barcodefontsoft.com

advanced material in .NET Assign barcode code39 in .NET advanced material

advanced material use none none integrated toattach none in none RM4SCC node 1 1 0 0 0. 0 1 0 1. 1 1 0 0. node 2 node 3 node 4 Figure 14.11. The d irected hyperlinks among Web pages can be represented using an adjacency matrix M: the entry Mi j is equal to 1 if there is a link from node i to node j ; otherwise, Mi j = 0.

. Hub and Authority U none none pdate Rules as Matrix Vector Multiplication. Let s consider the Hub Update Rule in terms of the notation we ve just de ned. For a node i, its hub score hi is updated to be the sum of aj over all nodes j to which i has an edge.

Note that these nodes j are precisely the ones for which Mij = 1. Thus, we can write the update rule as hi Mi1 a1 + Mi2 a2 + + Min an , (14.1).

where we use the no tation to mean that the quantity on the left-hand side is updated to become the quantity on the right-hand side. This is a correct way to write the update rule, since the values Mij as multipliers select out precisely the authority values that we wish to sum. But Equation (14.

1) corresponds exactly to the de nition of matrix-vector multiplication, so we can write it in the following equivalent way: h Ma. Figure 14.12 shows this for the example from Figure 14.

11: the authority scores (2, 6, 4, 3) lead to the hub scores (9, 7, 2, 4) via the Hub Update Rule. Indeed, this is an example of a general principle: if you re updating a collection of variables according to a rule that selects out certain ones to add up, you can often write this update rule as a matrix vector multiplication for a suitably chosen matrix and vector..

node 1 1 0 0 0. 0 1 0 1. 1 1 0 0. 2 6 4 3. node 2 7 2 4. node 3 node 4 Figure 14.12. By re presenting the link structure using an adjacency matrix, the Hub and Authority Update Rules become matrix-vector multiplication.

In this example, we show how multiplication by a vector of authority scores produces a new vector of hub scores.. link analysis and web search Specifying the Auth ority Update Rule in this style is strictly analogous, except that the scores ow in the other direction across the edges. That is, ai is updated to be the sum of hj over all nodes j that have an edge to i, so ai M1i h1 + M2i h2 + + Mni hn . (14.

2). This too correspond none none s to a matrix vector multiplication, but using a matrix where the entries have all been re ected so that the roles of rows and columns are interchanged. This can be speci ed using the transpose of the matrix M, denoted M T and de ned T by the property that the (i, j ) entry of M T is the (j, i) entry of M; that is, Mij = Mj i . Then Equation (14.

2) corresponds to the update rule a M T h. Unwinding the k-Step Hub Authority Computation. Thus far we have discussed a single application of each of the update rules.

What happens when we perform the k-step hub authority computation for some large value of k We start with initial vectors of authority and hub scores that we denote a 0 and h 0 , each of them equal to the vector whose coordinates are all 1. Now, let a k and h k denote the vectors of authority and hub scores after k applications of the Authority and then Hub Update Rules in order, as in Section 14.2.

If we simply follow the preceding formulas, we rst nd that a and h 1 = Ma.
Copyright © barcodefontsoft.com . All rights reserved.