dissimilarity {arules}

Dissimilarity Matrix Computation for Associations and Transactions

Description

Provides the generic function dissimilarity() and the 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 signature 'matrix'
dissimilarity(x, y = NULL, method = NULL, args = NULL)

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

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

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 element "transactions".

• "cosine": the Cosine distance.

• "dice": 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" A distance calculated by 1 - r if r>1 and 1 otherwise, where r is the Pearson's correlation coefficient.

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

• "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.

...

further arguments.

which

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

Value

returns an object of class dist.

Author(s)

Michael Hahsler

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

Other proximity classes and functions: affinity(), predict(), proximity-classes

Examples

## 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])