3,178 research outputs found
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
Exploring multimodal data fusion through joint decompositions with flexible couplings
A Bayesian framework is proposed to define flexible coupling models for joint
tensor decompositions of multiple data sets. Under this framework, a natural
formulation of the data fusion problem is to cast it in terms of a joint
maximum a posteriori (MAP) estimator. Data driven scenarios of joint posterior
distributions are provided, including general Gaussian priors and non Gaussian
coupling priors. We present and discuss implementation issues of algorithms
used to obtain the joint MAP estimator. We also show how this framework can be
adapted to tackle the problem of joint decompositions of large datasets. In the
case of a conditional Gaussian coupling with a linear transformation, we give
theoretical bounds on the data fusion performance using the Bayesian Cramer-Rao
bound. Simulations are reported for hybrid coupling models ranging from simple
additive Gaussian models, to Gamma-type models with positive variables and to
the coupling of data sets which are inherently of different size due to
different resolution of the measurement devices.Comment: 15 pages, 7 figures, revised versio
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