Evolving network representation learning based on random walks

Smooth Representation Clustering Based on Kernelized Random Walks

Random Walks on Evolving Graphs with Recurring Topologies

In this paper we consider dynamic networks that can change over time. Often, such networks have a repetitive pattern despite constant and otherwise unpredictable changes. Based on this observation, we introduce the notion of a ρ-recurring family of a dynamic network, which has the property that the dynamic network frequently contains a graph in the family, where frequently means at a rate 0<ρ≤1...

Burau Representation and Random Walks Onstring

Using a probabilistic interpretation of the Burau representation of the braid group ooered by Vaughan Jones, we generalize the Burau representation to a representation of the semigroup of string links. This representation is determined by a linear system, and is dominated by nite type string link invariants. For positive string links, the representation matrix can be interpreted as the transiti...

A Representation for Non-colliding Random Walks

Let D0(R+ ) denote the space of cadlag paths f : R+ → R with f(0) = 0. For f, g ∈ D0(R+ ), define f ⊗ g ∈ D0(R+ ) and f g ∈ D0(R+ ) by (f ⊗ g)(t) = inf 0≤s≤t [f(s) + g(t) − g(s)], and (f g)(t) = sup 0≤s≤t [f(s) + g(t) − g(s)]. Unless otherwise deleniated by parentheses, the default order of operations is from left to right; for example, when we write f ⊗ g ⊗ h, we mean (f ⊗ g) ⊗ h. Define a seq...

Learning Segmentation by Random Walks

The context here is image segmentation because it was in this domain that spectral clustering was introduced by Shi and Malik in 2000. Meila and Shi provide a random-walk interpretation of the spectral clustering algorithm, and then use a transition probability matrix to create a model which learns to segment images based on pixel intensity (which they call “edge strength”) and “co-circularity”...