13,481 research outputs found
Robust Temporally Coherent Laplacian Protrusion Segmentation of 3D Articulated Bodies
In motion analysis and understanding it is important to be able to fit a
suitable model or structure to the temporal series of observed data, in order
to describe motion patterns in a compact way, and to discriminate between them.
In an unsupervised context, i.e., no prior model of the moving object(s) is
available, such a structure has to be learned from the data in a bottom-up
fashion. In recent times, volumetric approaches in which the motion is captured
from a number of cameras and a voxel-set representation of the body is built
from the camera views, have gained ground due to attractive features such as
inherent view-invariance and robustness to occlusions. Automatic, unsupervised
segmentation of moving bodies along entire sequences, in a temporally-coherent
and robust way, has the potential to provide a means of constructing a
bottom-up model of the moving body, and track motion cues that may be later
exploited for motion classification. Spectral methods such as locally linear
embedding (LLE) can be useful in this context, as they preserve "protrusions",
i.e., high-curvature regions of the 3D volume, of articulated shapes, while
improving their separation in a lower dimensional space, making them in this
way easier to cluster. In this paper we therefore propose a spectral approach
to unsupervised and temporally-coherent body-protrusion segmentation along time
sequences. Volumetric shapes are clustered in an embedding space, clusters are
propagated in time to ensure coherence, and merged or split to accommodate
changes in the body's topology. Experiments on both synthetic and real
sequences of dense voxel-set data are shown. This supports the ability of the
proposed method to cluster body-parts consistently over time in a totally
unsupervised fashion, its robustness to sampling density and shape quality, and
its potential for bottom-up model constructionComment: 31 pages, 26 figure
Functional Factorial K-means Analysis
A new procedure for simultaneously finding the optimal cluster structure of
multivariate functional objects and finding the subspace to represent the
cluster structure is presented. The method is based on the -means criterion
for projected functional objects on a subspace in which a cluster structure
exists. An efficient alternating least-squares algorithm is described, and the
proposed method is extended to a regularized method for smoothness of weight
functions. To deal with the negative effect of the correlation of coefficient
matrix of the basis function expansion in the proposed algorithm, a two-step
approach to the proposed method is also described. Analyses of artificial and
real data demonstrate that the proposed method gives correct and interpretable
results compared with existing methods, the functional principal component
-means (FPCK) method and tandem clustering approach. It is also shown that
the proposed method can be considered complementary to FPCK.Comment: 39 pages, 17 figure
Dynamic Tensor Clustering
Dynamic tensor data are becoming prevalent in numerous applications. Existing
tensor clustering methods either fail to account for the dynamic nature of the
data, or are inapplicable to a general-order tensor. Also there is often a gap
between statistical guarantee and computational efficiency for existing tensor
clustering solutions. In this article, we aim to bridge this gap by proposing a
new dynamic tensor clustering method, which takes into account both sparsity
and fusion structures, and enjoys strong statistical guarantees as well as high
computational efficiency. Our proposal is based upon a new structured tensor
factorization that encourages both sparsity and smoothness in parameters along
the specified tensor modes. Computationally, we develop a highly efficient
optimization algorithm that benefits from substantial dimension reduction. In
theory, we first establish a non-asymptotic error bound for the estimator from
the structured tensor factorization. Built upon this error bound, we then
derive the rate of convergence of the estimated cluster centers, and show that
the estimated clusters recover the true cluster structures with a high
probability. Moreover, our proposed method can be naturally extended to
co-clustering of multiple modes of the tensor data. The efficacy of our
approach is illustrated via simulations and a brain dynamic functional
connectivity analysis from an Autism spectrum disorder study.Comment: Accepted at Journal of the American Statistical Associatio
A Bayesian approach to discrete object detection in astronomical datasets
A Bayesian approach is presented for detecting and characterising the signal
from discrete objects embedded in a diffuse background. The approach centres
around the evaluation of the posterior distribution for the parameters of the
discrete objects, given the observed data, and defines the
theoretically-optimal procedure for parametrised object detection. Two
alternative strategies are investigated: the simultaneous detection of all the
discrete objects in the dataset, and the iterative detection of objects. In
both cases, the parameter space characterising the object(s) is explored using
Markov-Chain Monte-Carlo sampling. For the iterative detection of objects,
another approach is to locate the global maximum of the posterior at each
iteration using a simulated annealing downhill simplex algorithm. The
techniques are applied to a two-dimensional toy problem consisting of Gaussian
objects embedded in uncorrelated pixel noise. A cosmological illustration of
the iterative approach is also presented, in which the thermal and kinetic
Sunyaev-Zel'dovich effects from clusters of galaxies are detected in microwave
maps dominated by emission from primordial cosmic microwave background
anisotropies.Comment: 20 pages, 12 figures, accepted by MNRAS; contains some additional
material in response to referee's comment
Learning with Clustering Structure
We study supervised learning problems using clustering constraints to impose
structure on either features or samples, seeking to help both prediction and
interpretation. The problem of clustering features arises naturally in text
classification for instance, to reduce dimensionality by grouping words
together and identify synonyms. The sample clustering problem on the other
hand, applies to multiclass problems where we are allowed to make multiple
predictions and the performance of the best answer is recorded. We derive a
unified optimization formulation highlighting the common structure of these
problems and produce algorithms whose core iteration complexity amounts to a
k-means clustering step, which can be approximated efficiently. We extend these
results to combine sparsity and clustering constraints, and develop a new
projection algorithm on the set of clustered sparse vectors. We prove
convergence of our algorithms on random instances, based on a union of
subspaces interpretation of the clustering structure. Finally, we test the
robustness of our methods on artificial data sets as well as real data
extracted from movie reviews.Comment: Completely rewritten. New convergence proofs in the clustered and
sparse clustered case. New projection algorithm on sparse clustered vector
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