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 SALSA creates a neighborhood graph using authority and hub pages and links

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

Neighborhood Graph G

Bipartite Graph G of Neighborhood Graph N

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? 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? Let L r be L with each nonzero row divided by its row sum let L c be L with each nonzero column divided by its column sum

H, SALSA’s hub matrix, consists of the nonzero rows and columns of L r L c T A, SALSA’s authority matrix, consists of the nonzero rows and columns of L c T L r

Eigenvectors Av = λv v T A = λ v T Numerically: Power Method

The Power Method X k+1 = AX k X k+1 T = X k T A Converges to the dominant eigenvector ( λ = 1).

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! 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 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 We can now perform the power method on each component for H and A

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

H: A:

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

Thank You For Your Time!