Results 1  10
of
290
Scalable knn graph construction for visual descriptors
 In CVPR
"... The kNN graph has played a central role in increasingly popular datadriven techniques for various learning and vision tasks; yet, finding an efficient and effective way to construct kNN graphs remains a challenge, especially for largescale highdimensional data. In this paper, we propose a new ..."
Abstract

Cited by 15 (4 self)
 Add to MetaCart
approach to construct approximate kNN graphs with emphasis in: efficiency and accuracy. We hierarchically and randomly divide the data points into subsets and build an exact neighborhood graph over each subset, achieving a base approximate neighborhood graph; we then repeat this process for several
Slice sampling
 Annals of Statistics
, 2000
"... Abstract. Markov chain sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample from a distribution by sampling uniformly from the region under the plot of its density function. A Markov chain th ..."
Abstract

Cited by 305 (5 self)
 Add to MetaCart
to each variable, based on the local properties of the density function. More ambitiously, such methods could potentially allow the sampling to adapt to dependencies between variables by constructing local quadratic approximations. Another approach is to improve sampling efficiency by suppressing random
Randomwalk computation of similarities between nodes of a graph, with application to collaborative recommendation
 IEEE Transactions on Knowledge and Data Engineering
"... ABSTRACT This work presents a new perspective on characterizing the similarity between elements of a database or, more generally, nodes of a weighted, undirected, graph. It is based on a Markovchain model of random walk through the database. More precisely, we compute quantities (the average commu ..."
Abstract

Cited by 194 (19 self)
 Add to MetaCart
ABSTRACT This work presents a new perspective on characterizing the similarity between elements of a database or, more generally, nodes of a weighted, undirected, graph. It is based on a Markovchain model of random walk through the database. More precisely, we compute quantities (the average
Random Walks and Graph Homomorphisms
"... In this report (whose basic approach is based on [12]) we introduce a general idea which gives rise to some necessary conditions for the existence of graph homomorphisms (directed and undirected), which is mainly based on available comparison techniques for Markov chains. We focus on the nite st ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
In this report (whose basic approach is based on [12]) we introduce a general idea which gives rise to some necessary conditions for the existence of graph homomorphisms (directed and undirected), which is mainly based on available comparison techniques for Markov chains. We focus on the nite
Diffusion maps and coarsegraining: A unified framework for dimensionality reduction, graph partitioning and data set parameterization
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2006
"... We provide evidence that nonlinear dimensionality reduction, clustering and data set parameterization can be solved within one and the same framework. The main idea is to define a system of coordinates with an explicit metric that reflects the connectivity of a given data set and that is robust to ..."
Abstract

Cited by 158 (5 self)
 Add to MetaCart
to noise. Our construction, which is based on a Markov random walk on the data, offers a general scheme of simultaneously reorganizing and subsampling graphs and arbitrarily shaped data sets in high dimensions using intrinsic geometry. We show that clustering in embedding spaces is equivalent
Graph construction and bmatching for semisupervised learning
 In International Conference on Machine Learning
"... Graph based semisupervised learning (SSL) methods play an increasingly important role in practical machine learning systems. A crucial step in graph based SSL methods is the conversion of data into a weighted graph. However, most of the SSL literature focuses on developing label inference algorithm ..."
Abstract

Cited by 65 (13 self)
 Add to MetaCart
) method, the Gaussian Random Field (GRF) method, the Graph Transduction via Alternating Minimization (GTAM) method as well as other techniques. Several approaches for graph construction, sparsification and weighting are explored including the popular knearest neighbors method (kNN) and the b
Homogeneous Superpixels from Markov Random Walks
 1 PAPER SPECIAL SECTION ON MACHINE VISION AND ITS APPLICATIONS
, 2011
"... This paper presents a novel algorithm to generate homogeneous superpixels from Markov random walks. We exploit Markov clustering (MCL) as the methodology, a generic graph clustering method based on stochastic flow circulation. In particular, we introduce a graph pruning strategy called compact prun ..."
Abstract
 Add to MetaCart
This paper presents a novel algorithm to generate homogeneous superpixels from Markov random walks. We exploit Markov clustering (MCL) as the methodology, a generic graph clustering method based on stochastic flow circulation. In particular, we introduce a graph pruning strategy called compact
SPECTRUM OF MARKOV GENERATORS ON SPARSE RANDOM GRAPHS
, 2014
"... We investigate the spectrum of the infinitesimal generator of the continuous time random walk on a randomly weighted oriented graph. This is the nonHermitian random n×n matrix L defined by Ljk = Xjk if k = j and Ljj = − ∑ k=j Ljk, where (Xjk)j=k are i.i.d. random weights. Under mild assumptions ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
We investigate the spectrum of the infinitesimal generator of the continuous time random walk on a randomly weighted oriented graph. This is the nonHermitian random n×n matrix L defined by Ljk = Xjk if k = j and Ljj = − ∑ k=j Ljk, where (Xjk)j=k are i.i.d. random weights. Under mild
Random Walks on Sierpiński Graphs: Hyperbolicity and Stochastic Homogenization
, 2002
"... We introduce two new techniques to the analysis on fractals. One is based on the presentation of the fractal as the boundary of a countable Gromov hyperbolic graph, whereas the other one consists in taking all possible “backward” extensions of the above hyperbolic graph and considering them as the c ..."
Abstract

Cited by 17 (0 self)
 Add to MetaCart
We introduce two new techniques to the analysis on fractals. One is based on the presentation of the fractal as the boundary of a countable Gromov hyperbolic graph, whereas the other one consists in taking all possible “backward” extensions of the above hyperbolic graph and considering them
Markov Chains On Graphs And Brownian Motion.
"... . We consider random walks with small xed steps inside of edges of a graph G, prescribing a natural rule of probabilities of jumps over a vertex. We show that after an appropriate rescaling such random walks weakly converge to the natural Brownian motion on G constructed in [1]. 1. Introduction Th ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
. We consider random walks with small xed steps inside of edges of a graph G, prescribing a natural rule of probabilities of jumps over a vertex. We show that after an appropriate rescaling such random walks weakly converge to the natural Brownian motion on G constructed in [1]. 1. Introduction
Results 1  10
of
290