# We can see, based on the brightest red entries, that highest lift occurs with the least confidence and support.

plot(rules@quality)

# We can see that lift is proportional to confidence in our linear groupings. This relationship is significant and worthy of further analysis.

slope <- sort(round(rules@quality$lift / rules@quality$confidence, 2))

# Display the number of times each slope appears in the dataset.

unlist(lapply(split(slope,f=slope), length))

# Using inspect() can provide us with more concise information to review.

inspect(head(sort(rules, by="lift"), 10))

# While these are interesting, our confidence threshold could be higher.

confidentRules <- rules[quality(rules)$confidence > 0.9]
confidentRules

     set of 127 rules

# This provides us with 127 rules, down from the previously 2918, that we can have a high level of confidence in. Let's get a visual.

plot(confidentRules, method="matrix", measure=c("lift", "confidence"), control=list(reorder=TRUE))

# This is a comprehensive graph that indicates how antecedent items can lead to consequent items; however, another visualization may offer "friendlier" insights.

highLiftRules <- head(sort(rules, by="lift"), 5)
plot(highLiftRules, method="graph", control=list(type="items"))
#############################################################################################
# CONCLUSION
#############################################################################################
# By using lift and leverage, we have discovered rules of interest that are not coincidental.
# The meaningfulness of certain discoveries may depend on the business case. We would create
# a kit of items based around frequent itemsets.

inspect(head(sort(rules, by="lift"), 10))

          lhs                                                                  rhs                  support     confidence lift
     [1]  {Instant food products,soda}                                      => {hamburger meat}     0.001220132 0.6315789  18.995654
     [2]  {soda,popcorn}                                                    => {salty snack}        0.001220132 0.6315789  16.697793
     [3]  {ham,processed cheese}                                            => {white bread}        0.001931876 0.6333333  15.045491
     [4]  {tropical fruit,other vegetables,yogurt,white bread}              => {butter}             0.001016777 0.6666667  12.030581
     [5]  {hamburger meat,yogurt,whipped/sour cream}                        => {butter}             0.001016777 0.6250000  11.278670
     [6]  {tropical fruit,other vegetables,whole milk,yogurt,domestic eggs} => {butter}             0.001016777 0.6250000  11.278670
     [7]  {liquor,red/blush wine}                                           => {bottled beer}       0.001931876 0.9047619  11.235269
     [8]  {other vegetables,butter,sugar}                                   => {whipped/sour cream} 0.001016777 0.7142857   9.964539
     [9]  {whole milk,butter,hard cheese}                                   => {whipped/sour cream} 0.001423488 0.6666667   9.300236
     [10] {tropical fruit,other vegetables,butter,fruit/vegetable juice}    => {whipped/sour cream} 0.001016777 0.6666667   9.300236