12,905 research outputs found
Photograph indexing and retrieval using star-graphs
International audienceWe present in this paper a relational approach for indexing and retrieving photographs from a collection. Instead of using simple keywords as an indexing language, we propose to use star-graphs as document descriptors. A star-graph is a conceptual graph that contains a single relation, with some concepts linked to it. They are elementary pieces of information describing combinations of concepts. We use star-graphs as descriptors - or index terms - for image content representation. This allows for relational indexing and expression of complex user needs, in comparison to classical text retrieval, where simple keywords are generally used as document descriptors. We present a document representation model, a weighting scheme for star-graphs inspired by the tf.idf used in text retrieval. We have applied our model to image retrieval, and show the system evaluation results
The Total Acquisition Number of the Randomly Weighted Path
There exists a significant body of work on determining the acquisition number
of various graphs when the vertices of those graphs are each initially
assigned a unit weight. We determine properties of the acquisition number of
the path, star, complete, complete bipartite, cycle, and wheel graphs for
variations on this initial weighting scheme, with the majority of our work
focusing on the expected acquisition number of randomly weighted graphs. In
particular, we bound the expected acquisition number of the
-path when distinguishable "units" of integral weight, or chips, are
randomly distributed across its vertices between and . With
computer support, we improve it by showing that lies between
and . We then use subadditivity to show that the limiting
ratio exists, and simulations reveal more exactly what the
limiting value equals. The Hoeffding-Azuma inequality is used to prove that the
acquisition number is tightly concentrated around its expected value.
Additionally, in a different context, we offer a non-optimal acquisition
protocol algorithm for the randomly weighted path and exactly compute the
expected size of the resultant residual set.Comment: 19 page
On The Effect of Hyperedge Weights On Hypergraph Learning
Hypergraph is a powerful representation in several computer vision, machine
learning and pattern recognition problems. In the last decade, many researchers
have been keen to develop different hypergraph models. In contrast, no much
attention has been paid to the design of hyperedge weights. However, many
studies on pairwise graphs show that the choice of edge weight can
significantly influence the performances of such graph algorithms. We argue
that this also applies to hypegraphs. In this paper, we empirically discuss the
influence of hyperedge weight on hypegraph learning via proposing three novel
hyperedge weights from the perspectives of geometry, multivariate statistical
analysis and linear regression. Extensive experiments on ORL, COIL20, JAFFE,
Sheffield, Scene15 and Caltech256 databases verify our hypothesis. Similar to
graph learning, several representative hyperedge weighting schemes can be
concluded by our experimental studies. Moreover, the experiments also
demonstrate that the combinations of such weighting schemes and conventional
hypergraph models can get very promising classification and clustering
performances in comparison with some recent state-of-the-art algorithms
A concept of weighted connectivity on connected graphs
The introduction of a {0,1}-valued game associated to a connected graph allows us to assign to each node a value of weighted connectivity to the different solutions that for the cooperative games are obtained by means of the semivalues. The marginal contributions of each node to the coalitions differentiate an active connectivity from another reactive connectivity, according to whether the node is essential to obtain the connection or it is the obstacle for the connection between the nodes in the coalition. Diverse properties of this concept of connectivity can be derived.Peer ReviewedPostprint (author’s final draft
Gradient descent for sparse rank-one matrix completion for crowd-sourced aggregation of sparsely interacting workers
We consider worker skill estimation for the singlecoin
Dawid-Skene crowdsourcing model. In
practice skill-estimation is challenging because
worker assignments are sparse and irregular due
to the arbitrary, and uncontrolled availability of
workers. We formulate skill estimation as a
rank-one correlation-matrix completion problem,
where the observed components correspond to
observed label correlation between workers. We
show that the correlation matrix can be successfully
recovered and skills identifiable if and only
if the sampling matrix (observed components) is
irreducible and aperiodic. We then propose an
efficient gradient descent scheme and show that
skill estimates converges to the desired global optima
for such sampling matrices. Our proof is
original and the results are surprising in light of
the fact that even the weighted rank-one matrix
factorization problem is NP hard in general. Next
we derive sample complexity bounds for the noisy
case in terms of spectral properties of the signless
Laplacian of the sampling matrix. Our proposed
scheme achieves state-of-art performance on a
number of real-world datasets.Published versio
Beyond pairwise clustering
We consider the problem of clustering in domains where the affinity relations are not dyadic (pairwise), but rather triadic, tetradic or higher. The problem is an instance of the hypergraph partitioning problem. We propose a two-step algorithm for solving this problem. In the first step we use a novel scheme to approximate the hypergraph using a weighted graph. In the second step a spectral partitioning algorithm is used to partition the vertices of this graph. The algorithm is capable of handling hyperedges of all orders including order two, thus incorporating information of all orders simultaneously. We present a theoretical analysis that relates our algorithm to an existing hypergraph partitioning algorithm and explain the reasons for its superior performance. We report the performance of our algorithm on a variety of computer vision problems and compare it to several existing hypergraph partitioning algorithms
Crowdsourcing with Sparsely Interacting Workers
We consider estimation of worker skills from worker-task interaction data
(with unknown labels) for the single-coin crowd-sourcing binary classification
model in symmetric noise. We define the (worker) interaction graph whose nodes
are workers and an edge between two nodes indicates whether or not the two
workers participated in a common task. We show that skills are asymptotically
identifiable if and only if an appropriate limiting version of the interaction
graph is irreducible and has odd-cycles. We then formulate a weighted rank-one
optimization problem to estimate skills based on observations on an
irreducible, aperiodic interaction graph. We propose a gradient descent scheme
and show that for such interaction graphs estimates converge asymptotically to
the global minimum. We characterize noise robustness of the gradient scheme in
terms of spectral properties of signless Laplacians of the interaction graph.
We then demonstrate that a plug-in estimator based on the estimated skills
achieves state-of-art performance on a number of real-world datasets. Our
results have implications for rank-one matrix completion problem in that
gradient descent can provably recover rank-one matrices based on
off-diagonal observations of a connected graph with a single odd-cycle
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