Dimensionality Reduction of SPD Data Based on Riemannian Manifold Tangent Spaces and Isometry

Gao, Wenxu; Ma, Zhengming; Gan, Weichao

doi:10.3390/e23091117

Cited by 3 publications

(1 citation statement)

References 39 publications

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“…Epochs were set to 150 and the batch size was 16. Loss function was identified using Contrastive Loss [16]. RMSprop was applied for stochastic optimization [17].…”

Section: Deep Learning and Testingmentioning

confidence: 99%

Deep Learning-Based Segmentation of Airway Morphology from Endobronchial Optical Coherence Tomography

et al. 2023

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Background: Manual measurement of endobronchial optical coherence tomography (EB-OCT) images means a heavy workload in the clinical practice, which can also introduce bias if the subjective opinions of doctors are involved. Objective: We aim to develop a convolutional neural network (CNN)-based EB-OCT image analysis algorithm to automatically identify and measure EB-OCT parameters of airway morphology. Methods: The ResUNet, MultiResUNet, and Siamese network were used for analyzing airway inner area (Ai), airway wall area (Aw), airway wall area percentage (Aw%), and airway bifurcate segmentation obtained from EB-OCT imaging, respectively. The accuracy of the automatic segmentations was verified by comparing with manual measurements. Results: Thirty-three patients who were diagnosed with asthma (n = 13), chronic obstructive pulmonary disease (COPD, n = 13), and normal airway (n = 7) were enrolled. EB-OCT was performed in RB9 segment (lateral basal segment of the right lower lobe), and a total of 17,820 OCT images were collected for CNN training, validation, and testing. After training, the Ai, Aw, and airway bifurcate were readily identified in both normal airway and airways of asthma and COPD. The ResUNet and the MultiResUNet resulted in a mean dice similarity coefficient of 0.97 and 0.95 for Ai and Aw segmentation. The accuracy Siamese network in identifying airway bifurcate was 96.6%. Bland-Altman analysis indicated there was a negligible bias between manual and CNN measurements for Ai (bias = −0.02 to 0.01, 95% CI = −0.12 to 0.14) and Aw% (bias = −0.06 to 0.12, 95% CI = −1.98 to 2.14). Conclusion: EB-OCT imaging in conjunction with ResUNet, MultiResUNet, and Siamese network could automatically measure normal and diseased airway structure with an accurate performance.

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“…Epochs were set to 150 and the batch size was 16. Loss function was identified using Contrastive Loss [16]. RMSprop was applied for stochastic optimization [17].…”

Section: Deep Learning and Testingmentioning

confidence: 99%

Deep Learning-Based Segmentation of Airway Morphology from Endobronchial Optical Coherence Tomography

et al. 2023

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Unsupervised manifold learning with polynomial mapping on symmetric positive definite matrices

2022

Information Sciences

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Reducing the Dimensionality of SPD Matrices with Neural Networks in BCI

Zhen

Zhao

et al. 2023

Mathematics

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In brain–computer interface (BCI)-based motor imagery, the symmetric positive definite (SPD) covariance matrices of electroencephalogram (EEG) signals with discriminative information features lie on a Riemannian manifold, which is currently attracting increasing attention. Under a Riemannian manifold perspective, we propose a non-linear dimensionality reduction algorithm based on neural networks to construct a more discriminative low-dimensional SPD manifold. To this end, we design a novel non-linear shrinkage layer to modify the extreme eigenvalues of the SPD matrix properly, then combine the traditional bilinear mapping to non-linearly reduce the dimensionality of SPD matrices from manifold to manifold. Further, we build the SPD manifold network on a Siamese architecture which can learn the similarity metric from the data. Subsequently, the effective signal classification method named minimum distance to Riemannian mean (MDRM) can be implemented directly on the low-dimensional manifold. Finally, a regularization layer is proposed to perform subject-to-subject transfer by exploiting the geometric relationships of multi-subject. Numerical experiments for synthetic data and EEG signal datasets indicate the effectiveness of the proposed manifold network.

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Dimensionality Reduction of SPD Data Based on Riemannian Manifold Tangent Spaces and Isometry

Cited by 3 publications

References 39 publications

Deep Learning-Based Segmentation of Airway Morphology from Endobronchial Optical Coherence Tomography

Deep Learning-Based Segmentation of Airway Morphology from Endobronchial Optical Coherence Tomography

Unsupervised manifold learning with polynomial mapping on symmetric positive definite matrices

Reducing the Dimensionality of SPD Matrices with Neural Networks in BCI

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