R. Lempel and S. Moran. Rank Stability and Rank Similarity of Web Link-Based Ranking Algorithms. Technical Report CS-2001-22, Technion - Israel Institute of Technology, 2001.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....all the weight to shift from C 1 to C 2 , and leaving the nodes in C 1 with zero weight. It follows that the two algorithms are neither stable nor rank stable. 2 The proof of Proposition 5 makes use of a disconnected graph in order to establish the instability of the algorithms. Lempel and Moran [16] have recently proved that the Kleinberg algorithm can also be shown to be rank unstable on an authority connected graph. Proposition 6 The SALSA algorithm, is neither stable, nor rank stable Proof: We first establish the rank instability of the SALSA algorithm. The example is similar to that ....

....and it would be interesting to know if other algorithms can be axiomatically characterized. In our work all the examples for instability are on disconnected graphs. It would be interesting to examine if instability can be proven for the class of connected graphs. The proof by Lempel and Moran [16] for the rank instability of Kleinberg algorithm, is the first step towards this direction. Recent work has shown that stability is tightly connected with the spectral properties of the underlying graph [18, 19, 3, 1] This seems a promising direction for proving stability results. 22 10 ....

R. Lempel and S. Moran. Rank Stability and Rank Similarity of Web Link-Based Ranking Algorithms. Technical Report CS-2001-22, Technion - Israel Institute of Technology, 2001.

....follows immediately from the definition of the SALSA algorithm and the definition of the authority connected class of graphs. Lemma 2 The SALSA algorithm is rank equivalent and similar to the INDEGREE algorithm on the class of authority connected graphs n . In a recent work, Lempel and Moran [35] showed that the HITS, INDEGREE (SALSA) and PAGERANK algorithms are not weakly rank similar on the class of authority connected graphs, n . 4.5 Stability In the previous section, we examined the similarity of two different algorithms on the same graph G. In this section, we are interested in ....

....We capture this requirement by the definition of stability. The notion of stability has been independently considered (but not explicitly defined) in a number of different papers [39, 40, 3, 1] For the definition of stability, we will use some of the terminology employed by Lempel and Moran [35]. n be a class of graphs, and let G = P, E) and G # = P, E # ) be two graphs in n . We define the link distance d # between graphs G and G # as follows. d # (G, G # ) E # E # ) E E # ) That is, d # (G, G # ) is the minimum number of links that we need to add and or remove ....

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R. Lempel and S. Moran. Rank stability and rank similarity of web link-based ranking algorithms. Technical Report CS-2001-22, Technion - Israel Institute of Technology, 2001.

....is a graph G such that the corresponding graph GB consists of a single connected component. We now present the following results. All proofs appear in [17] PROPOSITION 2. The MAX algorithm is unstable, and rank unstable on . Furthermore, in the counter example presented by Lempel and Moran [14] for the rank instability of HITS on N the MAX algorithm produces the same ranking as the HITS algorithm. Therefore, we have the following proposition. PROPOSITION 3. The MAX algorithm is rank unstable on N . We also study the similarity of the MAX algorithm with HITS and IN DEGREE ....

R. Lempel and S. Moran. Rank Stability and Rank Similarity of Web Link-Based Ranking Algorithms. Technical Report CS-2001-22, Technion - Israel Institute of Technology, 2001.

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