Amazon Product Recommendation Systems

In this tutorial, you will learn about Amazon product recommendation systems.

Over the past decade, Amazon has become the first place to look for any product we want. With hundreds of millions of items in its catalog, it has made shopping easy for customers by putting the items they are likely to purchase in front. Everyone who comes to amazon.com sees a different homepage personalized according to his interests and purchases.

Behind the scenes are state-of-the-art recommendation engines that suggest a few products (from a vast catalog) based on your interests, current context, past behavior, and purchases. For example, the app might suggest iPhone covers if you recently purchased an iPhone or are currently looking to purchase one. Another example would be recommending products (e.g., toothpaste, diapers, etc.) based on your purchasing history to promote repeat purchasing.

This lesson will cover several aspects of Amazon recommendations (e.g., related-product recommendations, repeat purchase recommendations, and search recommendations) and how they work behind the scenes.

This lesson is the 1st in a 3-part series on Deep Dive into Popular Recommendation Engines 102:

Amazon Product Recommendation Systems (this tutorial)
YouTube Video Recommendation Systems
Spotify Music Recommendation Systems

To learn how the Amazon recommender systems work, just keep reading.

Amazon Product Recommendation Systems

In this lesson, we will discuss Amazon’s three major recommendation systems: related product, repeat purchase, and query-attribute search recommendations.

Related-Product Recommendations

Recommending related products (Figure 1) to customers is important as it helps them find the right products easily on an e-commerce platform and, at the same time, helps them discover new products, thereby delivering them a great shopping experience. The goal of the related-product recommendation is to recommend top- $k$ products that are likely to be bought together with the query product.

Product Graph

Product Relationships

To formulate the problem statement, let’s assume $a$ , $b$ , and $c$ be any three products and $R_\text{cp}$ , $R_\text{cv}$ , and $R_\text{like}$ be three binary relationships where:

$aR_\text{cp}b$ represents that product $a$ is co-purchased with product $b$ .
$aR_\text{cv}b$ represents that product $a$ is co-viewed with product $b$ .
$aR_\text{like}b$ represents that product $a$ is similar to product $b$ .

Figure 2 illustrates a product graph where green and blue edges represent co-purchase and co-view edges. AC refers to the adapter, AP refers to AirPods, P refers to iPhone, and PC refers to the phone case. Phone case PC is co-viewed and similar to other phone cases PC1, PC2, and PC3. Note that co-purchase edges are directional as $aR_\text{cp}b \nRightarrow bR_\text{cp}a$ . This is called the product asymmetry challenge in a related-product recommendation.

**Figure 2:** Product graph representing co-purchase and co-view relationships between products (source: Amazon Science).

Selection Bias and Cold Start

Along with capturing the asymmetry in the co-purchase relationship, related-product recommendations suffer from the challenge of selection bias, which is inherent to historical purchase data due to product availability, price, etc.

For example, the first customer was presented with phone cases PC and PC1 due to the unavailability of PC2 in their location. At the same time, a second customer was presented with only PC and PC2 because PC1 was out of stock. However, both end up purchasing PC, but that doesn’t mean that PC is a better choice. This creates a selection bias problem.

To mitigate this, we also need to capture second-order relationships of the following types:

$aR_\text{cp}b \land bR_\text{cv}c \implies aR_\text{cp}c$
$aR_\text{cv}b \land bR_\text{cp}c \implies aR_\text{cp}c$

Another challenge in related-product recommendations is the cold start problem, where we might also need to suggest newly launched products. Assume $c$ is a new product, and $a$ and $b$ are existing products. To address this, we need to uncover relationships of the following type:

$cR_\text{like}a \land aR_\text{cp}b \implies cR_\text{cp}b$ when $c$ is the query product.
$aR_\text{cp}b \land bR_\text{like}c \implies aR_\text{cp}c$ when $c$ is the related product.

Graph Construction

Amazon uses graph neural networks (GNNs) to model these relationships between products by learning their respective product embeddings (Figure 3). Before describing the approach, let’s look at how the product graph is constructed.

**Figure 3:** Using GNNs for related-product recommendations (source: Amazon Science).

The product graph $G = (P, \{ E_\text{cp} \cup R_\text{cv} \}$ consists of a set of vertices $P$ that represents products. $E_\text{cp}$ represents the set of co-purchase edges (i.e., $E_\text{cp} = \{ (u,v) | \forall u,v \in P \land uR_\text{cp}v \}$ ).

However, $E_\text{cp}$ is prone to selection bias and might miss relationships of type $aR_\text{cp}b \land bR_\text{cv}c \implies aR_\text{cp}c$ and $aR_\text{cv}b \land bR_\text{cp}c \implies aR_\text{cp}c$ .

To address this, we also include $E_\text{cv}$ which represents the set of co-viewed edges (i.e., $E_\text{cv} = \{ (u,v) | \forall u,v \in P \land uR_\text{cv}v \}$ ).

With this, graph $G$ now handles asymmetry and selection bias by containing the following product relationships:

Asymmetry: $aR_\text{cp}b \nRightarrow bR_\text{cp}a$
Selection bias: $aR_\text{cp}b \land bR_\text{cv}c \implies aR_\text{cp}c$
Selection bias: $aR_\text{cv}b \land bR_\text{cp}c \implies aR_\text{cp}c$

Figure 4 illustrates what a product graph looks like.

**Figure 4:** Product graph representing co-purchase (uni-directed) and co-view (bi-directed) relationships between products (source: Amazon Science).

Product Embedding Generation: Forward Pass

Algorithm

The GNN approach learns two embeddings for each product: source and target. Source and target embeddings are used when the product is a query and recommended item, respectively.

Algorithm 1 explains the procedure for generating these embeddings. Let $(h^s_u)^l$ and $(h^t_u)^l$ denote the source and target embedding for product $u$ at the $l^\text{th}$ step in the algorithm. These embeddings are initialized with their respective product input features.

**Algorithm 1:** Generating product source and graph embeddings using the GNN approach (source: Amazon Science).

First, the algorithm extracts the co-purchase and co-view neighbors for each product $u$ . The source embedding of product $u$ at the $l^\text{th}$ step (i.e., $(h^s_u)^l$ ) is computed as a linear combination of two non-linear terms (Line 4 of Algorithm 1).

The first term is the non-linear aggregation of target representations of its co-purchase neighbors at the $(l-1)^\text{th}$ step. Similarly, the second term is the non-linear aggregation of target representations of its co-viewed neighbors at the $(l-1)^\text{th}$ step. In other words,

$(h^s_u)^l \leftarrow \text{ReLU} \left (\sum_{(u,v) \in E_\text{cp}} (h^t_v)^{l-1} W^l \right) + \text{ReLU} \left (\sum_{(u,v) \in E_\text{cv}} (h^t_v)^{l-1} W^l \right),$

where $\text{ReLU}$ is ReLU activation, and $W^l$ are weights of a fully connected layer at step $l$ .

We do similar things for generating target representation $(h^t_u)^l$ of each product $u$ (Line 5 of Algorithm 1). The source and target embeddings are then normalized (Lines 7 and 8 of Algorithm 1) to the unit norm, and this process is repeated till $L$ steps to generate the final source and target embeddings $\theta^s_u$ and $\theta^t_u$ for each product $u$ .

Related-Product Recommendation

Given a query product $q$ and its source embedding $\theta^s_q$ , we perform a nearest neighbor lookup in target embedding space and recommend top- $k$ products. The relevance or utility score $\text{relevance}(q,v)$ of a candidate product $v$ with respect to query product is calculated as:

$\text{relevance}(q, v) \ = \ (\theta^s_q)^T(\theta^t_v)$

Note that $\text{relevance}(q, v) \neq \text{relevance}(v, q)$ , which helps us capture the asymmetry in co-purchase relationships.

Given a cold-start product $c$ , we perform a neighbor lookup to identify $k$ similar products $\{c_1, c_2, \dots, c_k\}$ in the input product feature space. Then we augment the product graph with new edges $\{(c, c_1), (c, c_2), \dots, (c, c_k)\}$ and pass the sub-graph corresponding to product $c$ to Algorithm 1 to generate its source and target embeddings. These embeddings are then used in the same way to compute the utility score.

Loss Function and Training

To learn the fully connected layer parameters $W$ , we use an asymmetric loss function, as shown in Figure 5.

**Figure 5:** Loss function used for training GNN for related-product recommendation (source: Amazon Science).

The loss function contains three terms:

The first term in the loss function is a combination of two sub-terms. The first sub-term ensures that the source embedding of a product $u$ and the target embedding of its co-purchased product $v$ are similar.
In contrast, the second sub-term ensures that the source embedding of a product $u$ and the target embedding of a randomly selected product $v$ are dissimilar.

The second term ensures asymmetry by assigning a high score to a co-purchased pair $(u,v) \in E_\text{cp}$ and a low score to pair $(v,u) \notin E_\text{cp}$ .

The third term ensures that co-viewed product pairs’ source and target embeddings are similar. This helps mitigate selection bias as if products $u$ and $v$ are co-viewed, then $\text{relevance}(q,u) \approx \text{relevance}(q,v)$ for an arbitrary query product $q$ .

Repeat Purchase Recommendations

Repeat purchasing (i.e., a customer purchasing the same product multiple times) is an important phenomenon in e-commerce platforms (Figure 6). Modeling repeat purchases helps businesses increase their product click-through rate and makes the shopping experience easy for customers.

Repeat purchase recommendations estimate the probability of a customer purchasing a product again as a function of time from their last purchase. In other words, given a customer $C$ has already purchased a product $A_i$ $k$ -times with time intervals $t_1, t_2, \dots, t_k$ , we want to estimate the purchase probability density:

$P_{A_i}(t_{k+1} = t | t_1, t_2, \dots, t_k)$

In the above equation, we assume that the product purchases are independent of each other, and the equation can be decomposed into two components:

$P_{A_i}(t_{k+1} = t | t_1, t_2, \dots, t_k) \approx Q(A_i) \times R_{A_i}(t_{k+1} = t | t_1, t_2, \dots, t_k, A_i=1),$

where $Q(A_i)$ is the repeat purchase probability of a customer buying a product a $(k + 1)^\text{th}$ time given that they have bought it $k$ times. $R_{A_i}$ is the distribution of $t_{k+1}$ , conditioned on the customer repurchasing that product; indicated by $A_i = 1$ .

This lesson will discuss three frameworks Amazon uses to model repeat purchases.

Repeat Customer Probability Model

This framework is time-independent and is based on a frequency-based probabilistic model that computes the repeat customer probability $\text{RCP}(A_i)$ for each product $A_i$ by using aggregate repeat purchase statistics of products by customers. In other words, it assumes that $R_{A_i} = \text{constant}$ and $P_{A_i}(t_{k+1} = t | t_1, t_2, \dots, t_k) \approx Q(A_i) \approx \text{RCP}(A_i)$ .

$\text{RCP}(A_i) \ = \ \displaystyle\frac{\text{\#s of customers who bought product } A_i \text{ more than once}}{\text{\#s of customers who bought product } A_i \text{ at least once}}$

To ensure good quality of repeat product recommendations, we only recommend products for which $\text{RCP}(A_i) > r_\text{threshold}$ , where $r_\text{threshold}$ is an operating threshold.

Aggregate Time Distribution Model

Amazon analysis shows that most customers have only a few repeat purchases for a specific product (i.e., $\text{RCP}(A_i)$ is low). But there are many products for which Amazon has many customers making repeat purchases (i.e., $\text{RCP}(A_i)$ is high). Hence repeat purchases often depend on a customer’s purchase behavior.

Aggregate time distribution (ATD) model is a time-based model that assumes that product purchase density is only a function of past purchase behavior $R_{A_i}$ . In other words, $Q_{A_i} = \text{constant}$ and $P_{A_i}(t_{k+1} = t | t_1, t_2, \dots, t_k) \approx R_{A_i}(t_{k+1} = t | t_1, t_2, \dots, t_k, A_i=1)$ .

Amazon uses a log-normal distribution for defining $R_{A_i}$ :

$R_{A_i}(t) = \mathcal{N}(\ln(t); \mu_i, \sigma_i),$

where $\mu_i$ and $\sigma_i$ are the mean and variance of the Gaussian distribution.

Figure 7 illustrates the distribution of repeat purchase time intervals ( $t$ ) and log repeat purchase time intervals ( $\log(t)$ ) of a random consumable product across all its repeat purchasing customers.

**Figure 7:** Distribution of repeat purchase time intervals (t) and log repeat purchase time intervals (log(t)) of a random consumable product across all its repeat purchasing customers (source: Amazon Science).

Note that only the products having $\text{RCP}(A_i) > r_\text{threshold}$ are deemed repeat purchasable and vice versa. Finally, recommendations are generated by considering all the repeat purchasable products previously bought by customers and ranking them in the descending order of their estimated probability density $R_{A_i} (t)$ at a given time $t$ .

Poisson-Gamma Model

Poisson-gamma (PG) model is one of the most seminal works in modeling customer repeat purchases. It assumes the following two assumptions:

A customer’s repeat purchases follow a homogeneous Poisson process (Figure 8) with a repeat purchase rate $\lambda$ . In other words, they assume that successive repeat purchases are not correlated.
Assume a gamma prior on $\lambda$ (i.e., assume that $\lambda$ across all customers follows a Gamma distribution with shape $\alpha$ and rate $\beta$ ).

**Figure 8:** Poisson Distribution (source: Brilliant).

The parameters $\alpha$ and $\beta$ of the gamma distribution can be estimated using maximum likelihood estimation over the purchase rates of repeat customers. After this, the purchase rate $\lambda_{A_i, C}$ for a customer $C$ and product $A_i$ is given as:

$\lambda_{A_i, C} \ = \ \displaystyle\frac{k + \alpha_i}{t + \beta_i},$

where $\alpha_i$ and $\beta_i$ are the shape and rate parameters of gamma distribution for product $A_i$ , $k$ is the number of repeat purchases, and $t$ is the time elapsed since the first purchase of product $A_i$ by customer $C$ .

The $R_{A_i}$ is then assumed to be a Poisson distribution where the rate parameter is estimated using the above equation.

$R_{A_i, C}(t) \ = \ \displaystyle\sum_{m=1}^{\infty} \displaystyle\frac{\lambda^m_{A_i, C} \exp(\lambda_{A_i, C})}{m!}$

where $m$ is the expected number of purchases, this model assumes that $Q_{A_i}$ is fixed, just like the ATD approach.

Query-Attribute Search Recommendation

Amazon search queries are mostly related to products and are often short (three to four words) and not too descriptive. Such short and undescriptive queries can lead to suboptimal search results because of an information shortage. Amazon leverages attribute recommendations to improve the quality of search recommendations for short queries.

The attribute recommendation (Figure 9) takes the customer query as input and recommends implicit attributes that don’t explicitly appear in the search query. For example, for a search query “iphone 8,” the attribute recommendation will suggest additional attributes like “brand:apple,” “operating_system:ios,” “complements: phone case,” and “substitute_brand: samsung.” These additional attributes can enrich the search query and help the search engine provide better results.

**Figure 9:** Overview of Attribute recommendation at Amazon Search (source: Amazon Science).

The attribute recommendation model comprises three modules: query intent classification, explicit attribute recognition, and implicit attribute recommendation. We will now describe each of these in detail.

Query Intent Classification

The intent of a query is defined as the product type intent of the question. For example, the intent of the query “iPhone 14” is “phone,” and for “Nike shoes,” it is “shoes.” Amazon has more than 3000 product types; hence, it is posed as a multi-label classification where a query intent can be classified into one or more product types.

Given a query $q$ and country id $m$ , the model predicts whether each product type is relevant to the question. For training, Amazon uses past customer click behavior from the search logs. These logs contain the number of clicks on each product for a country and query pair.

Each product $a$ is assigned a product type $L_a$ from a catalog $L$ . Each country-query pair $x_i = (m_i, q_i)$ is assigned a label,

$y_{it} \ = \ \displaystyle\frac{\displaystyle\sum_{L_a = t} N_{ia}}{\displaystyle\sum_a N_{ia}},$

where $N_{ia}$ is the number of clicks on product $a$ for query $q_i$ .

As shown in Figure 10, the module uses a BERT (bidirectional encoder representations from transformers) model, which performs classification on top of classification token ([CLS]) output embedding. Since it’s a multi-country setting, each country has a different label space consisting of labels observed for products in that marketplace. Hence, we only get labels corresponding to that country’s marketplace. The architecture is shown in the figure below.

**Figure 10:** Intent classification model (source: Amazon Science).

Explicit Attribute Parsing

Explicit attribute parsing involves recognizing product attributes from the query (e.g., color, brand, etc.). This module uses a multilingual transformer-based model that performs recognition, as shown below. Each token goes through classification to get its classification label, denoting what attribute this token belongs to. This is illustrated in Figure 11:

Implicit Attribute Recommendation

This module first builds an attribute relation graph using two data sources: Amazon product attributes and query attributes. Amazon product attributes are the explicit attributes sellers provide while uploading the product on their platform. For example, iPhone 8 has the attribute brand “apple” and product type “phone.”

The query attribute data is collected from customer search queries, and their corresponding explicit attributes are extracted using the parsing module described before.

Then, the intent classification model obtains each query’s product intent, and each product’s intent is naturally obtained through catalog data. All this information is then used to construct the attribute relation graph shown in Figure 12.

**Figure 12:** Implicit attribute recommendation (source: Amazon Science).

The module used GNN to generate embeddings for each attribute. These embeddings are then used to construct relationships between different attributes. During online inference, given the explicit query attributes and intent, we use the attribute relation graph to recommend implicit attributes by doing a random walk through the graph.

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Summary

In this lesson, we discussed three Amazon recommender systems:

related-product recommendation
repeat purchase recommendation
query attribute recommendation

The goal of the related-product recommendation is to recommend top- $k$ products that are likely to be bought together with the query product. Amazon creates a product graph whose vertices denote all the products and whose edges represent co-purchase (directed) and co-viewed (undirected) relationships.

Graph neural networks (GNNs) are used to learn source and target embeddings for each product based on their relationships. The relevance of a candidate product with respect to the query product is calculated as the dot product between the source representation of the query product and the target representation of the candidate product.

Next, repeat purchase recommendations estimate the probability of a customer purchasing a product again as a function of time from their last purchase of that product. Amazon uses three probabilistic models for modeling repeat purchases.

The repeat customer probability model is a time-independent framework based on a frequency-based probabilistic model that computes the repeat customer probability for each product using aggregate repeat purchase statistics of products by customers.
The aggregate time distribution (ATD) model is a time-based model that assumes that product purchase density is only a function of past purchase behavior.
The Poisson-gamma (PG) model takes customers’ repeat purchases following a homogeneous Poisson process, and the purchase rate across all customers follows a Gamma distribution.

Lastly, the attribute recommendation takes the customer query as input and recommends implicit attributes that don’t explicitly appear in the search query. The attribute recommendation model comprises three modules:

query intent classification
explicit attribute recognition
implicit attribute recommendation

The intent classification model predicts whether each product type is relevant to the query. Explicit attribute parsing involves recognizing product attributes like color, brand, etc., from the query. Finally, the implicit attribute recommendation model builds an attribute relation graph using two data sources: amazon product attributes and query attributes.

However, this is just the tip of the iceberg. There is much more to the Amazon recommendation systems. We highly recommend going through their blog page to learn more.

Stay tuned for an upcoming lesson on YouTube video recommendation systems!

Citation Information

Mangla, P. “Amazon Product Recommendation Systems,” PyImageSearch, P. Chugh, A. R. Gosthipaty, S. Huot, K. Kidriavsteva, and R. Raha, eds., 2023, https://pyimg.co/m8ps5

@incollection{Mangla_2023_Amazon_Product_Recommendation_Systems,
  author = {Puneet Mangla},
  title = {Amazon Product Recommendation Systems},
  booktitle = {PyImageSearch},
  editor = {Puneet Chugh and Aritra Roy Gosthipaty and Susan Huot and Kseniia Kidriavsteva and Ritwik Raha},
  year = {2023},
  url = {https://pyimg.co/m8ps5},
}

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