Proceedings of the 2014 SIAM International Conference on Data Mining 2014
DOI: 10.1137/1.9781611973440.15
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DuSK: A Dual Structure-preserving Kernel for Supervised Tensor Learning with Applications to Neuroimages

Abstract: With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning community. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, however structural information within the tensors will be lost. In this paper, we introduce a new scheme to design struc… Show more

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Cited by 61 publications
(84 citation statements)
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References 19 publications
(42 reference statements)
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“…, m be a training set of instancelabeled pairs, X i ∈ R n 1 ×n 2 ×···×n N , and y i ∈ {−1, 1}. Given a tensor X i ∈ R n 1 ×n 2 ×···×n N , we assume that it may be mapped into a high dimensional tensor product feature space by a map function φ: X → φ(X) ∈ R h 1 ×h 2 ×···×h P , and then the optimization problem of tensor-based kernel learning may be written as [3]:…”
Section: Tensorial Kernel Functionmentioning
confidence: 99%
“…, m be a training set of instancelabeled pairs, X i ∈ R n 1 ×n 2 ×···×n N , and y i ∈ {−1, 1}. Given a tensor X i ∈ R n 1 ×n 2 ×···×n N , we assume that it may be mapped into a high dimensional tensor product feature space by a map function φ: X → φ(X) ∈ R h 1 ×h 2 ×···×h P , and then the optimization problem of tensor-based kernel learning may be written as [3]:…”
Section: Tensorial Kernel Functionmentioning
confidence: 99%
“…In [6,8], the neuroimage data are directly mined and represented as tensors to handle extremely high dimensionality within the data. In addition, many efforts have focused on mining important brain regions and estimating region/neuron connections [9,21,25].…”
Section: Related Workmentioning
confidence: 99%
“…The potential of mining the vast image data for the detection of alterations in neurological disorders has been demonstrated in many studies [3,8,15,16,19,24]. However, connectivities of brain regions are not investigated in these studies.…”
Section: Introductionmentioning
confidence: 99%
“…A common solution is to focus on the 3D spatial domain of the fMRI brain images [7,12]. For instance, in [12], the original 4D tensor of fMRI data is converted to a 3D tensor by averaging over the time dimension.…”
Section: Introductionmentioning
confidence: 99%
“…For instance, in [12], the original 4D tensor of fMRI data is converted to a 3D tensor by averaging over the time dimension. classification.…”
Section: Introductionmentioning
confidence: 99%