

Author(s)

Christian Buchta

See Also

Class timedsequences, transactions, function cspade.

Examples

## read example data
x <- read_baskets(con  = system.file("misc", "zaki.txt", package = 
                                     "arulesSequences"),
		  info = c("sequenceID","eventID","SIZE"))
as(x, "data.frame")

## Not run: 
## calendar dates
transactionInfo(x)$Date <-
    as.Date(transactionInfo(x)$eventID, origin = "2015-04-01")
transactionInfo(x)
all.equal(transactionInfo(x)$eventID,
          as.integer(transactionInfo(x)$Date - as.Date("2015-04-01")))

## End(Not run)

---

Induce Sequence Rules

Description

Induce a set of strong sequence rules from a set of frequent sequences, i.e. which (1) satisfy the minimum confidence threshold and (2) which contain the last element of the generating sequence as the right-hand side (consequent) sequence.

Usage

## S4 method for signature 'sequences'
ruleInduction(x, transactions, confidence = 0.8, control = NULL)

Arguments

x	an object.
transactions	an optional object of class transactions with temporal information.
confidence	a numeric value specifying the minimum confidence threshold.
control	a named list with logical component verbose specifying if progress and runtime information should be displayed.

Details

If transactions is not specified, the collection of sequences supplied must be closed with respect to the rules to be induced. That is, the left- and the right-hand side sequence of each candidate rule must be contained in the collection of sequences. However, using timing constraints in the mining step the set of frequent sequences may not be closed under rule induction.

Otherwise, x is completed (augmented) to be closed under rule induction and the support is computed from transactions, using method ptree. Note that, rules for added sequences, if any, are not induced.

Value

Returns an object of class sequencerules.

Author(s)

Christian Buchta

See Also

Class sequences, sequencerules, method support, function cspade.

Examples

## continue example
example(cspade)

## mine rules
r2 <- ruleInduction(s2, confidence = 0.5,
			control    = list(verbose = TRUE))
summary(r2)
as(r2, "data.frame")

---

Class "sequencerules" — Collections of Sequential Rules

Description

Represents a collection of sequential rules and their associated quality measure. That is, the elements in the consequent occur at a later time than the elements of the antecedent.

Objects from the Class

Typically objects are created by a sequence rule mining algorithm as the result value, e.g. method ruleInduction.

Objects can be created by calls of the form new("sequencerules", ...).

Slots

elements:

an object of class itemsets containing a sparse representation of the unique elements of a sequence.

lhs:

an object of class sgCMatrix containing a sparse representation of the left-hand sides of the rules (antecedent sequences).

rhs:

an object of class sgCMatrix containing a sparse representation of the right-hand sides of the rules (consequent sequences).

ruleInfo:

a data.frame which may contain additional information on a sequence rule.

quality:

a data.frame containing the quality measures of a sequence rule.

Extends

Class "associations", directly.

Methods

coerce

signature(from = "sequencerules", to = "list")

coerce

signature(from = "sequencerules", to = "data.frame")

coerce

signature(from = "sequencerules", to = "sequences"); coerce a collection of sequence rules to a collection of sequences by appending to each left-hand (antecedent) sequence its right-hand (consequent) sequence.

c

signature(x = "sequencerules")

coverage

signature(x = "sequencerules"); returns the support values of the left-hand side (antecedent) sequences.

duplicated

signature(x = "sequencerules")

labels

signature(x = "sequencerules")

ruleInfo

signature(object = "sequencerules")

ruleInfo<-

signature(object = "sequencerules")

inspect

signature(x = "sequencerules")

is.redundant

signature(x = "sequencerules"); returns a logical vector indicating if a rule has a proper subset in x which has the same right-hand side and the same or a higher confidence.

labels

signature(object = "sequencerules")

length

signature(x = "sequencerules")

lhs

signature(x = "sequencerules")

match

signature(x = "sequencerules")

rhs

signature(x = "sequencerules")

show

signature(object = "sequencerules")

size

signature(x = "sequencerules")

subset

signature(x = "sequencerules")

summary

signature(object = "sequencerules")

unique

signature(x = "sequencerules")

Note

Some of the methods for sequences are not implemented as objects of this class can be coerced to sequences.

Author(s)

Christian Buchta

See Also

Class sgCMatrix, itemsets, associations, sequences, method ruleInduction, is.redundant, function cspade

Examples

## continue example
example(ruleInduction, package = "arulesSequences")
cbind(as(r2, "data.frame"), 
      coverage = coverage(r2))

## coerce to sequences
as(as(r2, "sequences"), "data.frame")

## find redundant rules
is.redundant(r2, measure = "lift")

---

Class "sequences" — Collections of Sequences

Description

Represents a collection of sequences and the associated quality measures.

Objects from the Class

Most frequently, objects are created by a sequence mining algorithm such as cSPADE as the return value.

Objects can also be created by calls of the form new("sequences", ...).

Slots

elements:

an object of class itemsets containing a sparse representation of the unique elements of a sequence.

data:

an object of class sgCMatrix containing a sparse representation of ordered lists (collections of) indexes into the unique elements.

sequenceInfo:

a data frame which may contain additional information on a sequence.

quality:

a data.frame containing the quality measures of a sequence.

tidLists:

an object of class tidLists mapping supporting sequences, or NULL.

Extends

Class "associations", directly.

Methods

coerce

signature(from = "sequences", to = "list")

coerce

signature(from = "sequences", to = "data.frame")

coerce

signature(from = "list", to = "sequences")

%in%

signature(x = "sequences", table = "character")

%ain%

signature(x = "sequences", table = "character")

%pin%

signature(x = "sequences", table = "character")

%ein%

signature(x = "sequences", table = "character")

c

signature(x = "sequences")

dim

signature(x = "sequences")

duplicated

signature(x = "sequences")

labels

signature(object = "sequences")

length

signature(x = "sequences")

LIST

signature(x = "sequences")

match

signature(x = "sequences")

nitems

signature(x = "sequences")

sequenceInfo

signature(object = "sequences")

sequenceInfo<-

signature(object = "sequences")

inspect

signature(x = "sequences")

is.closed

signature(x = "sequences"); returns a logical vector indicating if a sequence has no proper superset in x which has the same support.

is.maximal

signature(x = "sequences"); returns a logical vector indicating if a sequence is not a subsequence of any other sequence in x.

is.subset

signature(x = "sequences")

is.superset

signature(x = "sequences")

itemFrequency

signature(x = "sequences")

itemInfo

signature(object = "sequences")

itemInfo<-

signature(object = "sequences")

itemLabels

signature(object = "sequences")

itemLabels<-

signature(object = "sequences")

itemTable

signature(x = "sequences")

itemsets

signature(x = "sequences"); returns the reference set of distinct itemsets (elements).

ruleInduction

signature(x = "sequences")

show

signature(object = "sequences")

size

signature(x = "sequences")

subset

signature(x = "sequences")

summary

signature(object = "sequences")

support

signature(x = "sequences")

unique

signature(x = "sequences")

Note

Coercion from an object of class transactions with temporal information to an object of class sequences is not provided as this information would be lost. Use class timedsequences instead.

Currently, a general method for concatenation of sequences similar to cbind, is not provided.

Author(s)

Christian Buchta

See Also

Class sgCMatrix, timedsequences, itemsets, associations, method ruleInduction, FIXME, function cspade, data zaki.

Examples

## 3 example sequences
x <- list("01" = list(c("A","B"), "C"), 
          "02" = list("C"), 
	  "03" = list("B", "B"))

## coerce
s <- as(x, "sequences")
as(s, "data.frame")

## get reference set
as(itemsets(s), "data.frame")

---

Class "sgCMatrix" – Sparse Ordered Lists of Symbols

Description

Sparse pseudo matrices in column-compressed form for storing ordered lists of symbols.

Objects from the Class

Most frequently, an object is created upon creation of an object of class sequences or
sequencerules.

Objects can also be created by calls of the form new("sgCMatrix", ...).

Slots

p:

an integer vector of length the number of columns in the matrix plus one. These are zero-based pointers into i, i.e. to the first element of a list. However, note that the last element contains the number of elements of i.

i:

an integer vector of length the number of non-zero elements in the matrix. These are zero-based symbol indexes, i.e. pointers into the row names if such exist.

Dim:

an integer vector representing the number of symbols and the number of lists.

Dimnames:

a list with components for symbol and list labels.

factors:

unused, for compatibility with package Matrix only.

Methods

coerce

signature(from = "sgCMatrix", to = "list")

coerce

signature(from = "list", to = "sgCMatrix")

coerce

signature(from = "ngCMatrix", to = "sgCMatrix")

dim

signature(x = "sgCMatrix")

dimnames

signature(x = "sgCMatrix")

dimnames<-

signature(x = "sgCMatrix", value = "ANY")

show

signature(x = "sgCMatrix")

Note

The number of rows can be larger than the number of symbols actually occurring. Thus i need not be recoded upon subsetting or two collections of lists with the same index base can be easily combined (column or row-wise).

Many of the methods of this class implemented in C are currently not interfaced as R methods.

Author(s)

Christian Buchta

See Also

Class sequences, timedsequences, sequencerules.

Examples

## 3 example sequences
x <- list("01" = list(c("A","B"), "C"), 
          "02" = list("C"), 
	  "03" = list("B", "B"))

## uses paste
s <- as(x, "sgCMatrix")
s

##
dim(s)
dimnames(s)

---

Compute Similarities

Description

Provides the generic function similarity and the S4 method to compute similarities among a collection of sequences.

is.subset, is.superset find subsequence or supersequence relationships among a collection of sequences.

Usage

similarity(x, y = NULL, ...)

## S4 method for signature 'sequences'
similarity(x, y = NULL,
           method = c("jaccard", "dice", "cosine", "subset"),
	   strict = FALSE)

## S4 method for signature 'sequences'
is.subset(x, y = NULL, proper = FALSE)
## S4 method for signature 'sequences'
is.superset(x, y = NULL, proper = FALSE)

Arguments

x, y	an object.
...	further (unused) arguments.
method	a string specifying the similarity measure to use (see details).
strict	a logical value specifying if strict itemset matching should be used.
proper	a logical value specifying if only strict relationships (omitting equality) should be indicated.

Details

Let the number of common elements of two sequences refer to those that occur in a longest common subsequence. The following similarity measures are implemented:

jaccard:

The number of common elements divided by the total number of elements (the sum of the lengths of the sequences minus the length of the longest common subsequence).

dice:

Uses two times the number of common elements.

cosine:

Uses the square root of the product of the sequence lengths for the denominator.

subset:

Zero if the first sequence is not a subsequence of the second. Otherwise the number of common elements divided by the number of elements in the first sequence.

If strict = TRUE the elements (itemsets) of the sequences must be equal to be matched. Otherwise matches are quantified by the similarity of the itemsets (as specified by method) thresholded at 0.5, and the common sequence by the sum of the similarities.

Value

For similarity, returns an object of class dsCMatrix if the result is symmetric (or method = "subset") and and object of class dgCMatrix otherwise.

For is.subset, is.superset returns an object of class lgCMatrix.

Note

Computation of the longest common subsequence of two sequences of length n, m takes O(n*m) time.

The supported set of operations for the above matrix classes depends on package Matrix. In case of problems, expand to full storage representation using as(x, "matrix") or as.matrix(x).

For efficiency use as(x, "dist") to convert a symmetric result matrix for clustering.

Author(s)

Christian Buchta

See Also

Class sequences, method dissimilarity.

Examples

## use example data
data(zaki)
z <- as(zaki, "timedsequences")
similarity(z)

# require equality
similarity(z, strict = TRUE)

## emphasize common
similarity(z, method = "dice")

## 
is.subset(z)
is.subset(z, proper = TRUE)

---

Compute the Size of Sequences

Description

size computes the size of a sequence. This can be either the number of (distinct) itemsets (elements) or items occurring in a sequence.

ritems compute the minimum (maximum) number an item or itemset (element) is repeatedly occurring in a sequence.

Usage

## S4 method for signature 'sequences'
size(x, type = c("size", "itemsets", "length", "items"))

## S4 method for signature 'sequences'
ritems(x, type = c("min", "max"), itemsets = FALSE)

Arguments

x	an object.
type, itemsets	as string (logical) value specifying the type of count to be computed.

Value

Returns a vector of counts corresponding with the elements of object x.

Note

The total number of items occurring in a sequence is often referred to as the length of the sequence. Similarly, we refer to the total number of itemsets as the size of the sequence. Note that we follow this terminology in the summary methods.

For use with a collection of rules use the accessors lhs or rhs, or coerce to sequences.

Author(s)

Christian Buchta

See Also

Class sequences, timedsequences.

Examples

## continue example
example(cspade)

## default size
size(s2)
size(s2, "itemsets")
size(s2, "length")
size(s2, "items")

## crosstab
table(length = size(s1, "length"),
      items  = size(s1, "items"))

## repetitions
ritems(s1)
ritems(s1, "max")
ritems(s1, "max", TRUE)

---

Class "SPcontrol" — cSPADE Control Parameters

Description

Provides control parameters for the cSPADE algorithm for mining frequent sequences.

Objects from the Class

A suitable default parameter object will be automatically created by a call to cspade. However, the values can be replaced by specifying a named list with the names (partially) matching the slot names of the SPparameter class.

Objects can be created by calls of the form new("SPcontrol", ...).

Slots

memsize:

an integer value specifying the maximum amount of memory to use (default none [32 MB], range >= 16).

numpart:

an integer value specifying the number of database partitions to use (default auto, range >= 1).

timeout:

an integer value specifying the maximum runtime in seconds (default none, range >= 1).

bfstype:

a logical value specifying if a breadth-first type of search should be performed (default FALSE [DFS]).

verbose:

a logical value specifying if progress and runtime information should be displayed (default FALSE).

summary:

a logical value specifying if summary information should be preserved (default FALSE).

tidLists:

a logical value specifying if transaction ID lists should be included in the result (default FALSE).

Methods

coerce

signature(from = "NULL", to = "SPcontrol")

coerce

signature(from = "list", to = "SPcontrol")

coerce

signature(from = "SPcontrol", to = "character")

coerce

signature(from = "SPcontrol", to = "data.frame")

coerce

signature(from = "SPcontrol", to = "list")

coerce

signature(from = "SPcontrol", to = "vector")

format

signature(x = "SPcontrol")

Note

User-supplied values are silently coerced to the target class, e.g. integer.

Parameters with no (default) value are not supplied to the mining algorithm, i.e., take the default values implemented there. A default can be unset using NULL.

The value of memsize implicitly determines the number of database partitions used unless overridden by numpart. Usually, the more partitions the less the runtime in the mining stage. However, there may be a trade-off with preprocessing time.

If summary = TRUE informational output from the system calls in the preprocessing and mining steps will be preserved in the file summary.out in the current working directory.

Author(s)

Christian Buchta

See Also

Class SPparameter, function cspade.

Examples

## coerce from list 
p <- as(list(verbose = TRUE), "SPcontrol")
p

## coerce to
as(p, "vector")
as(p, "data.frame")

---

Class "SPparameter" — cSPADE Mining Parameters

Description

Provides the constraint parameters for the cSPADE algorithm for mining frequent sequences.

Objects from the Class

A suitable default parameter object will be automatically created by a call to cspade. However, the values can be replaced by specifying a named list with the names (partially) matching the slot names of the SPparameter class.

Objects can be created by calls of the form new("SPparameter", support, ...).

Slots

support:

a numeric value specifying the minimum support of a sequence (default 0.1, range [0,1]).

maxsize:

an integer value specifying the maximum number of items of an element of a sequence (default 10, range > 0).

maxlen:

an integer value specifying the maximum number of elements of a sequence (default 10, range > 0).

mingap:

an integer value specifying the minimum time difference between consecutive elements of a sequence (default none, range >= 1).

maxgap:

an integer value specifying the maximum time difference between consecutive elements of a sequence (default none, range >= 0).

maxwin:

an integer value specifying the maximum time difference between any two elements of a sequence (default none, range >= 0).

Methods

coerce

signature(from = "NULL", to = "SPparameter")

coerce

signature(from = "list", to = "SPparameter")

coerce

signature(from = "SPparameter", to = "character")

coerce

signature(from = "SPparameter", to = "data.frame")

coerce

signature(from = "SPparameter", to = "list")

coerce

signature(from = "SPparameter", to = "vector")

format

signature(x = "SPparameter")

Note

User-supplied values are silently coerced to the target class, e.g. integer.

Parameters with no (default) value are not supplied to the mining algorithm, i.e., take the default values implemented there. A value can be unset using NULL.

Author(s)

Christian Buchta

See Also

Class SPcontrol, function cspade.

Examples

## coerce from list 
p <- as(list(maxsize = NULL, maxwin = 5), "SPparameter")
p

## coerce to
as(p, "vector")
as(p, "data.frame")

---

Subset Objects

Description

subset extracts a subset of a collection of sequences or sequence rules which meet conditions specified with respect to their associated (or derived) quality measures, additional information, or patterns of items or itemsets.

[ extracts subsets from a collection of (timed) sequences or sequence rules.

unique extracts the unique set of sequences or sequence rules from a collection of sequences or sequence rules.

lhs, rhs extract the left-hand (antecedent) or right-hand side (consequent) sequences from a collection of sequence rules.

Usage

## S4 method for signature 'sequences'
subset(x, subset)

## S4 method for signature 'sequencerules'
subset(x, subset)


## S4 method for signature 'sequences'
x[i, j, ..., reduce = FALSE, drop = FALSE]

## S4 method for signature 'timedsequences'
x[i, j, k, ..., reduce = FALSE, drop = FALSE]

## S4 method for signature 'sequencerules'
x[i, j, ..., drop = FALSE]

## S4 method for signature 'sequences'
unique(x, incomparables = FALSE)

## S4 method for signature 'sequencerules'
unique(x, incomparables = FALSE)

## S4 method for signature 'sequencerules'
lhs(x)

## S4 method for signature 'sequencerules'
rhs(x)

Arguments

x	an object.
subset	an expression specifying the conditions where the columns in quality and info must be referenced by their names, and the object itself as x.
i	a vector specifying the subset of elements to be extracted.
k	a vector specifying the subset of event times to be extracted.
reduce	a logical value specifying if the reference set of distinct itemsets should be reduced if possible.
j, ..., drop	unused arguments (for compatibility with package Matrix only).
incomparables	not used.

Value

For subset, [, and unique returns an object of the same class as x.

For lhs and rhs returns an object of class sequences.

Note

In package arules, somewhat confusingly, the object itself has to be referenced as items. We do not provide this, as well as any of the references items, lhs, or rhs.

After extraction the reference set of distinct itemsets may be larger than the set actually referred to unless reduction to this set is explicitly requested. However, this may increase memory consumption.

Event time indexes of mode character are matched against the time labels. Any duplicate indexes are ignored and their order does not matter, i.e. reordering of a sequence is not possible.

The accessors lhs and rhs impute the support of a sequence from the support and confidence of a rule. This may lead to numerically inaccuracies over back-to-back derivations.

Author(s)

Christian Buchta

See Also

Class sequences, timedsequences, sequencerules, method lhs, rhs, match, nitems, c.

Examples

## continue example
example(ruleInduction, package = "arulesSequences")

## matching a pattern
as(subset(s2, size(x) > 1), "data.frame")
as(subset(s2, x %ain% c("B", "F")), "data.frame")

## as well as a measure
as(subset(s2, x %ain% c("B", "F") & support == 1), "data.frame")

## matching a pattern in the left-hand side
as(subset(r2, lhs(x) %ain% c("B", "F")), "data.frame")

## matching a derived measure
as(subset(r2, coverage(x) == 1), "data.frame")

## reduce
s <- s2[11, reduce = TRUE]
itemLabels(s)
itemLabels(s2)

## drop initial events
z <- as(zaki, "timedsequences")
summary(z[1,,-1])

---

Support Counting for Sequences

Description

Compute the relative or absolute support of an arbitrary collection of sequences among a set of transactions with additional sequence and temporal information.

Usage

## S4 method for signature 'sequences'
support(x, transactions, type= c("relative", "absolute"),
           control = NULL)

## S4 method for signature 'sequences'
supportingTransactions(x, transactions, ...)

Arguments

x	an object.
transactions	an object of class transactions or sequences.
type	a character value specifying the scale of support (relative or absolute).
control	a named list with logical component verbose specifying if progress and runtime information should be displayed and list component parameter (see details).
...	currently not used.

Details

Provides support counting using either method ptree (default), or idlists (for details see the reference in cspade) and timing constraints.

parameter can be an object of class SPparameter or a named list with corresponding components. Note that constraints which do not relate to the timing information of transactions are ignored.

If sequences are used for transactions missing event times are replaced with the order indexes of events.

The supporting sequences are all sequences (of transactions) of which the sequence representing the association is a subset of.

Note that supportingTransactions does not support timing constraints.

Value

For support a numeric vector the elements of which correspond with the elements of x.

For supportingTransactions an object of class tidLists containing one sequence ID list per association in x.

Author(s)

Christian Buchta

See Also

Class sequences, method ruleInduction, function cspade, read_baskets.

Examples

## continue example
example(cspade)

## recompute support
s <- support(s2, zaki, control = list(verbose = TRUE, 
                     parameter = list(maxwin = 5)))
data.frame(as(s2, "data.frame"), support = s)

## use default method
k <- support(s2, zaki, control = list(verbose = TRUE))
table(size(s2), sign(k - s))

## the same
s <- supportingTransactions(s2, zaki)
itemFrequency(s)

---

Class "timedsequences" — Collections of Sequences with Timing Information

Description

Represents a collection of (observed) sequences and the associated timing information.

Objects from the Class

Typically, objects are created by coercion from an object of class transactions.

Objects can also be created by calls of the form new("timedsequences", ...).

Slots

time:

an object of class ngCMatrix" containing a sparse representation of the event times of the elements of the sequences. note that the storage layout is the same as for slot data.

timeInfo:

a data frame containing the set of time identifiers (column eventID) and possibly distinct labels.

elements:

inherited from class sequences.

data:

inherited from class sequences.

sequenceInfo:

inherited from class sequences.

quality:

inherited from class sequences, usually empty.

Extends

Class "sequences", directly. Class "associations", by class "sequences", distance 2.

Methods

coerce

signature(from = "transactions", to = "timedsequences")

coerce

signature(from = "timedsequences", to = "transactions")

c

signature(x = "timedsequences")

dim

signature(x = "timedsequences")

labels

signature(object = "timedsequences")

LIST

signature(x = "timedsequences")

inspect

signature(x = "timedsequences")

show

signature(object = "timedsequences")

summary

signature(object = "timedsequences")

timeFrequency

signature(x = "timedsequences")

timeInfo<-

signature(object = "timedsequences")

timeInfo

signature(object = "timedsequences")

timesets

signature(object = "timedsequences")

times

signature(x = "timedsequences")

timesets

signature(x = "timedsequences"); returns a collection of sequences of event times as an object of class itemMatrix.

timeTable

signature(x = "timedsequences")

Note

The temporal information is taken from components sequenceID and eventID of transactionInfo. It may be either on an ordinal or metric scale. The former is always assumed if column eventID is a factor.

Note that a sequence must not contain two or more events with the same eventID.

Coercion from an object of class sequences is not provided as this class does not contain timing information.

Author(s)

Christian Buchta

See Also

Class itemMatrix, transactions, sequences.

Examples

## use example data
data(zaki)

## coerce
z <- as(zaki, "timedsequences")
z

## get time sequences
summary(timesets(z))

## coerce back
as(z, "transactions")

---

Count Event Times

Description

timeFrequency counts the number of occurrences of event times, of the time gaps between the events of a sequence, the minimum or maximum gap of a sequence, or the span of a sequence.

timeTable cross-tabulates the above statistics for items or itemsets. For items the sequences are reduced to the events containing the item.

firstOrder computes a first order model, i.e. a table of counts of state changes among a collection of timed sequences, where the elements or the times can be the states.

Usage

## S4 method for signature 'timedsequences'
timeFrequency(x, type = c("times", "gaps", "mingap", "maxgap",
                          "span"))

## S4 method for signature 'timedsequences'
timeTable(x, type = c("times","gaps", "mingap", "maxgap", "span"),
	  itemsets = FALSE)

## S4 method for signature 'timedsequences'
firstOrder(x, times = FALSE)

Arguments

x	an object.
type, itemsets, times	a string (logical) value specifying the type of count.

Value

For timeFrequency returns a vector of counts corresponding with the set of distinct event times, the set of gaps or spans as indicated by the names attribute.

For timeTable returns a table of counts with the rownames corresponding with the reference set of distinct items or itemsets.

For firstOrder a matrix of counts corresponding with the set of distinct itemsets or event times.

Note

Undefined values are not included in the counts, e.g. the mingap of a sequence with one element only. Thus, except for times and gaps the counts (per item or itemset) always add up to less than or equal the number of sequences, i.e. length(x).

Author(s)

Christian Buchta

See Also

Class sequences, timedsequences, method size, times, itemFrequency.

Examples

## continue example
example("timedsequences-class")

## totals
timeFrequency(z)
timeFrequency(z, "gaps")
timeFrequency(z, "span")

## default items
timeTable(z)
timeTable(z, "gaps")
timeTable(z, "span")

## beware of large data sets
timeTable(z, itemsets = TRUE)


## first order models
firstOrder(z)
firstOrder(z, times = TRUE)

---

Compute Time Statistics of Sequences

Description

Computes the gaps, the minimum or maximum gap, or the span of sequences.

Usage

## S4 method for signature 'timedsequences'
times(x, type = c("times", "gaps", "mingap", "maxgap", "span"))

Arguments

x	an object.
type	a string value specifying the type of statistic.

Value

If type = "items" returns a list of vectors of events times corresponding with the elements of a sequence.

If type = "gaps" returns a list of vectors of time differences between consecutive elements of a sequence.

Otherwise, a vector corresponding with the elements of x.

Note

Gap statistics are not defined for sequences of size one, i.e. which contain a single element. NA is used for undefined values.

FIXME lists are silently reduced to vector if possible.

Author(s)

Christian Buchta

See Also

Class sequences, timedsequences, method size, itemFrequency, timeFrequency.

Examples

## continue example
example("timedsequences-class")

##
times(z)
times(z, "gaps")

## all defined
times(z, "span")

## crosstab
table(size = size(z), span = times(z, "span"))

---

Zaki Data Set

Description

A small example database for sequence mining provided as an object of class transactions and as a text file.

Usage

data(zaki)

Details

The data set contains the sequential database described in the paper by M. J. Zaki for illustration of the concepts of sequence mining. sequenceID and eventID denote the sequence and event (time) identifiers of the transactions.

Source

M. J. Zaki. (2001). SPADE: An Efficient Algorithm for Mining Frequent Sequences. Machine Learning Journal, 42, 31–60.

See Also

Class transactions, sequences, function cspade.

Examples

data(zaki)
summary(zaki)
as(zaki, "data.frame")

---