interestMeasure {arules}R Documentation

Calculating various additional interest measures

Description

Provides the generic function interestMeasure and the needed S4 method to calculate various additional interest measures for existing sets of itemsets or rules.

Usage

interestMeasure(x, method, transactions = NULL, reuse = TRUE, ...)

Arguments

x

a set of itemsets or rules.

method

name or vector of names of the desired interest measures (see details for available measures).

transactions

the transaction data set used to mine the associations.

reuse

logical indicating if information in quality slot should be reuse for calculating the measures. This speeds up the process significantly since only very little (or no) transaction counting is necessary if support, confidence and lift are already available. Use reuse=FALSE to force counting (might be very slow).

...

further arguments for the measure calculation.

Details

For itemsets the following measures are implemented:

"allConfidence"

(see, Omiencinski, 2003) is defined on itemsets as the minimum confidence of all possible rule generated from the itemset.

"crossSupportRatio"

(see, Xiong et al., 2003) is defined on itemsets as the ratio of the support of the least frequent item to the support of the most frequent item. Cross-support patterns have a ratio smaller than a set threshold. Normally many found patterns are cross-support patterns which contain frequent as well as rare items. Such patterns often tend to be spurious.

"support"

calculate itemset support.

For rules the following measures are implemented:

"chiSquare"

(see Liu et al. 1999). The chi-square statistic to test for independence between the lhs and rhs of the rule. The critical value of the chi-square distribution with 1 degree of freedom (2x2 contingency table) at alpha=0.05 is 3.84; higher chi-square values indicate that the lhs and the rhs are not independent. Note that the contingency table is likely to have cells with low expected values and that thus Fisher's Exact Test might be more appropriate (see below).

"confidence"

calculate rule confidence. Range 0…1.

"conviction"

(see Brin et al. 1997) defined as P(X)P(not Y)/P(X and not Y). Range: 0.5…1… Inf (1 indicates unrelated items).

"cosine"

(see Tan et al. 2004) equivalent to the IS measure. Range: 0…1.

"coverage"

calculate rule coverage (support of LHS). Range: 0…1.

"doc"

calculate difference of confidence, which is defined by Hofmann and Wilhelm (2001) as conf(X -> Y)-conf(!X -> Y). Range: -1…1.

"gini"

gini index (see Tan et al. 2004). Range: 0…1.

"hyperLift"

(see, Hahsler and Hornik, 2007) is an adaptation of the lift measure which is more robust for low counts. It is based on the idea that under independence the count c_{XY} of the transactions which contain all items in a rule X -> Y follows a hypergeometric distribution (represented by the random variable C_{XY}) with the parameters given by the counts c_X and c_Y.

Lift is defined for the rule X -> Y as:

lift(X -> Y) = P(X+Y)/(P(X)*P(Y)) = c_XY / E[C_XY],

where E[C_{XY}] = c_X c_Y / m with m being the number of transactions in the database.

Hyper-lift is defined as:

hyperlift(X -> Y) = c_XY / Q_d[C_XY],

where Q_d[C_XY] is the quantile of the hypergeometric distribution given by d. The quantile can be given as parameter d (default: d=0.99). Range: 0… Inf.

"hyperConfidence"

(Hahsler and Hornik, 2007) calculates the confidence level that we observe too high/low counts for rules X -> Y using the hypergeometric model. Since the counts are drawn from a hypergeometric distribution (represented by the random variable C_{XY}) with known parameters given by the counts c_X and c_Y, we can calculate a confidence interval for the observed counts c_{XY} stemming from the distribution. Hyper-confidence reports the confidence level (significance level if significance=TRUE is used) for

complements -
1 - P[C_{XY} >= c_{XY} | c_X, c_Y]
substitutes -
1 - P[C_{XY} < c_{XY} | c_X, c_Y]

.

A confidence level of, e.g., > 0.95 indicates that there is only a 5% chance that the count for the rule was generated randomly.

Per default complementary effects are mined, substitutes can be found by using the parameter complements = FALSE. Range: 0…1.

"fishersExactTest"

Fisher's Exact Test is a statistical significance test used in the analysis of contingency tables where sample sizes are small. Returns the p-value. Note that it is equal to hyper-confidence with significance=TRUE.

"improvement"

(see Bayardo et al. 2000) the improvement of a rule is the minimum difference between its confidence and the confidence of any proper sub-rule with the same consequent. Range: 0…1.

"leverage"

(see Piatetsky-Shapiro 1991) defined as P(X->Y) - (P(X)P(Y)). It measures the difference of X and Y appearing together in the data set and what would be expected if X and Y where statistically dependent. Range: -1...1.

"lift"

calculate rule lift. Range: 0… Inf.

"oddsRatio"

(see Tan et al. 2004). The odds of finding X in transactions which contain Y divided by the odds of finding X in transactions which do not contain Y. Range: 0…1… Inf ( 1 indicates that Y is not associated to X).

"phi"

the correlation coefficient phi (see Tan et al. 2004) Range: -1 (perfect neg. correlation) to +1 (perfect pos. correlation).

"RLD"

(Relative Linkage Disequilibrium; see Kenett and Salini 2008). RLD evaluates the deviation of the support of the whole rule from the support expected under in- dependence given the supports of the LHS and the RHS. The code was contributed by Silvia Salini. Range: 0…1.

"support"

calculate rule support. Range: 0…1.

Value

If only one method is used, the function returns a numeric vector containing the values of the interest measure for each association in the set of associations x.

If more than one methods are specified, the result is a data.frame containing the different measures for each association.

References

R. Bayardo, R. Agrawal, and D. Gunopulos (2000). Constraint-based rule mining in large, dense databases. Data Mining and Knowledge Discovery, 4(2/3):217–240, 2000.

Sergey Brin, Rajeev Motwani, Jeffrey D. Ullman, and Shalom Tsur (1997). Dynamic itemset counting and implication rules for market basket data. In SIGMOD 1997, Proceedings ACM SIGMOD International Conference on Management of Data, pages 255–264, Tucson, Arizona, USA.

Michael Hahsler and Kurt Hornik. New probabilistic interest measures for association rules. Intelligent Data Analysis, 11(5):437–455, 2007

Heike Hofmann and Adalbert Wilhelm. Visual comparison of association rules. Computational Statistics, 16(3):399–415, 2001.

Ron Kenett and Silvia Salini. Relative Linkage Disequilibrium: A New measure for association rules. In 8th Industrial Conference on Data Mining ICDM 2008 July 16–18, 2008, Leipzig/Germany, to appear, 2008.

Bing Liu, Wynne Hsu, and Yiming Ma (1999). Pruning and summarizing the discovered associations. In KDD '99: Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining, pages 125–134. ACM Press, 1999.

Edward R. Omiecinski (2003). Alternative interest measures for mining associations in databases. IEEE Transactions on Knowledge and Data Engineering, 15(1):57–69, Jan/Feb 2003.

Pang-Ning Tan, Vipin Kumar, and Jaideep Srivastava (2004). Selecting the right objective measure for association analysis. Information Systems, 29(4):293–313.

Piatetsky-Shapiro, G. (1991). Discovery, analysis, and presentation of strong rules. In: Knowledge Discovery in Databases, pages 229–248.

Hui Xiong, Pang-Ning Tan, and Vipin Kumar (2003). Mining strong affinity association patterns in data sets with skewed support distribution. In Bart Goethals and Mohammed J. Zaki, editors, Proceedings of the IEEE International Conference on Data Mining, November 19–22, 2003, Melbourne, Florida, pages 387–394.

See Also

itemsets-class, rules-class

Examples

data("Income")
rules <- apriori(Income)

## calculate a single measure and add it to the quality slot
quality(rules) <- cbind(quality(rules), 
	hyperConfidence = interestMeasure(rules, method = "hyperConfidence", 
	Income))

inspect(head(SORT(rules, by = "hyperConfidence")))

## calculate several measures
m <- interestMeasure(rules, c("confidence", "oddsRatio", "leverage"), Income)
inspect(head(rules))
head(m)

[Package arules version 1.0-7 Index]