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Stochastic Approach for Link Structure Analysis (SALSA)

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Stochastic Approach for Link Structure Analysis (SALSA). Presented by Adam Simkins. SALSA. Created by Lempel Moran in 2000 Combination of HITS and PageRank. SALSA’s similarities to HITS and PageRank. SALSA uses authority and hub score

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salsa
SALSA
  • Created by Lempel Moran in 2000
  • Combination of HITS and PageRank
salsa s similarities to hits and pagerank
SALSA’s similarities to HITS and PageRank
  • SALSA uses authority and hub score
  • SALSA creates a neighborhood graph using authority and hub pages and links
salsa s differences between hits and pagerank
SALSA’s differences between HITS and PageRank
  • The SALSA method create a bipartite graph of the authority and hub pages in the neighborhood graph.
  • One set contains hub pages
  • One set contains authority pages
  • Each page may be located in both sets
markov chains
Markov Chains
  • Two matrices formed from bipartite graph G
  • A hub Markov chain with matrix H
  • An authority Markov chain with matrix A
where does salsa fit in
Where does SALSA fit in?
  • Matrices H and A can be derived from the adjacency matrix L used in the HITS and PageRank methods
  • HITS used unweighted matrix L
  • PageRank uses a row weighted version of matrix L
  • SALSA uses both row and column weighting
how are h and a computed
How are H and A computed?
  • Let Lrbe L with each nonzero row divided by its row sum
  • let Lcbe L with each nonzero column divided by its column sum
slide11
H, SALSA’s hub matrix, consists of the nonzero rows and columns of LrLcT
  • A, SALSA’s authority matrix,consists of the nonzero rows and columns of LcTLr
eigenvectors
Eigenvectors
  • Av = λv
  • vTA = λ vT
  • Numerically: Power Method
the power method
The Power Method
  • Xk+1 = AXk
  • Xk+1T = XkTA
  • Converges to the dominant eigenvector

( λ = 1).

the power method16
The Power Method
  • Matrices H and A must be irreducible for the power method to converge to a unique eigenvector given any starting value
  • If our neighborhood graph G is connected, then both H and A are irreducible
  • If G is not connected, then performing the power method on H and A will not result in the convergence to a unique dominant eigenvector
our graph is not connected
Our Graph is not connected!
  • In our example it is clear to see that the graph is not connected as page 2 in the hub set is only connected to page 1 in the authority set and vice versa.
  • H and A are reducible and therefore contain multiple irreducible connected components
connected components
Connected Components
  • H contains two connected components, C = {2} and D = {1, 3, 6, 10}
  • A contains two connected components, E = {1} and F = {3, 5, 6}
cutting and pasting part i
Cutting and Pasting. Part I
  • We can now perform the power method on each component for H and A
cutting and pasting part ii
Cutting and Pasting. Part II
  • We can now paste the two components together for each matrix
  • We must multiply each entry in the vector by its appropriate weight
slide22

H:

A:

strengths and weaknesses
Strengths and Weaknesses
  • Not affected as much my topic drift like HITS
  • It gives authority and hub scores.
  • Handles spamming better than HITS, but not near as good as PageRank
  • query dependence
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