Calculate Additional Interest Measures

Provides the generic function interestMeasure() and the methods to calculate various additional interest measures for existing sets of itemsets or rules.

Usage

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

# S4 method for class 'itemsets'
interestMeasure(x, measure, transactions = NULL, reuse = TRUE, ...)

# S4 method for class 'rules'
interestMeasure(x, measure, transactions = NULL, reuse = TRUE, ...)

Arguments

x

a set of itemsets or rules.

measure

name or vector of names of the desired interest measures (see the Details section for available measures). If measure is missing then all available measures are calculated.

transactions

the transactions used to mine the associations or a set of different transactions to calculate interest measures from (Note: you need to set reuse = FALSE in the later case).

reuse

logical indicating if information in the 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 but is necessary if you use a different set of transactions than was used for mining).

...

further arguments for the measure calculation. Many measures are based on contingency table counts and zero counts can produce NaN values (division by zero). This issue can be resolved by using the additional parameter smoothCounts which performs additive smoothing by adds a "pseudo count" of smoothCounts to each cell in the contingency table. Use smoothCounts = 1 or larger values for Laplace smoothing. Use smoothCounts = .5 for Haldane-Anscombe correction (Haldan, 1940; Anscombe, 1956) which is often used for chi-squared, phi correlation and related measures.

Value

If only one measure 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 measures are specified, the result is a data.frame containing the different measures for each association as columns.

NA is returned for rules/itemsets for which a certain measure is not defined.

Details

A searchable list of definitions, equations and references for all available interest measures can be found at https://mhahsler.github.io/arules/docs/measures. The descriptions are also linked in the list below.

The following measures are implemented for itemsets:

• "support": Support.

• "count": Support Count.

• "allConfidence": All-Confidence.

• "crossSupportRatio": Cross-Support Ratio.

• "lift": Lift.

The following measures are implemented for rules:

• "support": Support.

• "confidence": Confidence.

• "lift": Lift.

• "count": Support Count.

• "addedValue": Added Value.

• "boost": Confidence Boost.

• "causalConfidence": Causal Confidence.

• "causalSupport": Causal Support.

• "accuracy": Accuracy.

• "balancedAccuracy": Balanced Accuracy.

• "centeredConfidence": Centered Confidence.

• "certainty": Certainty Factor.

• "chiSquared": Chi-Squared. Additional parameters are: significance = TRUE returns the p-value of the test for independence instead of the chi-squared statistic. For p-values, substitution effects (the occurrence of one item makes the occurrence of another item less likely) can be tested using the parameter complements = FALSE. Note: Correction for multiple comparisons can be done using stats::p.adjust().

• "collectiveStrength": Collective Strength.

• "confirmedConfidence": Descriptive Confirmed Confidence.

• "conviction": Conviction.

• "cosine": Cosine.

• "counterexample": Example and Counter-Example Rate.

• "coverage": Coverage.

• "doc": Difference of Confidence.

• "fishersExactTest": Fisher's Exact Test. By default complementary effects are mined, substitutes can be found by using the parameter complements = FALSE. Note that Fisher's exact test is equal to hyper-confidence with significance = TRUE. Correction for multiple comparisons can be done using stats::p.adjust().

• "gini": Gini Index.

• "hyperConfidence": Hyper-Confidence. Reports the confidence level by default and the significance level if significance = TRUE is used. By default complementary effects are mined, substitutes (too low co-occurrence counts) can be found by using the parameter complements = FALSE.

• "hyperLift": Hyper-Lift. The used quantile can be changed using parameter level (default: level = 0.99).

• "imbalance": Imbalance Ratio.

• "implicationIndex": Implication Index.

• "importance": Importance.

• "improvement": Improvement. The additional parameter improvementMeasure (default: 'confidence') can be used to specify the measure used for the improvement calculation. See Generalized improvement.

• "jaccard": Jaccard Coefficient.

• "jMeasure": J-Measure.

• "kappa": Kappa.

• "kulczynski": Kulczynski.

• "lambda": Lambda.

• "laplace": Laplace Corrected Confidence. Parameter k can be used to specify the number of classes (default is 2).

• "leastContradiction": Least Contradiction.

• "lerman": Lerman Similarity.

• "leverage": Leverage.

• "LIC": Lift Increase. The additional parameter improvementMeasure (default: 'lift') can be used to specify the measure used for the increase calculation. See Generalized increase ratio.

• "maxconfidence": Max-Confidence.

• "mutualInformation": Mutual Information.

• "netconf": Netconf.

• "oddsRatio": Odds Ratio.

• "phi": Phi Correlation Coefficient.

• "ralambondrainy": Ralambondrainy.

• "relativeRisk": Relative Risk.

• "rhsSupport": Right-Hand-Side Support.

• "RLD": Relative Linkage Disequilibrium.

• "rulePowerFactor": Rule Power Factor.

• "precision": Precision.

• "recall": Recall.

• "fScore": F-score.

• "sebag": Sebag-Schoenauer.

• "stdLift": Standardized Lift.

• "table": Contingency Table. Returns the four counts for the contingency table. The entries are labeled n11, n01, n10, and n00 (the first subscript is for X and the second is for Y; 1 indicated presence and 0 indicates absence). If several measures are specified, then the counts have the prefix table.

• "varyingLiaison": Varying Rates Liaison.

• "zhang": Zhang's Measure.

• "yuleQ": Yule's Q.

• "yuleY": Yule's Y.

References

Hahsler, Michael (2015). A Probabilistic Comparison of Commonly Used Interest Measures for Association Rules, 2015, URL: https://mhahsler.github.io/arules/docs/measures.

Haldane, J.B.S. (1940). "The mean and variance of the moments of chi-squared when used as a test of homogeneity, when expectations are small". Biometrika, 29, 133-134.

Anscombe, F.J. (1956). "On estimating binomial response relations". Biometrika, 43, 461-464.

See also

itemsets, rules

Other interest measures: confint, coverage(), is.redundant(), is.significant(), support()

Author

Michael Hahsler

Examples

data("Income")
rules <- apriori(Income)
#> Apriori
#> 
#> Parameter specification:
#>  confidence minval smax arem  aval originalSupport maxtime support minlen
#>         0.8    0.1    1 none FALSE            TRUE       5     0.1      1
#>  maxlen target  ext
#>      10  rules TRUE
#> 
#> Algorithmic control:
#>  filter tree heap memopt load sort verbose
#>     0.1 TRUE TRUE  FALSE TRUE    2    TRUE
#> 
#> Absolute minimum support count: 687 
#> 
#> set item appearances ...[0 item(s)] done [0.00s].
#> set transactions ...[50 item(s), 6876 transaction(s)] done [0.00s].
#> sorting and recoding items ... [30 item(s)] done [0.00s].
#> creating transaction tree ... done [0.00s].
#> checking subsets of size 1 2 3 4 5 6 7 8 done [0.04s].
#> writing ... [8664 rule(s)] done [0.00s].
#> creating S4 object  ... done [0.00s].

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

inspect(head(rules, by = "hyperConfidence"))
#>     lhs                                 rhs                               support confidence  coverage     lift count hyperConfidence
#> [1] {ethnic classification=hispanic} => {education=no college graduate} 0.1096568  0.8636884 0.1269634 1.224731   754               1
#> [2] {dual incomes=no}                => {marital status=married}        0.1400524  0.9441176 0.1483421 2.447871   963               1
#> [3] {occupation=student}             => {marital status=single}         0.1449971  0.8838652 0.1640489 2.160490   997               1
#> [4] {occupation=student}             => {age=14-34}                     0.1592496  0.9707447 0.1640489 1.658345  1095               1
#> [5] {occupation=student}             => {dual incomes=not married}      0.1535777  0.9361702 0.1640489 1.564683  1056               1
#> [6] {occupation=student}             => {income=$0-$40,000}             0.1381617  0.8421986 0.1640489 1.353027   950               1

## calculate several measures
m <- interestMeasure(rules, c("confidence", "oddsRatio", "leverage"),
  transactions = Income
)
inspect(head(rules))
#>     lhs                                 rhs                               support confidence  coverage     lift count hyperConfidence
#> [1] {}                               => {language in home=english}      0.9128854  0.9128854 1.0000000 1.000000  6277       0.0000000
#> [2] {occupation=clerical/service}    => {language in home=english}      0.1127109  0.9292566 0.1212914 1.017933   775       0.9601859
#> [3] {ethnic classification=hispanic} => {education=no college graduate} 0.1096568  0.8636884 0.1269634 1.224731   754       1.0000000
#> [4] {dual incomes=no}                => {marital status=married}        0.1400524  0.9441176 0.1483421 2.447871   963       1.0000000
#> [5] {dual incomes=no}                => {language in home=english}      0.1364165  0.9196078 0.1483421 1.007364   938       0.7763615
#> [6] {occupation=student}             => {marital status=single}         0.1449971  0.8838652 0.1640489 2.160490   997       1.0000000
head(m)
#>   confidence oddsRatio     leverage
#> 1  0.9128854       NaN 0.0000000000
#> 2  0.9292566  1.289208 0.0019856861
#> 3  0.8636884  2.952221 0.0201213950
#> 4  0.9441176 41.681686 0.0828384029
#> 5  0.9196078  1.107694 0.0009972213
#> 6  0.8838652 16.478646 0.0778840228

## calculate all available measures for the first 5 rules and show them as a
## table with the measures as rows
t(interestMeasure(head(rules, 5), transactions = Income))
#>                             [,1]          [,2]          [,3]          [,4]
#> support                0.9128854  1.127109e-01  1.096568e-01  1.400524e-01
#> confidence             0.9128854  9.292566e-01  8.636884e-01  9.441176e-01
#> lift                   1.0000000  1.017933e+00  1.224731e+00  2.447871e+00
#> count               6277.0000000  7.750000e+02  7.540000e+02  9.630000e+02
#> addedValue             0.0000000  1.637120e-02  1.584819e-01  5.584283e-01
#> boost                        Inf  1.017933e+00           Inf           Inf
#> causalConfidence       0.4564427  9.153795e-01  9.024905e-01  9.653117e-01
#> causalSupport          0.9128854  1.912449e-01  3.871437e-01  7.460733e-01
#> accuracy               0.9128854  1.912449e-01  3.871437e-01  7.460733e-01
#> balancedAccuracy       0.5000000  5.124846e-01  5.483943e-01  6.748139e-01
#> centeredConfidence     0.0000000  1.637120e-02  1.584819e-01  5.584283e-01
#> certainty              0.0000000  1.879271e-01  5.376032e-01  9.090324e-01
#> chiSquared                   NaN  3.198710e+00  1.208111e+02  1.576319e+03
#> collectiveStrength     1.0000000  1.026221e+00  1.189288e+00  2.124161e+00
#> confirmedConfidence    0.8257708  8.585132e-01  7.273769e-01  8.882353e-01
#> conviction             1.0000000  1.231417e+00  2.162645e+00  1.099293e+01
#> cosine                 0.9554504  3.387214e-01  3.664698e-01  5.855169e-01
#> counterexample         0.9045722  9.238710e-01  8.421751e-01  9.408100e-01
#> coverage               1.0000000  1.212914e-01  1.269634e-01  1.483421e-01
#> doc                          NaN  1.863097e-02  1.815295e-01  6.556955e-01
#> fishersExactTest       1.0000000  3.981412e-02  9.791397e-32  0.000000e+00
#> gini                         NaN  7.399053e-05  7.305254e-03  1.086335e-01
#> hyperConfidence        0.0000000  9.601859e-01  1.000000e+00  1.000000e+00
#> hyperLift              1.0000000  9.948652e-01  1.168992e+00  2.255269e+00
#> imbalance              0.0871146  8.590593e-01  8.003221e-01  6.024363e-01
#> implicationIndex       0.0000000 -1.601836e+00 -8.624380e+00 -2.275482e+01
#> importance             0.2613891  8.380387e-03  1.020920e-01  5.144888e-01
#> improvement            0.9128854  1.637120e-02  8.636884e-01  9.441176e-01
#> jaccard                0.9128854  1.223169e-01  1.517713e-01  3.554817e-01
#> jMeasure               0.0000000  2.172097e-04  8.880664e-03  1.055050e-01
#> kappa                  0.0000000  4.886481e-03  6.161820e-02  3.948413e-01
#> kulczynski             0.9564427  5.263616e-01  5.095922e-01  6.536199e-01
#> lambda                 0.0000000  0.000000e+00  0.000000e+00  3.416290e-01
#> laplace                0.9127653  9.282297e-01  8.628571e-01  9.432485e-01
#> leastContradiction     0.9045722  1.140672e-01  1.309548e-01  3.416290e-01
#> lerman                 0.0000000  4.948292e-01  5.576076e+00  2.871764e+01
#> leverage               0.0000000  1.985686e-03  2.012140e-02  8.283840e-02
#> LIC                          Inf  1.017933e+00           Inf           Inf
#> maxconfidence          1.0000000  9.292566e-01  8.636884e-01  9.441176e-01
#> mutualInformation            NaN  8.289227e-04  2.622346e-02  2.934492e-01
#> netconf                      NaN  1.863097e-02  1.815295e-01  6.556955e-01
#> oddsRatio                    NaN  1.289208e+00  2.952221e+00  4.168169e+01
#> phi                          NaN  2.156848e-02  1.325518e-01  4.788000e-01
#> ralambondrainy         0.0871146  8.580570e-03  1.730657e-02  8.289703e-03
#> relativeRisk                 NaN  1.020460e+00  1.266110e+00  3.273388e+00
#> rhsSupport             0.9128854  9.128854e-01  7.052065e-01  3.856894e-01
#> RLD                           NA  1.879271e-01  5.376032e-01  9.090324e-01
#> rulePowerFactor        0.8333598  1.047373e-01  9.470929e-02  1.322259e-01
#> precision              0.9128854  9.292566e-01  8.636884e-01  9.441176e-01
#> recall                 1.0000000  1.234666e-01  1.554960e-01  3.631222e-01
#> fScore                 0.9544591  2.179722e-01  2.635442e-01  5.245098e-01
#> sebag                 10.4791319  1.313559e+01  6.336134e+00  1.689474e+01
#> stdLift                1.0000000  5.969945e-01  3.184422e-01  7.205882e-01
#> table.n11           6277.0000000  7.750000e+02  7.540000e+02  9.630000e+02
#> table.n01              0.0000000  5.502000e+03  4.095000e+03  1.689000e+03
#> table.n10            599.0000000  5.900000e+01  1.190000e+02  5.700000e+01
#> table.n00              0.0000000  5.400000e+02  1.908000e+03  4.167000e+03
#> varyingLiaison         0.0000000  1.793346e-02  2.247312e-01  1.447871e+00
#> zhang                  0.0000000  1.664773e-02  1.686951e-01  6.945062e-01
#> yuleQ                        NaN  1.263353e-01  4.939554e-01  9.531415e-01
#> yuleY                        NaN  6.342171e-02  2.642197e-01  7.317645e-01
#>                              [,5]
#> support              1.364165e-01
#> confidence           9.196078e-01
#> lift                 1.007364e+00
#> count                9.380000e+02
#> addedValue           6.722445e-03
#> boost                1.007364e+00
#> causalConfidence     8.913565e-01
#> causalSupport        2.116056e-01
#> accuracy             2.116056e-01
#> balancedAccuracy     5.062698e-01
#> centeredConfidence   6.722445e-03
#> certainty            7.716783e-02
#> chiSquared           6.805848e-01
#> collectiveStrength   1.012069e+00
#> confirmedConfidence  8.392157e-01
#> conviction           1.083621e+00
#> cosine               3.707035e-01
#> counterexample       9.125800e-01
#> coverage             1.483421e-01
#> doc                  7.893362e-03
#> fishersExactTest     2.236385e-01
#> gini                 1.574286e-05
#> hyperConfidence      7.763615e-01
#> hyperLift            9.873684e-01
#> imbalance            8.267023e-01
#> implicationIndex    -7.274143e-01
#> importance           3.422807e-03
#> improvement          6.722445e-03
#> jaccard              1.475075e-01
#> jMeasure             4.316924e-05
#> kappa                2.523369e-03
#> kulczynski           5.345211e-01
#> lambda               0.000000e+00
#> laplace              9.187867e-01
#> leastContradiction   1.363709e-01
#> lerman               2.247083e-01
#> leverage             9.972213e-04
#> LIC                  1.007364e+00
#> maxconfidence        9.196078e-01
#> mutualInformation    1.706534e-04
#> netconf              7.893362e-03
#> oddsRatio            1.107694e+00
#> phi                  9.948857e-03
#> ralambondrainy       1.192554e-02
#> relativeRisk         1.008658e+00
#> rhsSupport           9.128854e-01
#> RLD                  7.716783e-02
#> rulePowerFactor      1.254497e-01
#> precision            9.196078e-01
#> recall               1.494344e-01
#> fScore               2.570920e-01
#> sebag                1.143902e+01
#> stdLift              5.980392e-01
#> table.n11            9.380000e+02
#> table.n01            5.339000e+03
#> table.n10            8.200000e+01
#> table.n00            5.170000e+02
#> varyingLiaison       7.363952e-03
#> zhang                8.360571e-03
#> yuleQ                5.109543e-02
#> yuleY                2.556441e-02

## calculate measures on a different set of transactions (I use a sample here)
## Note: reuse = TRUE (default) would just return the stored support on the
##   data set used for mining
newTrans <- sample(Income, 100)
m2 <- interestMeasure(rules, "support", transactions = newTrans, reuse = FALSE)
head(m2)
#> [1] 0.86 0.15 0.12 0.18 0.15 0.13

## calculate all available measures for the 5 frequent itemsets with highest support
its <- apriori(Income, parameter = list(target = "frequent itemsets"))
#> Apriori
#> 
#> Parameter specification:
#>  confidence minval smax arem  aval originalSupport maxtime support minlen
#>          NA    0.1    1 none FALSE            TRUE       5     0.1      1
#>  maxlen            target  ext
#>      10 frequent itemsets TRUE
#> 
#> Algorithmic control:
#>  filter tree heap memopt load sort verbose
#>     0.1 TRUE TRUE  FALSE TRUE    2    TRUE
#> 
#> Absolute minimum support count: 687 
#> 
#> set item appearances ...[0 item(s)] done [0.00s].
#> set transactions ...[50 item(s), 6876 transaction(s)] done [0.00s].
#> sorting and recoding items ... [30 item(s)] done [0.00s].
#> creating transaction tree ... done [0.00s].
#> checking subsets of size 1 2 3 4 5 6 7 8 done [0.05s].
#> sorting transactions ... done [0.00s].
#> writing ... [5571 set(s)] done [0.00s].
#> creating S4 object  ... done [0.00s].
its <- head(its, 5, by = "support")
inspect(its)
#>     items                             support count
#> [1] {language in home=english}      0.9128854  6277
#> [2] {education=no college graduate} 0.7052065  4849
#> [3] {number in household=1}         0.6918266  4757
#> [4] {ethnic classification=white}   0.6697208  4605
#> [5] {ethnic classification=white,                  
#>      language in home=english}      0.6595404  4535

interestMeasure(its, transactions = Income)
#>     support count allConfidence crossSupportRatio     lift
#> 1 0.9128854  6277     0.9128854         1.0000000 1.000000
#> 2 0.7052065  4849     0.7052065         1.0000000 1.000000
#> 3 0.6918266  4757     0.6918266         1.0000000 1.000000
#> 4 0.6697208  4605     0.6697208         1.0000000 1.000000
#> 5 0.6595404  4535     0.7224789         0.7336307 1.078776