High Order Random Walks: Beyond Spectral Gap
نویسندگان
چکیده
منابع مشابه
Spectral solution of delayed random walks.
We develop a spectral method for computing the probability density function for delayed random walks; for such problems, the method is exact to machine precision and faster than existing approaches. In conjunction with a step function approximation and the weak Euler-Maruyama discretization, the spectral method can be applied to nonlinear stochastic delay differential equations (SDDE). In essen...
متن کاملA Random Walks View of Spectral Segmentation
We present a new view of clustering and segmentation by pairwise similarities. We interpret the similarities as edge ows in a Markov random walk and study the eigenvalues and eigenvectors of the walk's transition matrix. This view shows that spectral methods for clustering and segmentation have a probabilistic foundation. We prove that the Normalized Cut method arises naturally from our framewo...
متن کاملGap Amplification for Small-Set Expansion via Random Walks
In this work, we achieve gap amplification for the Small-Set Expansion problem. Specifically, we show that an instance of the Small-Set Expansion Problem with completeness ε and soundness 12 is at least as difficult as Small-Set Expansion with completeness ε and soundness f (ε), for any function f (ε) which grows faster than √ ε. We achieve this amplification via random walks – the output graph...
متن کاملA Random Walks View of Spectral Segmentation , by Marina Meila
Thus, NCut is small when a partitioning of the graph produces two partitions that are both high in volume, containing many vertices with a high sum of similarities to other vertices, but where the sum of the similarities between vertices in different partitions is small. The NCut problem is to find a partition of the graph which minimizes the NCut criterion. Minimizing the NCut for a graph, how...
متن کاملNon-parametric resampling of random walks for spectral network clustering
Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to replicate structural features of complex networks based on the non-parametric resampling of the transition matrix associated with an unbiased random walk on the g...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Combinatorica
سال: 2020
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-019-3847-0