Personalization has gained a lot of traction in the e-commerce domain since there is ample evidence for short-term and long-term benefits of understanding user preferences and ensuring user satisfaction. However, efectively personalizing recommendations is a challenging task, especially at scale. Price is often a key consideration for purchases, and user behavior varies widely depending on demographic and psychological factors. While dificult to model, this is an important signal to consider for user-item recommendation. In this paper, we focus on personalizing and improving the relevance of item recommendations for e-commerce users by leveraging price as an essential input. More concretely, we segregate items into price bands indicating how expensive they are, infer user afinity to price bands based on historical behavior and use features derived from this knowledge to re-rank items in a real-world recommendation scenario. We experiment with various statistical and machine learning methods to determine item price bands, user price afinities and item price similarities, and demonstrate impact on the recommendation quality for millions of users and items.
Recommender systems are ubiquitous on websites today.
Recommendation algorithms can be based on item-item interactions or
user-item feedback. In recent times, websites are increasingly
focusing on providing an experience tailored to their users [
For most users, price is often a key factor for making purchases
[
However, defining what constitutes a high-priced or low-priced item is a dificult task. In the e-commerce domain, products, of course, have price associated with them. But, we do not know whether a given price is considered expensive or inexpensive for a given type of product, for example, a light bulb and a laptop. $100 may be a bargain for the laptop, but the same price-tag for the light bulb might make it very expensive. Similarly, we need to understand item prices for each product type and categorize them into diferent price bands (e.g. low vs. high) based on this. Subsequently, we can start understanding which price bands users are likely to purchase from for diferent product types.
To summarize, using price to personalize item recommendation is challenging because user price preferences need to be implicitly inferred and vary based on the type of product. Additionally, item prices are not suficient to determine if a product is considered expensive versus not, and need to be standardized such that they can be compared across diferent types of products. In this paper, we aim to model user price afinity and item price similarity, and utilize them as input signals along with item-item relevance scores to personalize and improve the quality of item recommendations for e-commerce users. We achieve this using the following: • Unsupervised methods to divide items into price bands indicating their degree of expensiveness • Supervised methods to compute user afinity to diferent price bands based on their historical interactions • Item and user price-related features to re-rank items in an actual user-item recommendation setting This is done at the Product Type (PT) level which is the most granular level of the product taxonomy available in the Walmart product catalog. We use a large e-commerce dataset, and experiment with multiple statistical and machine learning methods to determine item price bands, user price afinities and item price similarities. We quantitatively show the positive impact on recommendation quality upon including price-related features in the re-ranking algorithm. 2
There has been extensive research on recommender systems and
personalization. Many research eforts have been focused on
collaborative filtering-based techniques. Traditional matrix factorization
(MF) models [
Price is an important factor to consider for users while making
an online purchase. In [
However, price has received relatively less attention as an input
signal for recommendation. Price is used as a feature in [
In our work, we explore several methods to compute item price bands and explicitly model user price afinity for various types of products, such that these input signals can be leveraged generally for use cases such as recommendation and search. We demonstrate results for user-item and item-item price-related features obtained from diferent model variations used together with an item-item relevance score for personalizing item-anchored recommendations. 3
Our goal is to use past item interaction data (such as clicks and add to carts) for a given user and predict their afinity for a particular price band, and eventually incorporate this price understanding into recommendations. To achieve this, items are clustered into price bands at the product type level (Section 3.1), and then user activity patterns are learnt with respect to these item price bands to predict the probability that the user will purchase an item from a particular price band versus others for that product type. These predicted user-item price band afinity scores (Section 3.2) and item-item price band similarity scores (Section 3.3) are used as features along with relevance scores to re-rank item-anchored recommendations (Section 3.4) for personalization using price understanding. 3.1
Item prices vary a lot, from less than 10 dollars for a USB drive to thousands of dollars for a QLED television. However, to decide if an item is expensive or not, just the absolute value of price is insufifcient. It is also important to take into consideration the product type since a price of $100 might be low for televisions, but high for a USB drive. Thus, we need to create representations for prices of items for each product type such that they are directly comparable across diferent items. So, we assign each item to one out of bands using unsupervised methods since labels are unavailable. 3.1.1 Statistical Methods. We first explore statistical methods using item prices for each product type.
• Range-Based: For example, say television prices vary from $100 to $5100, and we decide to create 3 price bands with price range ratios 3:5:2. Then one unit of the range becomes ($5100 - $100)/(3+5+2) = $500, and the lowest price band extends from $100 to $100 + 3*$500 (= $1600), the middle from $1600 to $2600 + 5*$500 (= $4100) and the highest from $4100 to $4100 + 2*$500 (= $5100). • Percentile-Based: For example, say, in the above situation, we decide to create 3 price bands with percentiles 30%, 50% and 20%. If there are 200 televisions on our item catalog with 60 TVs having price less than $500, 100 TVs with prices between $500 - $2500 and 40 TVs with prices greater than $2500, then those delineate the price bands.
Splitting items into equal bins based on range or percentiles did not work well in practice due to skew in item price distributions and transaction volumes. Creating unequal bins needs extensive manual tuning. 3.1.2 Clustering. Next, we use some common clustering methods to automatically put items from each product type into clusters using the item price values.
• K-Means [
user_price_afinity
(, ) =
# of trx in ,
# of trx in
(1)
3.2.2 Machine Learning. We consider user price afinity prediction
as a multi-class classification (supervised machine learning)
problem with number of classes equal to the number of price bands ().
For each user and product type, we use features such as number
of transactions, add to carts and views of items per price band per
month (for 6 months) by that user for that product type. We did not
have ground truth data for labels. As a proxy, we use the price band
which has the maximum number of transactions by the user for
that product type, as the label. The aggregation of data for labels
is done using the month following the last month used for feature
generation. Thus, each data point is used to predict price afinities
of a specific user towards diferent price bands in a particular
product type. Subsequently, we use these features and labels to train
and test multi-class Logistic Regression (LR) [
In LR, for each input data point (feature vector and label ), the model learns weights (weight vector ) and outputs a probability distribution over the price bands () for a given user and product type ( ) which represents their afinity.
user_price_afinity
(, ) = Í=1 exp
exp
(2)
We use two variants - unweighted (LR-unbal) which is the vanilla
model and weighted (LR-bal) based on class imbalance, where
each data point is assigned a weight while contributing to the
loss/gradient computation. The weight balancing heuristic used
n_samples
[
In DT, data is continuously split based on a certain feature at each step. We also consider random forests and fit multiple decision trees 3.3 Another input is the similarity between price bands for items across product types based on user transaction patterns. For example, users who purchase medium-priced televisions might be likely to purchase high-priced sound bars and these ( , ) pairs are similar. This is also used as a feature while re-ranking to capture the itemitem price similarity.
Pearson Correlation [
price2price = , =
cov( , )
∗
Matrix Factorization [
price2price = ( ) =
· || || || || (3) (4) 3.4
To tie everything up, we have a re-ranker engine that is capable of incorporating user price understanding and item price similarity into any item recommendation set such as Viewed also Viewed and Bought also Bought. We use an inference function to combine features related to user preference and item relevance, and predict user-item interactions: ( interacts with | just interacted with ) = ((, ), ℎ (, )) (5) where is the user, is the anchor item, is the recommended item, (, ) represents ’s preference for , and ℎ (, ) represents item relevance between and . Currently, the inference function we use is simple logistic regression where user preference score and relevance score are combined linearly. The weights can be learned either at the global level (i.e. same weights across all product types) or at the product type level. There are more details in Section 4.4. 4
We use a real-world proprietary e-commerce dataset from walmart.com for demonstrating results. We determine price bands for few million items and predict price afinity scores for millions of users across around 6000 product types. 4.1
We explored the trade-of between granularity for more useful user afinity scores and data sparsity issues in user-price band interactions as the number of price bands per product type increases, and decided to use = 5 item price bands for our experiments. We evaluate the discovered item price bands qualitatively, since ground truth labels are unavailable. One way is to look at how price ranges for diferent products were being split based on diferent methods described in Section 3.1. Of these, (as shown in Figure 1) we pick k-means and transaction balancing (transac-bal) as methods to further evaluate in the subsequent steps of predicting user afinities and using these to re-rank recommendations. We observe that clustering methods such as k-means put fewer very high priced items into the higher price bands, whereas trying to equalize number of transactions puts fewer items into the lower price bands, which is expected since less expensive items usually have more transactions. We also randomly sample items and inspect the quality of price bands. An example of televisions from 5 price bands (v low-0, low-1, medium-2, high-3 and v high-4) is shown in Figure 2. 4.2
We hold out 20% of data to test the trained user price afinity
models described in Section 3.2. We use precision, recall and F1 score,
which are common multi-class classification evaluation metrics, to
assess the performance of diferent models. Since the classes in the
data are not balanced, accuracy is not a good metric. Additionally,
we also use the Mean Reciprocal Rank (MRR) to check whether
even if the max transaction price band (ground truth label) does
not get the maximum price afinity score, it gets a reasonably low
(better) rank. Results for diferent models when price bands are
determined using k-means and transac-bal are shown in Table 1 and
Table 2 respectively. Random forests did not give much
improvement over simple decision trees, so we have omitted those results.
For the baseline, we obtain an overall MRR of around 0.51 for
kmeans and around 0.37 for transac-bal. All the machine learning
methods performed better than the baseline. For logistic regression,
we explored hyperparameters aggregation depth: [
We show how price understanding models perform when implemented on the "customers who viewed also viewed" (VAV) application (example shown in Figure 5). We take few million anchor items from VAV and limit to <= 30 recommendations for each item ranked by a "relevance" score. This relevance score is based on item-item features such as number of co-views, title match and popularity. The price understanding model ofers two additional features for re-ranking on top of the relevance score: user price afinity score and price2price similarity score.
We first test out various methods used to develop user price
afinity. We start with two main methods for item price banding:
k-means and transaction balancing. For each item price banding
model we have four variations for user price afinity: baseline,
logistic regression (unbalanced), logistic regression (balanced) and
decision trees. This gives us a total of eight versions of user price
afinity scores. The inference function for re-ranking is balanced
logistic regression:
= 0 + 1 × relevance + 2 × user_price_afinity
(6)
The weights in the equation above are trained at the global level
(as opposed to at each product-type level) and are optimized for
items that are co-viewed within each user session. To evaluate
performance, we use common ranking evaluation metrics Normalized
Discounted Cumulative Gain (NDCG) [
We now expand on the previously established best performing model and supplement it with item price similarity information between the anchor item and the recommended item. We have two variations of item similarity scores to compare: Pearson correlation and matrix factorization. The inference function now has an additional feature, as follows: = 0 + 1 × relevance + 2 × user_price_afinity + 3 × price2price_similarity (7) Again we adopt a balanced logistic regression model to train the above objective function and learn the weights at the global level. The results are shown in Table 5. We observe an even greater boost in performance by adding the price2price feature. Overall, the best performing model uses price2price scores derived from matrix factorization. Compared to the relevance only model, this method shows 0.64% improvement in NDCG, 1% improvement in MHR, and 0.93% improvement in MAP. The improvements in NDCG, MHR and MAP@5 are statistically significant at 5% level in our ofline evaluation. Though the MRR is slightly lower, the diference is not statistically significant. Also, since 5-6 recommended items are typically shown on the first pane of the module, metrics such as MHR become more important.
We further study the weights, 1 2 3 from the inference function to gauge feature importance. After adjusting for feature variance (standard scaling of features), the ratio among the weights 1 : 2 : 3 = 33:3:1. This tells us that the relevance score from the VAV model contributes the most even during re-ranking, but price-related features also add value. The user price afinity feature has greater weight than the price2price feature.
In this paper, we discuss a novel approach to incorporate pricerelated user-item signals into recommender systems to personalize their output. This is done by assigning price bands to items of different types, using historical user-item data to predict user price afinity and using this afinity along with an item price band similarity score to re-rank item recommendations anchored on a (user,
User Price Afinity Method
k-means k-means k-means k-means transac-bal transac-bal transac-bal transac-bal - Relevance
LR (unbalanced) LR (balanced) Decision Trees
LR (balanced) Decision Trees - Relevance
Matrix Factorization item) pair. We demonstrate statistically significant improvement in ofline ranking metrics after explicitly including price inputs (user price afinity using balanced logistic regression with transactionbalanced price bands; item price similarity using matrix factorization). To compute price afinities, other user-website interaction data such as user’s historical search queries can also be used. In the future, we plan to learn embeddings which implicitly encode item price information and user representations such that similarity between user and item embeddings is indicative of price afinity. We can also experiment with other pairwise or listwise learning to rank methods to improve the current pointwise ranking function.