A seminorm regularized alternating least squares algorithm for canonical tensor decomposition

Chen, Yannan; Sun, Wei; Xi, Min; Yuan, Jinyun

doi:10.1016/j.cam.2018.05.046

Cited by 3 publications

(3 citation statements)

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“…Then, with a similar argument for the proofs of Theorems 4.1 and 4.4, Lemma 4.8 and Theorem 4.9 of [6], we have Theorem 4.2. Before stating the theorem, we first state the definition of the well-known KL inequality [6]. Definition 4.1 Let f : U → , where U ⊆ N is an open set, be an analytic function.…”

Section: Convergence Analysis Of Algorithmmentioning

confidence: 65%

“…Note that as we set λ > 0, our algorithm is not an ALS method, but a modified ALS method. An argument following Lemma 4.2 of [6] justifies this.…”

Section: Convergence Analysis Of Algorithmmentioning

confidence: 75%

“…Our algorithm is closer to the seminorm regularized alternating least squares (SRALS) algorithm for CP tensor decomposition presented in [6]. There are two differences between our algorithm and the SRALS algorithm.…”

Section: Convergence Analysis Of Algorithmmentioning

confidence: 91%

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Triple Decomposition and Tensor Recovery of Third Order Tensors

Chen

Bakshi

et al. 2020

Preprint

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In this paper, we introduce a new tensor decomposition for third order tensors, which decomposes a third order tensor to three third order low rank tensors in a balanced way. We call such a decomposition the triple decomposition, and the corresponding rank the triple rank. For a third order tensor, its CP decomposition can be regarded as a special case of its triple decomposition. The triple rank of a third order tensor is not greater than the middle value of the Tucker rank, and is strictly less than the middle value of the Tucker rank for an essential class of examples. These indicate that practical data can be approximated by low rank triple decomposition as long as it can be approximated by low rank CP or Tucker decomposition. This theoretical discovery is confirmed numerically. Numerical tests show that third order tensor data from practical applications such as internet traffic and video image are of low triple ranks. A tensor recovery method based on low rank triple decomposition is proposed. Its convergence and convergence rate are established. Numerical experiments confirm the efficiency of this method.

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Section: Convergence Analysis Of Algorithmmentioning

confidence: 65%

“…Note that as we set λ > 0, our algorithm is not an ALS method, but a modified ALS method. An argument following Lemma 4.2 of [6] justifies this.…”

Section: Convergence Analysis Of Algorithmmentioning

confidence: 75%