P2V Methodology

The Product2Vec model analyzes co-occurrences of products in shopping baskets. The idea is that products that frequently appear together in customer transactions (i.e., items bought in the same shopping trip) likely share some hidden, or latent, attributes. For example, if hot dogs and hot dog buns often appear together in baskets, the model interprets them as related, even without explicit knowledge of their categories. In addition, the model understand products' similarity if the products occur in similar shopping baskets, even if they never, or very rarely, occur together (e.g., two different detergents brands). By doing this for large datasets of transactions, P2V automatically identifies relationships across a retailer’s full assortment.

Each product is represented by D-dimensional vector. P2V generates product vectors by training a neural network model using market basket data. The training task is framed as a binary classification problem, where the model learns to predict whether two products co-occur in the same basket. For each product pair, the model produces a similarity score, and the training objective is to classify product pairs as either co-occurring (positive samples) or not co-occurring (negative samples). The loss function used is the binary cross-entropy loss, which penalizes incorrect predictions based on the dot product of the product vectors. The learning procedure involves stochastic gradient descent (SGD), where product vectors are iteratively updated to minimize the classification error. Negative sampling is employed to efficiently handle the large number of product pairs that do not co-occur, ensuring scalability to large datasets.

Fun with Product Vectors

To illustrate that product vectors capture meaningful information, consider the following example. We take the product vector for Diet Coke, add the product vector for Gilette Fusion razor blades, and subtract the product vector for Gilette Venus razor blades. Out of more than 30,000 product vectors, the vector most similar to Diet Coke + Gilette Fusion - Gilette Venus is Coke Zero. Both difference, Coke Zero - Diet Coke and Gilette Fusion - Gilette Venus capture the different in the products’ target audience.

The table below illustrates that similar calculations work for a variety of other product characteristics, such as packaging size, private label, gluten-free and so on.

Attribute	Product A	Product B	Product C	Product D
Low-calorie	Fanta Orange 1l	Coca-Cola Zero 2l	Coca-Cola 2l	Fanta Orange Zero 1l
Frozen	Mars 6pc	Snickers ice cream 6pc	Snickers 6pc	Mars ice cream 6pc
Organic	Bananas	Onions red 500g organic	Onions red 500g	Bananas organic
Private label	Jacobs coffee pads 16pc	PL coffee 500g	Jacobs coffee 500g	PL coffee pads 20pc
Alcohol-free	Krombacher Pilsner .33l	Rotkäppchen .75l alcohol free	Rotkäppchen .75l	Krombacher Pilsner .33l alcohol free
Low-fat	Geramont camembert 200g 60% fat	Bärenmarke milk 1l 1.5% fat	Bärenmarke milk 1l 3.8% fat	Geramont camembert 200g light 16% fat
Gluten-free	Leibniz biscuits 200g	Dr. Schär Zwieback 165g	Brandt Zwieback 225g	Dr. Schär biscuits 165g
Lactose-free	Bärenmarke whipping cream 32%	Minus L(actose) coffee creamers 10%	Bärenmarke 8% coffee creamers	Minus L(actose) whipping cream 33%
Vegetarian	Rügenwalder bologna 80g	Mühlen meatballs 165g vegetarian	Mühlen meatballs 165g	Rügenwalder bologna 80g vegetarian
Flavor	Landliebe yogurt 150g strawberry	Schwartau jam 340g cherry	Schwartau jam 340g strawberry	Landliebe yogurt 150g cherry
Category	Cherry tomatoes 250g	PL carrot juice .5l	Carrots	PL tomato juice .5l JP
Size	JP Chenet Syrah .75l	Rotkäppchen .25l	Rotkäppchen .75l	Chenet Syrah .25l
Multi-pack	Hohes C multivitamins 1l	Hohes C orange 3x.2l	Hohes C orange 1l	Hohes C multivitamins 3x.2l
Packaging	Italian parsley 50g bunch	French parsley 40g flowpack	French parsley 50g bunch	Italian parsley 40g flowpack
Season	Lindt Easter bunny 100g	Merci Santa Claus 120g	Merci Easter bunny 120g	Lindt Santa Claus 70g