Data point Neighborhood approach
Make data pts vs data pts matrix which measures similarities; filled using labels from various, usually similar, viewpoints. Thence predict label from target viewpoint. Eg: Amazon: ‘others who bought this also bought that’.
Collaborative filtering
Latent factor approach
Assume small number of latent random variables, which combine together to form various view points and data points, cause the labels.
Low rank factorization
Let values of latent RV behind data pt j be \(v_{j}\), behind viewpoint i be \(u_{i}\); then get \(Y_{i,j} = u_{i}^{T}v_{j}\). Want to have few random variables, so want \(Y = U^{T}V; U \in R^{q \times N}; V \in R^{q \times D}\), a low rank factorization of Y. Thence fill missing values.
Can use SVD: finds best rank \(k\) solution to \(\norm{Y - (U\SW )V^{*}}_F\). instead want to find \(\norm{W \kron (Y - U^{T}V)}\), where W is mask matrix to indicate known values in Y.
Association rule mining
Look at co-occurances of various items. Eg: Walmart purchases.
Very slow.