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Rule-Based Collaborative Filtering, Association

Rules, Naive Bayes Collaborative Filtering,

Neural Network, Singular Value Decomposition,

Stochastic Gradient Descent, Regularization.

Rule-Based Collaborative Filtering

Using Association Rules

Relationship Between Association Rules and Collaborative Filtering

• (^) Association rule mining was originally used to discover relationships in supermarket transaction data.
• (^) It is naturally defined over binary data but can be extended to categorical and numerical data by conversion.
• (^) In supermarket transactions and implicit feedback datasets, unary data is common, where 1s indicate a purchase and 0s indicate missing values (often approximated as "not purchased").

Example of Support in Market Basket Data (Table 3.1)

• (^) Two frequent itemsets identified:
  • (^) {Bread, Butter, Milk}
  • (^) {Fish, Beef, Ham}
• (^) These itemsets have a support of at least 0.2 , meaning they appear in at least 20% of transactions.
• (^) Implication for Recommendation Systems:
  • (^) If a customer buys {Butter, Milk}, they are likely to buy Bread (like Mary in the table).
  • (^) If a customer buys {Fish, Ham}, they are likely to buy Beef (like John in the table).

Association Rules and Confidence

• (^) Definition: An association rule is an implication of the form X ⇒ Y , where:
• (^) X (antecedent): Items already purchased.
• (^) Y (consequent): Items that can be recommended.
• (^) Example Rule: {Butter, Milk} ⇒ {Bread}
  • (^) Useful for recommending Bread to Mary , since she has already bought Butter and Milk.
• (^) Confidence Measure: The strength of the rule is measured by confidence:

Importance of Association Rule Mining in Collaborative Filtering

• (^) Helps in discovering hidden correlations between products in transactional data.
• (^) Useful for:
  • (^) Personalized recommendations (e.g., suggesting items frequently bought together).
  • (^) Targeted marketing strategies (e.g., offering discounts on complementary items).
• (^) Comparison with Collaborative Filtering:
  • (^) Unlike traditional collaborative filtering , association rules do not require user ratings.
  • (^) More effective in cases where implicit feedback (purchase history) is available.

Leveraging Association Rules for Collaborative Filtering

Association Rules and Unary Ratings Matrices

• (^) Unary ratings matrices arise from customer activities (e.g., purchases) where a customer only indicates a "like" (not a dislike).
• (^) Unary Data Representation:
  • (^) Items purchased (liked) → 1
  • (^) Missing items (not purchased) → 0
• (^) Unlike typical rating matrices, missing values in unary matrices are approximated as 0 to simplify processing.
• (^) Unary matrices are sparse , meaning most values are 0, making it acceptable to assume missing values are "not purchased."
• (^) The matrix is treated as binary data , allowing association rules to be applied.

Recommending Items to a Customer

• (^) Consider a customer A , and we want to recommend relevant items.
• (^) Steps:
  • (^) Identify all rules "fired" for customer A , meaning the antecedents of the rule match items A has purchased.
  • (^) Sort fired rules by decreasing confidence.
  • (^) Top-k items in the consequents of these rules are recommended to the customer.

Handling Numeric Ratings in Association Rules

• (^) Unary matrices only capture "likes," but real-world ratings involve numeric values (e.g., 1-5 stars).
• (^) Approach for Numeric Ratings:
  • (^) Convert each (item, rating) pair into a pseudo-item.
  • (^) Example: (Item = Bread, Rating = Dislike) is treated as a distinct item.
  • (^) Construct rules using pseudo-items rather than simple item names.

Weighted Voting for Prediction

• (^) Instead of strict rules, ratings can be numerically aggregated.
• (^) Steps:
  • (^) Identify all fired rules predicting ratings for a given item.
  • (^) Sum up votes for each rating based on the rule’s confidence.
  • (^) The highest weighted rating determines the predicted rating.
  • (^) The sorted list of top-rated items is recommended to the user. Using Interval-Based Ratings
• (^) When the rating scale has many possible values (e.g., 1-5 stars) :
  • (^) Convert the scale into a smaller set of intervals (e.g., 1-2 = "Low", 3 = "Medium", 4-5 = "High").
  • (^) Apply Association rule mining on the interval-based ratings.
  • (^) This allows handling continuous ratings in a structured way

Item-Specific Support for Better Recommendations

• (^) Instead of one global support threshold , different items can have different support values.
• (^) Example:
  • (^) A rarely purchased item may still be important, so a lower support threshold should be used.
  • (^) A frequently purchased item should have a higher support threshold.
• (^) Using item-specific support can improve the quality of recommendations.

Naïve Bayes Model in Collaborative Filtering

Application of Bayes' Theorem

• (^) We compute the probability of a missing rating based on observed ratings: Estimating Conditional Probabilities
• (^) The Naïve Bayes assumption is applied: Ratings are independent given a specific rating for item j.