Feature engineering suggestion required

Question

I am having a problem during feature engineering. Looking for some suggestions. Problem statement: I have usage data of multiple customers for 3 days. Some have just 1 day usage some 2 and some 3. Data is related to number of emails sent / contacts added on each day etc.

I am converting this time series data to column-wise ie., number of emails sent by a customer on day1 as one feature, number of emails sent by a customer on day2 as one feature and so on. But problem is that, the usage can be of either increasing order or decreasing order for different customers.

ie., example 1: customer 'A' --> 'number of emails sent on 1st . day' = 100 . ' number of emails sent on 2nd day'=0

example 2: customer 'B' --> 'number of emails sent on 1st . day' = 0 . ' number of emails sent on 2nd day'=100

example 3: customer 'C' --> 'number of emails sent on 1st . day' = 0 . ' number of emails sent on 2nd day'=0

example 4: customer 'D' --> 'number of emails sent on 1st . day' = 100 . ' number of emails sent on 2nd day'=100

In the first two cases => My new feature will have "-100" and "100" as values. Which I guess is good for differentiating. But the problem arises for 3rd and 4th columns when the new feature value will be "0" in both scenarios Can anyone suggest a way to handle this.

One way to handle this:

I can add "No change" in those scenarios, but I am confused about one thing. If I do that, I will have to make the new feature as categorical, which is not ideal as the other values will be continuous.

Instead, I can have absolute values in the new feature and indicate the trend as "+1" or increasing "-1" for decreasing "no change" for no change and "0" if both the values have been "0". Would that be a good approach though?

The end goal is to predict if a user would continue using the application or not. So it basically would be a two-class model. And I would want to capture even the scale of usage i.e., "A user sending 100 emails every day" should be different from "B user sending 10000 emails every day"

Answer 1

Well, you want to identify change in usage you could try something like:

$$ f(day_1,day2) = \frac{day_2-day_1 + \delta}{||day_2-day_1+\delta||} \times \Biggr|\Biggr|\frac{day_2+day_1}{(day_2+day_1+1)(day_2-day_1+1)}\Biggl|\Biggl| $$

where $\delta$ is the eps of your machine (minimum value needed to be summed to differ it from other floats)

that will give you $$f(100,0) \approx -98.02$$ $$f(0,100) = 100$$ $$f(100,100) \approx 0.995$$ $$f(0,0) = 0$$

You can look at my experiment here

This will map all non-changes from $[0,1]$ where $f(0,0)$ maps to $0$ and $f(\infty,\infty)$ maps to $1$

Where is it from? Just tuned the function manually. But I think this might suffice for your application

Explaining the idea

You want to have a feature that packs a lot of information: - Is the usage greater than zero? - Is it increasing or decreasing? - If it is stalled, how much is the usage?

Well, your usage vary in integer values so you can map the entire non-changing but above 0 case to a previously non-used interval.

The function above will map in $[0,1]$ all non-changing possibilities, in a exponential kind of way ($a^{(-\frac{1}{usage})}$) also you can extract the actual value from positive changes and the approximate value for negative change (been a better approximation when the drop is high)

This is not the perfect scenario but it is the maximum information I could compress into 1 variable with little loss.