What is good consolidated/normalized metric with funnel page views data? I am currently working on a best way to represent product interest score based on page views.
Working on an ecommerce use case having homepage, search page, and product page interaction data available. I want to build a customer interest score on a product and work on an effective way to represent it.
Simplest metric would be summing up all the interaction associated with the product i.e. home + search + product page i.e. if a product A was seen by 5 users on Home, 10 users in search and 2 users in product page, the total count would be 17. However, my theory is that we need to give more bias/weight to the product page since customers have specifically viewed this page as compared all the other product published in home and search page. Something like:
(5x + 10y + 2z)/(x+y+z), where x,y,z are the weights associated with home, search, and item page respectively. In my theory, z > y > x
How to best represent this metric by weighting the pages accordingly?

If the product seen on home or search page can be just a result of randomly scanning the page by the user and might not necessarily mean that the user expresses an interest for the product, while something that has been seen on the product page means that the user clicks into that page, I think it would be interesting to represent this information in one-dimension by applying PCA, and check if the most variance in the component does come from the variable z. If so, you could probably use the PCA component scores as an indication of interest level.
