Accelerating PARAFAC2 algorithms for non-negative complex tensor decomposition

Author(s):  
Huiwen Yu ◽  
Dillen Augustijn ◽  
Rasmus Bro
Author(s):  
Jonathan D. Hauenstein ◽  
Luke Oeding ◽  
Giorgio Ottaviani ◽  
Andrew J. Sommese

AbstractLetTbe a general complex tensor of format{(n_{1},\dots,n_{d})}. When the fraction{\prod_{i}n_{i}/[1+\sum_{i}(n_{i}-1)]}is an integer, and a natural inequality (called balancedness) is satisfied, it is expected thatThas finitely many minimal decomposition as a sum of decomposable tensors. We show how homotopy techniques allow us to find all the decompositions ofT, starting from a given one. Computationally, this gives a guess regarding the total number of such decompositions. This guess matches exactly with all cases previously known, and predicts several unknown cases. Some surprising experiments yielded two new cases of generic identifiability: formats{(3,4,5)}and{(2,2,2,3)}which have a unique decomposition as the sum of six and four decomposable tensors, respectively. We conjecture that these two cases together with the classically known matrix pencils are the only cases where generic identifiability holds, i.e., the onlyidentifiablecases. Building on the computational experiments, we use algebraic geometry to prove these two new cases are indeed generically identifiable.


Author(s):  
Ricardo Augusto Borsoi ◽  
Clemence Prevost ◽  
Konstantin Usevich ◽  
David Brie ◽  
Jose Carlos M. Bermudez ◽  
...  

Author(s):  
Xuewu Zhang ◽  
Yansheng Gong ◽  
Chen Qiao ◽  
Wenfeng Jing

AbstractThis article mainly focuses on the most common types of high-speed railways malfunctions in overhead contact systems, namely, unstressed droppers, foreign-body invasions, and pole number-plate malfunctions, to establish a deep-network detection model. By fusing the feature maps of the shallow and deep layers in the pretraining network, global and local features of the malfunction area are combined to enhance the network's ability of identifying small objects. Further, in order to share the fully connected layers of the pretraining network and reduce the complexity of the model, Tucker tensor decomposition is used to extract features from the fused-feature map. The operation greatly reduces training time. Through the detection of images collected on the Lanxin railway line, experiments result show that the proposed multiview Faster R-CNN based on tensor decomposition had lower miss probability and higher detection accuracy for the three types faults. Compared with object-detection methods YOLOv3, SSD, and the original Faster R-CNN, the average miss probability of the improved Faster R-CNN model in this paper is decreased by 37.83%, 51.27%, and 43.79%, respectively, and average detection accuracy is increased by 3.6%, 9.75%, and 5.9%, respectively.


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