Collaborative Filtering Techniques

• Collaborative filtering (CF) involves a list of m users and a list of n items.
• Each user has a list of items with an associated opinion or rating.

Opinion Types

• Explicit, like a 3-star rating on Google Play Store,
• Implicit, such as purchasing a product.
• An active user is the target for whom the CF prediction task occurs.
• Metrics measure similarity between users.
• Methods select a subset of the closest neighbors.

Collaborative Filtering

• It uses "similarities" to recommend items to the active user.
• It is a prominent, well-understood approach that utilizes various algorithms across domains like movies and e-commerce.
• User-based CF finds similar users and recommends the items they liked.
• Item-based CF recommends items similar to those the active user frequently likes.
• CF input is a matrix of user-item ratings.
• CF output is a numerical prediction indicating the degree to which the active user will like an item.
• Top-N recommended items are provided in a list

User-Based Filtering (Basic Steps)

• Given an active user X and an item i not yet seen by X.
• Find users that also liked what X liked in the past
• Average ratings predict how much X will like item i.
• This is done for all items X hasn't seen, recommending the best-rated.
• Find k users who are the nearest neighbors.
• User-based nearest neighbor collaborative filtering.

User-Based Filtering Example

• A matrix of users and their ratings for items, with User 1 being the active user.
• The main challenge is to predict the rating of User 1 for Item 5.
• Consider issues like measuring similarity, determining neighbor count, and generating predictions from neighbor ratings.

Measuring User Similarity

• Similarity is calculated as a measure of "anti-distance".
• Similarity is the inverse of distance.
• Similarity = 1 – Distance

Similarity Measures

• Euclidean
• Jaccard
• Cosine
• Adjusted cosine,
• Raw cosine
• Pearson correlation.
• Euclidean distance is determined between two vectors v1 = (3, 10) and v2 = (7, 13).
• Straight-line distance: d = √((x2 - x1)² + (y2 - y1)²) which simplifies to d = √((7-3)² + (13 – 10)²) = 5.
• Euclidean distance is found between User 1 and all other users to find k nearest neighbors.
• When Euclidean or Manhattan distance cannot correctly detect patterns, cosine distance, or similarity, is another measure that can be used.
• CosineSim = Cos(0)
• Cosine similarity calculates: Σ (AᵢBᵢ) / √Σ(Aᵢ²) √Σ(Bᵢ²).

Pearson Correlation Coefficient (r)

• It measures both magnitude and orientation between data points, between -1 and 1
  • -1: strong negative correlation
  • 0: no correlation
  • 1: strong positive correlation
• Pearson Correlation Coefficient calculation: r= Σ((xi – x)(yi – ỳ) / √( Σ(xi – x)² Σ(yi – ỳ)²)
• Having found the most similar users to active users, the next step is to predict the active user's rating
• Various prediction functions include the average of neighbor ratings.

User-Based Filtering Prediction

• R15 calculation =(3*0.85)+(4*0.70) / |0.85|+|0.70| = 3.45, where R15 ≈ 3
• Pearson Correlation Coefficient and k = 2 nearest neighbors.
• Predicted rating of User 1 is approximately 3.
• A key problem with Pearson Correlation Coefficient is the underlying assumption that users dislike what they rated below average.
• This assumption is often false.
• The correlation flattens in cases of uniformly distributed ratings.

Mean Centered Prediction Function

• A mean-centered prediction function required.
• Consider User 3 and their ratings for unseen Item 1 and Item 6 to determine the top-rated item.
• Ratings are predicted without mean-centering and result in User 3 more likely than average to enjoy both Item 1 and Item 6,
• A mean-centered prediction function removes bias.
• Ru = ra + Σb∈n sim(a, b) * (rb,p - rb) / Σb ∈n sim(a, b)
• Final predicted ratings with mean-centered equations = 3.35 for Item 1 and 0.86 for Item 6.
• Conclusion: item 3 still appears to be the most liked item by User 3, and item 6 is now clearly the least liked item by User 3.

Item-Based Collaborative Filtering.

• The idea is the same as user-based except using item similarity, and not other user's similarities, to predict ratings.

• Item-based is more stable than user based.

• For User 3, predict ratings for Item 1 and Item 6

• Use Adjusted Cosine similarity

• It is Cosine similarity that is mean-adjusted

• Sim(a,b)= Σ (ru,a – ru )(ru,b – ru) / √(Σ(ru,a – ru )² Σ(ru,b – ru )²)

• Adjusted Cosine(I1, I3) = (1.5*1.5)+(-1.5*-0.5)+(-1*-1) / √1.5²+(-1.5)²+(-1)². √1.5²+(-0.5)²+(-1)²

• Similarity of I1 is calculated with all other items

• the R31 equation is: (3*0.735)+(3*0.912) / |0.735|+|0.912|=3

Collaborative Filtering Vs Classification

• Filtering lacks a distinction between dependent/independent variables, unlike typical classification.
• Collaborative Filtering resembles a missing value analysis with a larger matrix.

Improving CF

• Significance weighting increases reliability.
• The reliability of any similarity function sim(u, v) between two users u and v is often affected by the number of common ratings between u and v i.e. (Iu ∩ Iv)
• If the two users only have a small number of ratings in common, the similarity function sim(u, v) should include a discount factor to de-emphasize the importance of that particular user pair
• This method is known as Significance Weighting.
• The discount factor kicks in when the number of common ratings between the two users is less than a particular threshold β.
• DiscountSim(u, v) = Sim(u, v) * min{(Iu∩Iv), β} / β
• Iu∩Iv = common ratings between u/v
• Sim(u,v) original similarity score.
• Beta is the threshold value.

User-Based Pros

• More diverse recommendations
• It is better if the number of users us smaller than the number of items

User-Based Cons

• Generally not as stable as user preferences change quickly
• Cannot offer in-depth analysis on individual user

Item-Based Pros

• More accurate recommendations
• Better if the number of items is larger than the number of users
• More stable
• Can provide in-depth analysis

Item-Based Cons

• Prone to shilling attacks (malicious user degrading an item)
• Provides less diversity

Collaborative Filtering Issues

• Serendipity: Expand the user’s taste into neighboring areas -Cold Start: Using collaborative filtering without initial data
• Long Tail: Only rating popular items
• Scaling: Collaborative filtering requires a lot of computational operations

Recommender Systems

• These Can be Memory-based or Model-based
• Memory-based systems use entire data every time
• User-based Collaborative Filtering
• Model-based systems use the data once and can predict without needing the entire data each time
• Item-based Collaborative Filtering
• Content-based Recommender System