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Hello and welcome to this art tutorial.

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So in the previous tutorial
we did the data pre-processing step.

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We first imported the data set
the usual way with the recursive function,

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but then we explained that we needed
to create a sparse matrix containing

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all the transactions that occurred
in the store during the whole week,

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and to build the sparse matrix
we used to read that transaction function,

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including the arm duplicates argument
to remove all the duplicates.

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And this sparse matrix

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is exactly what we need to train
our apriori model on the data set.

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And that's what we are going to do
in this tutorial.

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We're going to make the rules
if I can say that okay.

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So now thanks to the rules package,
the training is going to be very simple

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because we're just going to use
one function, which is by the way

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called the apriori function
with only two arguments.

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So let's do it.

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We're going to create a new variable
and we will call it rules.

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Because this variable will contain
in some way the different rules

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of our business problem.

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So rules here and then equals.

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And that's where we use the apriori
function with the different arguments.

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And so we're going to input two arguments.

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The first argument
is going to be our data set.

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And the second argument is going to be
the parameter argument that will contain

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the choice of a minimum support
and a choice of a confidence support.

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So let's have a look at these arguments.

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I'm going to press F1 here.

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And here I have some info
about the primary function.

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So as you can see
the first argument is data.

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So let's input it.

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Now that's the easiest argument to input.

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So data equals data set.

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And then comma.

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And then the second argument.

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So the second argument is parameter.

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And as it's written here the parameter is
an object of class a parameter.

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And so this object will contain
the minimum support

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that we will set ourselves
and a minimum confidence.

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And we can also specify a maximum of items
you want to have in the rules.

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So that's given with Max then.

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And actually it's also possible
to include a minimum specifying

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the minimum number of products
you want to have in your rules,

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but we won't actually need that.

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And what we will need inevitably
is the support and the confidence.

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So let's input that so parameter here.

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And we need to include the support
and the confidence in this parameter

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the following way
we're going to take the list function.

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And in this list we're going
to input the support and the confidence.

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So I'm going to add
the two arguments here.

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And then we'll see what value
we will input for these two arguments.

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All right.

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So let's take the slide of the intuition
tutorial about the apriori algorithm.

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And let's see what
the different steps of this algorithm are.

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So the first step as you can see is to set
a minimum support and confidence.

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So that's exactly what we are about to do
right now.

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We are in the first step
of the apriori algorithm.

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And that consists of choosing a support
and a confidence.

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So the choice of a support
and confidence is not a general rule.

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We cannot express to support all
the confidence with an explicit equation.

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It actually depends
on the business problem itself.

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It actually depends on your goals.

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The goal related to your business problem.

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It also depends on your data

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set, the number of observations
you have, the number of items.

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So that depends on different circumstances
that don't allow us

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to make some general rule about how to
calculate the support and the confidence.

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But don't worry,

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it will make a lot of sense
when we explain

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how we calculate the support
and the confidence here.

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And you will be able to apply it
to your business problem.

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Okay, so let's start with the support.

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The support of a set of items AI is equal

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to the number of transactions
containing this set of items.

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I divided
by the total number of transactions.

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And the support argument
that we're inputting here

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is actually the minimum support
you want to have in your rules.

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That means that the items
that are going to appear in your rules

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will have a higher support than this
minimum support here.

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And same for the confidence.

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So what we must ask ourselves
is that what supports do we want to have

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of our different items in the rules
so that the rules are relevant?

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Because, for example,
if we go back to the plot here with

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actually the 100 observations,
which is this one, if we zoom on it, well,

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we can see that we have a lot of products
that are not purchased very frequently.

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And these specific products
are the products with small supports

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because a few transactions
contain these products here.

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So when you divide the number
of transactions containing these products

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by the total number of transactions,
then you will get a small support.

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And you know, since these products
are not purchased very often,

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they're not very relevant

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for our optimization problem because,
you know, we want to optimize the sales,

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but what we want to optimize
overall is the revenue.

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And since the revenue is a linear
combination of the different numbers

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of products where the coefficients
are actually the prices of these products,

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well, in order to optimize the revenue,
we would need to optimize the sales

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of these products here that are purchased
very often,

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rather than these products here
that are less purchased.

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And so what we need to choose
here is a support

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that will only include the products

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on the left of this vertical bar here
that will correspond

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to the minimum support.

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So for example, let's say
the value here on the y axis is 0.05.

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Then that means that all the products
on the left of this vertical

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bar will have a support higher than 0.05.

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And so if we set a minimum support
of 0.05, then the rules will only contain

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the different products of this left side
of the vertical bar here.

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And so now how to choose to support.

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Well we need to look at the products
that are purchased rather frequently.

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Like at least 3 or 4 times a day.

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Again that depends on your business goal.

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But what's for sure is that if we managed
to find some strong rules about items

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that are bought,
at least 3 or 4 times a day,

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then by associating them
and placing them together, customers

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will be more likely
to put them in their basket

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and therefore more of these products
will be purchased

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and therefore the sales will increase.

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So that will be the starting point of how
we are going to set the minimum support.

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We are going to consider the product

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that are purchased
at least 3 or 4 times a day.

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And then we will look at the rules.

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And of course,

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if we're not convinced by the rules,
we will change this value of the support.

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That's how we work with the apriori model.

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You know,

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we try different values of the support,
different values of the confidence

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until we are satisfied with the rules
and until we think it makes sense.

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And, you know, we can also try these rules
within a certain period of time.

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And then we look
at the impact on the revenue.

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And if we don't observe a meaningful
increase in the sales revenue,

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we can later change the support
and the confidence to change the rules

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and then experience again

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until we find the strongest rules
that optimize the sales.

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So that's actually
what happened in real life.

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But of course, in these tutorials,
we're going to try

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with products
purchased 3 or 4 times a day.

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And so we'll see what happens okay.

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So actually we didn't set the support yet.

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We just decided that we will

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look at the products that are purchased
at least 3 or 4 times a day.

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But that will quickly
lead us to the support.

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Because if a product is bought,
let's say three times a day,

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that means it's purchased
three times seven equals 21 times a week.

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And since the support
is the number of transactions

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contained in this product,
over the total number of transactions,

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and since there are 7500 transactions,
then we get the minimum support

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that is equal to seven times
three over 7005 hundred.

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So let me explain that
by writing this here.

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So okay,
we said we considered the products

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that are purchased three times a day.

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So that's three here.

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Then since the total number of
transactions where register over a week,

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that means that
if we consider the products

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that are purchased three times a day,
that means that a purchase

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on average three times seven times a week.

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So this three times seven equals 21.

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Here is the number of transactions
containing

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this product bought three times
a day over the whole week.

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And now we need to divide
by the total number

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of transactions
to get this minimum support.

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And the total number of transactions
is actually 7005 hundred.

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And this value here that we're about to
compute is nothing else

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than the support of a product
that is purchased three times a day.

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And, you know,

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we want our rules to consider only
the products that are at least purchased

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three times a day.

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So all the products of our rules
will have a higher support

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than this support here
that we're about to compute.

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So let's compute it.

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Let's find out what it is.

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And that's the value we will give to
this support parameter here.

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So right now I just need to press enter.

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And that's the value 0.00 28.

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We will round this to 0.03.

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And so that is the minimum support

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of the product
that will be considered by our rules.

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So let's input it 0.003 right okay.

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So that's it for the support.

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Now the second step of our step
one is to set a minimum confidence.

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So the choice of the confidence
still depends

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on the business problem
but mostly on your business goals.

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So what we'll do now
is we're not going to compute a confidence

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like we computed the support.

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So we are going to start
with the default value and then decrease

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the confidence step by step
until we get some relevant rules.

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Because you know the confidence
is kind of an arbitrary choice.

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We don't want to have a too

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high confidence
because if we get it too high confidence,

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we will get to obvious rules,
you know, rules that we don't need

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a machine learning algorithm to understand
where we need to place the products

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next to each other.

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And we shouldn't
have a too small confidence,

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because if we get a too small confidence,
we will get some nonsense rules.

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Like, like, you know, if I'm buying
chocolate, I want to buy shampoo.

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That's a nonsense rule
that doesn't make any sense.

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And that's the kind of rule we will get
if we set it to small confidence.

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So we will start with the default value,
which is actually open eight.

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I think we will have a look at it.

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We can go back to help here
to look at the description.

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And if we want to have the info
about these two arguments here, support

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and confidence.

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What we need to do is click on this API
parameter here, which is the class.

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And here we go
that gives you the information

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of the parameter arguments of apriori
and class.

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The other model
that will make after this section.

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And as you can see we get informations

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about the support and confidence
and other arguments.

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So these are actually the arguments
that are both in apriori and eclat.

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And below
you have some additional arguments

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that are only for apriori, because you'll
see that the Eclair algorithm doesn't

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have a confidence in its algorithm
and only consider this support.

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We will see that afterwards.

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But right now what we're interested in
is actually the confidence.

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And you can see that
the default value is 0.8.

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So that's what we will start with.

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I'm not saying
we will get some interesting results.

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You can already imagine
what we're going to get

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because 0.8 is a very high confidence.

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Try to guess what
we'll get with this high confidence 0.8.

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And don't worry, we will divide it by two
to try some smaller

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confidences
until we get some relevant rules.

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Okay, so that's actually ready
with the single line

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of code containing
only these two parameters, the data set

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and this parameter here with the minimum
support and the minimum confidence

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we train our primary model
on our data set.

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So let's select this line and execute.

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And here we go.

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Our apriori model is created.

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And by the way the rules are also created.

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So let's have a look at the info here.

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All right. So that's the apriori model.

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And here we have the default parameters
of this parameter argument here.

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So we can see that
we have the minimum confidence here 0.8.

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And the minimum support 0.03.

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And we also have
the midlane of the basket.

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That means that the basket
that the rules will consider will contain

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at least one product.

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Well, we could have actually set two here
to have at least two products in the row.

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We'll see if we get a problem with that.

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But so far the most important arguments
we need to input are the support

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and the confidence.

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Okay.

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So the algorithmic control
that's not very important for us.

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Now that's kind of a little more advanced.

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And here we get some other interesting
informations.

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The most important information we need to
look at here is the number of rules.

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We can actually see zero rules here.

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That means that
when we trained our apriori model here,

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this model actually found zero rule.

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And can you guess why.

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Well of course it's due to the choice
of our minimum confidence.

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Because by setting this minimum confidence
0.8, that means that all the rules

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made by our apriori algorithm
have a confidence higher than 0.8.

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And what does that mean?

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That means that each rule
should be correct

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at least on 80% of the transactions.

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So 80% is a lot.

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That means that the rule must be true
at least four times out of five.

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And that's why the apriori found zero rule
with a minimum confidence of 0.8,

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because no rule is true
at least four transactions out of five.

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So that's what I was telling you.

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We can start with the default value,
but since we have a lot of transactions

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and a lot of products
that the customers can purchase, well,

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of course
we need to set smaller confidence.

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00:13:38,366 --> 00:13:40,633
So we will divided by two.

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So we will try now. 0.4.

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And now let's see what we get.

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So let's re-execute this line.

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It will retrain the model on a data set

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and recreate some new rules. Here we go.

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Now we have 281 rules.

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Much better. So that's a relief.

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And now of course what we're going to do
is look at the rules themselves.

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We're
going to visually see what the rules are.

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So we're going to see exactly

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which products should be placed
next to each other.

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And we will see the strongest association
rules.

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00:14:11,133 --> 00:14:15,133
We will see what product customers
purchase if they buy another product.

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So we will see all this very explicitly.

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And that's what we are going to do
in the next tutorial.

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So I look forward
to discovering these rules with you.

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And until then, enjoy machine learning.