Inverse Exit times ∗
نویسنده
چکیده
Normalized cut is a widely used measure of separation between clusters in a graph. In this paper we provide a novel probabilistic perspective on this measure. We show that for a partition of a graph into two weakly connected sets, V = A B, the multiway normalized cut is approximately MNcut ≈ 1/τA→B + 1/τB→A, where τA→B is the unidirectional characteristic exit time of a random walk from subset A to subset B. Using matrix perturbation theory, we show that this approximation is exact to first order in the connection strength between the two subsets A and B, and we derive an explicit bound for the approximation error. Our result implies that for a Markov chain composed of a reversible subset A that is weakly connected to an absorbing subset B, the easy-to-compute normalized cut measure is a reliable proxy for the chain’s spectral gap.
منابع مشابه
Reconstruction of a persistent random walk from exit time distributions
In this paper, we study the inverse problem of reconstructing the spatially dependent transition rate F (x) of a one-dimensional Broadwell process from exit time distributions. In such a process, an advecting particle is assumed to undergo transitions between states with constant positive (+v) and negative (−v) velocities. The goal is to reconstruct the transition rate function F (x) from the e...
متن کاملReconstructing the Transition Rate Function of a Broadwell Random Walk from Exit Times
In this paper, we utilize the layer stripping method, a method used in seismology by geophysicists, to study a stochastic inverse problem arising from a one-dimensional Broadwell process. The Broadwell process can be described as a random walk of a particle that transitions, with a spatially dependent flip rate, between two states associated with the same speed but with different signs of veloc...
متن کامل20 09 Production of short lived radioactive beams of radium
Short lived Ra isotopes have been produced at the TRIμP facility in inverse kinematics via the fusion-evaporation reaction Pb+C at 8 MeV/u. Isotopes are separated from other reaction products online using the TRIμP magnetic separator. The energetic radium (Ra) isotopes at the exit of the separator were converted into low energy ions with a thermal ionizer. Ra isotopes have been identified by ob...
متن کاملAttentional Theory Is a Viable Explanation of the Inverse Base Rate Effect: A Reply to Winman, Wennerholm, and Juslin (2003)
A. Winman, P. Wennerholm, and P. Juslin (2003) have admitted that J. K. Kruschke (2001a) cogently demonstrated the shortcomings of eliminative inference as an explanation of the inverse base rate effect, but they raise criticisms of Kruschke’s attentionally based explanation. First, Winman et al. pointed out that attentional shifting does not improve learning performance in Kruschke’s (1996) AD...
متن کامل3 On L 1 - distance between first exit times from two regions ∗ †
First exit times from regions and their dependence on variations of boundaries are discussed for diffusion processes. The paper presents an estimate of L1-distance between exit times from two regions via expectations of exit times. Abbreviated title: On L1-distance between first exit times It is known that first exit times from a region for smooth solutions of ordinary equations does not depend...
متن کاملExit time of turbulent signals: a way to detect the intermediate dissipative range.
The exit-time statistics of experimental turbulent data is analyzed. By looking at the exit-time moments (inverse structure functions) it is possible to have a direct measurement of scaling properties of the laminar statistics. It turns out that the inverse structure functions show a much more extended intermediate dissipative range than the structure functions, leading to the first clear evide...
متن کامل