Dr. Damien Fay. - University of Cambridge

More documents

Recommendations

Info

Background theory. A random walk cycle: the probability of starting at a node taking a path of length N and returning to the original node. Several alternative 3-cycles available. The N-cycles are a measure of the local connectivity of a node.
Theory: random walk cycles. L G=I −D −1 /2 −1 /2 AD Defining the matrix on the right as B: B=D −1 /2 −1 /2 AD The elements of B may be expressed in terms of degrees and the adjacency matrix as: B i , j = A i , j d i d j (B N ) i,j is the sum of products of all paths of length N starting at node i and ending at node j As 1-λ i are the eigenvalues of B : ∑ i 1− i N =tr B N We defining a random walk cycle to be a random walk of length N that starts and end at the same node (repeats included). This may be expressed in terms of B by noting : A i , j Bi , j B j , k ... Bl ,i= d i d j A j ,k d j d k ... A l ,i 1 = d l d d i i d j ... dk
Page 1 and 2: The weighted spectral distribution;
Page 3 and 4: A metric for graph distance. Both g
Page 5: Background theory. A random walk cy
Page 9 and 10: Background theory. A random walk cy
Page 11 and 12: Theory: metric definition. Finally
Page 13 and 14: WSD taken over 51 bins. WSD example
Page 15 and 16: Normalised Laplacian eigenvectors.
Page 17 and 18: WSD example The effect is to move t
Page 19 and 20: Random Projection. Random projectio
Page 21 and 22: Given ● matrix A = M×K, Multi-di
Page 23 and 24: example
Page 25 and 26: Internet AS topology models We comp
Page 27 and 28: Application 1: Tuning topology gene
Page 29 and 30: A 3-D view and example of speeding
Page 31 and 32: Application 2: Tracking evolution o
Page 33 and 34: Application 3: Discriminating betwe
Page 35 and 36: CAIDA data* Application 4: Network
Page 37 and 38: Example: MP2P
Page 39 and 40: Result using random projection.
Page 41 and 42: From a different angle.
Page 43 and 44: Application 5: The Orbis topology g
Page 45 and 46: The Orbis topology generator. Conne
Page 47 and 48: Orbis: results An AB model with 500
Page 49 and 50: Application 6: Facial expression re
Page 51 and 52: Resized image. ●
Page 53 and 54: Graph construction. ●
Page 55 and 56: Weighted graph (face 1). ●
Page 57 and 58:
WSD. ●
Page 59 and 60:
Quadtree All images, overview. Grap
Page 61 and 62:
➢ Only 5 subjects shown for clari
Page 63:
Questions ? Fay, D. , Haddadi, H.,
show all

Dr. Damien Fay. - University of Cambridge

Create successful ePaper yourself

Delete template?

Save as template?