User Profiling: Collaborative Filtering

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User Profiling Collaborative Filtering

• Miha Grcar,
• JSI
• October 2004

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User Profiling

• User profiling constructing a model of a user
• Goal without any effort from the user
• The profile is machine readable
• The profile reflects the users interests
• Two profiles can be compared to determine the
  degree of similarity in interests of two users
• Long-term, short-term interests

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Collaborative Filtering

• Goal recommend items of interest to the active
  user / try to predict the users rating of an
  item
• Idea consult other users (explore their
  profiles)
• A simple example we want to predict how much we
  will like the movie Beautiful Mind
• Naïve approach look at its average rating at
  IMDb.com (already a collaborative approach)
• Better approach ask a friend who is considered
  to have a similar taste (true collaborative
  filtering)

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The k Nearest Neighbors Approach

• Define the similarity measure in order to be able
  to compare two user profiles
• To the active user, find k most similar users
  that have rated the item in question
• Predict the users rating of the item by
  calculating the weighted1 average of the ratings
  given to the item by other users
• ????
• 1Weights are usually the similarity values.
• 2 fundamental problems
• Sparsity of the data
• Scalability problem

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Similarity Measures

• Cosine similarity
• Used in information retrieval
• Pearson correlation coefficient
• Used in statistics to evaluate the degree of
  linear relationship between two variables

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Weights

• Weight is proportional to similarity value
• Confidence in computed weights
• many overlapping values?? high
• few overlapping values?? low
• Weights amplification reward weights closer to 1
  and punish those closer to 0
• Inverse user frequency universally liked items
  are less relevant for predictions
• (log n / nj)

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The Sparsity Problem

• Many missing values in feature vectors
• Solving the sparsity problem
• Default rating
• Using content
• Dimensionality reduction techniques also
  counter the scalability issue!
• Simple approaches
• Remove users with low support
• Random sampling
• More advanced
• Latent Semantic Analysis (LSA)
• Probabilistic LSA (pLSA)

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Latent Semantic Analysis (LSA)

• On the basis of Singular Value Decomposition
  (SVD)
• M U?VT ? M U?VT
• M the user-item matrix
• ? the diagonal matrix of the singular values of
  M
• U, V two unitary matrices

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Probabilistic Latent Semantic Analysis (pLSA)

• On the basis of LSA (SVD)
• Observation pair (u, i)
• P(u, i) P(z)P(u z)P(i z) z latent
  variable
• P(u, i) ? P(i u)
• Incorporating a rating value
• P(u, i, r) ? P(i, r u)
• Relation to LSA (SVD)
• M U?VT, ui,k P(ui zk),??k,k P(zk), vj,k
  P(ij zk)
• M U?VT ? M U?VT

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CF as a Classification Task

• Classes different rating scores
• For each user we train a separate classifier
• Train set feature vectors representing items the
  user already rated the users rating given
  class label
• Test set feature vectors representing items the
  user did not rate yet classification
  prediction of the users rating of the item
• A problem with the sparsity of the data
• Possible solution representing one user with
  many instances

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Item-based CF

• First compute item-to-item similarities
• To predict user us rating of item i, compute a
  weighted average of k most similar items to item
  i that u already rated
• User-user similarity measures can be applied to
  compute item-item similarities

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• Thank you.