Did you notice any difference in contemporary and past e-commerce platforms? Why has the number of combo recommendations decreased on e-commerce platforms? There used to be hundreds of combo recommendations, but nowadays, you find very few of them. Did you ever give it a thought?

Well, in this blog, I am going to discuss the possible reasons which are worth contemplating. Also, I will discuss the motivation behind my latest research and the problem it solves. With the number of products, users, and related data burgeoning day-by-day, it has already become a challenging task for the recommendation engines to compute the associated products’ ranking. Let’s try to understand this by an example.

Whenever you aim to purchase any product online, the recommendation engines, with the use several techniques, such as machine learning,  always recommend the products under the categories: “Frequently bought together,” “Bought Together,” “Customers who bought this item also bought,” or “Sponsored products related to this item.”

Searching is deemed as one of the most tiresome jobs now. Not only it utilizes a lot of CPU time but also tolls the users. The following are some proven factors which influence the users’ tendency to purchase something:

1. The time it takes to load available products in the catalog on the screen.
2. The amount of effort required by the user to search the products.
3. The availability of combos and companion products corresponding to those products in which the user is interested (Also known popularly as Product Bundling).
4. Promotion offers.

Combos are generally bought by the users if offered at a similar or a lower price.

The users also prefer combos if they are of better quality or if the users change their minds to buy something extra that they haven’t thought of before.

Nowadays, we only see the individual products (as we saw in Fig.1 and Fig. 2), but the pairs, triplets, or combos. The apparent reason behind this is the growing number of products in the catalog and the total number of possible product pairs or combos.

For example, if there are N products in the catalog, and a combo is the pair of any two products, there are total NC2 = (N*(N-1)/2) pairs possible.

But then the following questions arise in our mind:

1. Why should anyone be interested in all the pairs instead of the top N pairs?
2. Will computing only the top N pairs suffice?
3. What is the use of the product pairs, which are down the order or have a higher rank?
4. If the recommendation engine is computing the list of most related products, why not list the associated products’ pairs?

Knowing the exact answers to these questions is difficult unless:

1. You work for such MNCs.
2. You have designed/studied the model for the recommendation engine (For insiders’ eyes only).
3. You are aware of the company’s business policies.

Before trying to contemplate the answers to these questions, let us have a look at how the engine computes the list of related products.

The engines use a concept of the relatability index. Each product, including the main one (the one in which the user is interested), is assigned a value or relatability index according to the measure of its correspondence w.r.t the main product. In that case, the main product gets the highest value, and the others get a relatively lower one.

For example: Considering the current Corona crisis, if I wish to buy a face mask, the mask is assigned the highest score or index. The other related products, such as hand sanitizers, goggles, face shields, hand gloves, will get a relatively lower score, depending on several factors. For example, these factors can be the product’s popularity, current demand in the market, brand, and cost.

Have a look at the scores assigned by the engine to the related products in Fig. 4. Also, note that the main product got the highest value. The list of combos is sorted in non-increasing order.

Now, if the engine computes the list of pairs, it will look as follows:

Figure 5: The list of corresponding/related combos computed by the engine.

Make a note that the combo’s index value is determined by adding the products’ individual indices. The list of the combos is sorted in non-increasing order, as depicted in Fig. 5. If two combos have the same value of the overall index, then a higher priority will be given to that combo, which has the product will the highest individual index. Therefore, the combo of face mask and gloves (having index=5) got higher priority than hand sanitizer and goggle (having index=5). For 4 products, the total number of possible pairs = 4C2 = 6.

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Now, coming back to the questions.

Q1) Why should anyone be interested in all the pairs instead of the top N pairs?

Ans: It is not likely for every user to think similarly, as suggested by the recommendation engine. Not every time, users tend to buy things that are trending in the market. User’s tendency to buy a particular item is also strongly influenced by their own respective personal needs. Therefore, the engines make use of personalized recommendations (that are present in the list of top N recommendations that get rendered on the page). But what about the newly launched brands? They are not widespread, nor they have original user reviews, and therefore, they may get a lower score or higher rank in the list. There are two ways to address these issues:

1. Paid promotions carried out by e-commerce management.
2. Random recommendations to provide a fair chance for these products to get rendered on the page and come to users’ attention. This way, the recommendation engine intern learns from the actions performed by the users.

Q2) Will computing only the top N pairs suffice?

Ans: You got it correct. It will not. The products or the products’ pairs, which get a higher rank, have a low possibility of getting rendered on the end-users’ screens.

The page size is also limited, so engines are themselves left with a few options to be recommended.

Also, if the number of recommendations increases, the users may fall into the analysis paralysis trap.

Q3) What is the use of the pairs who are down the order or have a higher rank?

Ans: When users positively react to these, the engine internally learns about users by collecting information.

Q4) If the recommendation engine is computing the list of most related products, why not list the pairs of related products?

Ans: The variety of products in the catalog is increasing every day. Imagine if there are 1 million products in the catalog. Then the total number of possible pairs is nearly 4,99,99,95,00,000.

Also, other than recommendations, there are many things to be rendered on the page within a fraction of seconds. Otherwise, you lose the customer.

Where does my research come into play?

Earlier, we saw the importance of random recommendations. To compute any single Nth pair, the existing methods available in the market require a worst-case time complexity of O(N² log(N)).

Please give it a thought!

HINT: Make use of priority queues.

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Now imagine if we have 1 million products in the catalog, up to 10 million active users, and the server is capable of computing 1 million operations per second.

Then the worst approximate total time to suggest 1 random recommendation to each of the 10 million users = (10¹² * log(10⁶) * 10,000,000) / 1,000,000.

The first part (10¹² * log(10⁶)) comes from the N² log(N).

The second part of 10,000,000 comes from 10 million users.

And finally, the division part comes from 1million operations/second.

So, worst approximate total time = 7 * 10¹³ seconds = 19,444,444,444.444 hours = 810,185,185.18 days = 2,219,685.43 years.

Over 2 million years!

In my upcoming research paper, which will be published in the Proceedings of 8th ICICSE, LNNS, Springer Journal, I have discussed the solution to compute the pairs in real time and provide a fair chance to the pairs who are ranked higher in the order.

Thanks for your time, and I look forward to discussing it with you on the same.

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NOTE: I haven’t included any references here to avoid plagiarism issues, as the paper is still in the process of publication.

A special thanks to Shubham Sawant (@moghya), my all-time last moment savior, who inspired me to write this blog.