Binary Labels

Binary Labels: Favs, Likes and Clicks

From Ratings to Binary Engagement

“Many important applications of recommender systems or collective filtering algorithms involved binary labels where instead of a user giving you a one to five star or zero to five star rating, they just somehow give you a sense of they like this item or they did not like this item.”

Binary Label Examples

Dataset Structure

Binary collaborative filtering uses:

• 1: “The user liked or engaged with a particular movie”
• 0: User did not engage after being shown the item
• ?: “The user has not yet seen the item”

Practical Interpretations

Label 1 could mean:

• “Alice watched the movie Love at last all the way to the end”
• “She explicitly hit like or favorite on an app”
• User spent sufficient time with content

Label 0 could mean:

• “After playing a few minutes of nonstop car chases decided to stop the video”
• “Did not hit like” after being exposed to the item

Note

Question Mark Usage “Usually means the user has not yet seen the item and so they weren’t in a position to decide whether or not to hit like or favorite on that particular item.”

Common Binary Label Definitions

E-commerce Applications

• Purchase behavior: “Whether or not user j chose to purchase an item after they were exposed to it”
  • 1 = purchased after exposure
  • 0 = did not purchase after exposure
  • ? = not shown the item

Social Media Applications

• Engagement actions: “Did the user favorite or like an item after they were shown it”
• Time-based engagement: “If a user spends at least 30 seconds of an item” assign label 1
• Click behavior: “See that the user click on an item” (common in online advertising)

General Pattern

Label 1: “The user engaged after being shown an item” (clicked, spent time, favorited, purchased) Label 0: “The user not engaging after being shown the item” Question Mark: “The item not yet having been shown to the user”

Algorithm Adaptation: Linear to Logistic

Previous Approach (Continuous Ratings)

prediction = w^(j) · X^(i) + b^(j)

New Approach (Binary Labels)

P(y^(i,j) = 1) = g(w^(j) · X^(i) + b^(j))
where g(z) = 1/(1 + e^(-z))

“This is the logistic function just like we saw in logistic regression.”

The model now predicts “the probability of y^(i,j) being 1 that is of the user having engaged with or like the item.”

Cost Function Modification

From Squared Error to Cross-Entropy

Previous cost function used squared error for continuous ratings.

New cost function uses “binary cross entropy cost function”:

Loss = -y*log(f) - (1-y)*log(1-f)

Complete Binary Collaborative Filtering Cost

J(w,b,X) = Σ[(i,j): r(i,j)=1] Loss(f^(i,j), y^(i,j)) + regularization

Where:

• f^(i,j) = g(w^(j) · X^(i) + b^(j))
• Loss uses the binary cross-entropy function
• Regularization terms remain similar to previous approach

Tip

Expanded Applications “This actually very significantly opens up the set of applications you can address with this algorithm” since binary engagement data is much more common than explicit ratings.

Implementation Advantages

Binary labels are often easier to collect than explicit ratings:

• Users naturally engage/don’t engage with content
• Implicit feedback from user behavior
• No need to ask users for explicit ratings
• Can work with click-through data, time spent, purchases, etc.

The transition from linear regression-like collaborative filtering to logistic regression-like collaborative filtering follows the same mathematical principles but opens up recommender systems to a much broader range of practical applications where explicit ratings aren’t available.