# dissimilarity

##### Dissimilarity Computation

Provides the generic function `dissimilarity`

and the S4 methods to
compute and returns distances for binary data in a `matrix`

,
`'>transactions`

or `'>associations`

which
can be used for grouping and clustering. See Hahsler (2016)
for an introduction to distance-based
clustering of association rules.

##### Usage

`dissimilarity(x, y = NULL, method = NULL, args = NULL, …)`# S4 method for itemMatrix
dissimilarity(x, y = NULL, method = NULL, args = NULL,
which = "transactions")

# S4 method for associations
dissimilarity(x, y = NULL, method = NULL, args = NULL,
which = "associations")

# S4 method for matrix
dissimilarity(x, y = NULL, method = NULL, args = NULL)

##### Arguments

- x
the set of elements (e.g.,

`matrix, itemMatrix, transactions, itemsets, rules`

).- y
`NULL`

or a second set to calculate cross dissimilarities.- method
the distance measure to be used. Implemented measures are (defaults to

`"jaccard"`

):`"affinity"`

:measure based on the

`affinity`

, a similarity measure between items. It is defined as the average*affinity*between the items in two transactions (see Aggarwal et al. (2002)). If`x`

is not the full transaction set`args`

needs to contain either precalculated affinities as element`"affinities"`

or the transaction set as`"transactions"`

.`"cosine"`

:the

*cosine*distance.`"dice"`

:the

*Dice's coefficient*defined by Dice (1945). Similar to*Jaccard*but gives double the weight to agreeing items.`"euclidean"`

:the

*euclidean*distance.`"jaccard"`

:the number of items which occur in both elements divided by the total number of items in the elements (Sneath, 1957). This measure is often also called:

*binary, asymmetric binary,*etc.`"matching"`

:the

*Matching coefficient*defined by Sokal and Michener (1958). This coefficient gives the same weight to presents and absence of items.`"pearson"`

:\(1 - r\) if \(r>1\) and \(1\) otherwise. \(r\) is

*Pearson's correlation coefficient*.`"phi"`

:same as pearson. Pearson's correlation coefficient reduces to the phi coefficient for the 2x2 contingency tables used here.

For associations the following additional measures are available:

`"toivonen"`

:Method described in Toivonen et al. (1995). For rules this measure is only defined between rules with the same consequent. The distance between two rules is defined as the number of transactions which is covered by only one of the two rules. The transactions used to mine the associations has to be passed on via

`args`

as element`"transactions"`

.`"gupta"`

:Method described in Gupta et al. (1999). The distance between two rules is defined as 1 minus the proportion of transactions which are covered by both rules in the transactions covered by each rule individually. The transactions used to mine the associations has to be passed on via

`args`

as element`"transactions"`

.

- args
a list of additional arguments for the methods.

- which
a character string indicating if the dissimilarity should be calculated between transactions/associations (default) or items (use

`"items"`

).- …
further arguments.

##### Value

returns an object of class `dist`

.

##### References

Aggarwal, C.C., Cecilia Procopiuc, and Philip S. Yu. (2002)
Finding localized associations in market basket data.
*IEEE Trans. on Knowledge and Data Engineering* 14(1):51--62.

Dice, L. R. (1945) Measures of the amount of ecologic association
between species. *Ecology* 26, pages 297--302.

Gupta, G., Strehl, A., and Ghosh, J. (1999) Distance based clustering
of association rules. *In Intelligent Engineering
Systems Through Artificial Neural Networks (Proceedings
of ANNIE 1999)*, pages 759-764. ASME Press.

Hahsler, M. (2016) Grouping association rules using lift. In C. Iyigun, R. Moghaddess, and A. Oztekin, editors, 11th INFORMS Workshop on Data Mining and Decision Analytics (DM-DA 2016).

Sneath, P. H. A. (1957) Some thoughts on bacterial classification.
*Journal of General Microbiology* 17, pages 184--200.

Sokal, R. R. and Michener, C. D. (1958) A statistical method for evaluating
systematic relationships. *University of Kansas Science Bulletin* 38,
pages 1409--1438.

Toivonen, H., Klemettinen, M., Ronkainen, P.,
Hatonen, K. and Mannila H. (1995) Pruning and grouping discovered
association rules. *In Proceedings of KDD'95*.

##### See Also

##### Examples

```
# NOT RUN {
## cluster items in Groceries with support > 5%
data("Groceries")
s <- Groceries[,itemFrequency(Groceries)>0.05]
d_jaccard <- dissimilarity(s, which = "items")
plot(hclust(d_jaccard, method = "ward.D2"), main = "Dendrogram for items")
## cluster transactions for a sample of Adult
data("Adult")
s <- sample(Adult, 500)
## calculate Jaccard distances and do hclust
d_jaccard <- dissimilarity(s)
hc <- hclust(d_jaccard, method = "ward.D2")
plot(hc, labels = FALSE, main = "Dendrogram for Transactions (Jaccard)")
## get 20 clusters and look at the difference of the item frequencies (bars)
## for the top 20 items) in cluster 1 compared to the data (line)
assign <- cutree(hc, 20)
itemFrequencyPlot(s[assign==1], population=s, topN=20)
## calculate affinity-based distances between transactions and do hclust
d_affinity <- dissimilarity(s, method = "affinity")
hc <- hclust(d_affinity, method = "ward.D2")
plot(hc, labels = FALSE, main = "Dendrogram for Transactions (Affinity)")
## cluster association rules
rules <- apriori(Adult, parameter=list(support=0.3))
rules <- subset(rules, subset = lift > 2)
## use affinity to cluster rules
## Note: we need to supply the transactions (or affinities) from the
## dataset (sample).
d_affinity <- dissimilarity(rules, method = "affinity",
args = list(transactions = s))
hc <- hclust(d_affinity, method = "ward.D2")
plot(hc, main = "Dendrogram for Rules (Affinity)")
## create 4 groups and inspect the rules in the first group.
assign <- cutree(hc, k = 3)
inspect(rules[assign == 1])
# }
```

*Documentation reproduced from package arules, version 1.5-5, License: GPL-3*