Recommendation Systems, Dim Red, Page Rank

Latent Factors

Number of hidden factors (the hidden dimension r in UV decomp)

SVD

Produces three matrices:

USV^T.

To map to concept space, given input vector x, compute Vx.

Lower dimensioned original data matrix is US.

Collaborative Filtering

Two types: Item-item, User-user. Item item: for item i, find other similar items, estimate rating for item i based on ratings for similar items.

Basic Page Rank

At each iteration, given transition matrix M, we keep computing

v = Mv

We initialize v to all 1/N's (ie. randomly distribute crawlers)

Dead Ends & Spider Traps

Dead ends = no more exits

Spider traps = all exits go back to itself

Use teleport sets (can be all nodes, or 'relevant' sets).

v = (1-tp)Mv + tp

Transition Matrix

Given N nodes, this is an N x N matrix of probabilities (that is, how likely a crawler is to transition to new node).

Hubs & Authorities

Hubs - links to many authorities

Authorities - is liked to by many hubs

Hubbiness and Authority of each Page

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