Mathematics

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16 pages, 1723 KiB

Open AccessCommunication

Fast Generalized Sliding Sinusoidal Transforms

by Vitaly Kober

Mathematics 2023, 11(18), 3829; https://doi.org/10.3390/math11183829 - 6 Sep 2023

Viewed by 1145

Discrete cosine and sine transforms closely approximate the Karhunen–Loeve transform for first-order Markov stationary signals with high and low correlation coefficients, respectively. Discrete sinusoidal transforms can be used in data compression, digital filtering, spectral analysis and pattern recognition. Short-time transforms based on discrete [...] Read more.

Discrete cosine and sine transforms closely approximate the Karhunen–Loeve transform for first-order Markov stationary signals with high and low correlation coefficients, respectively. Discrete sinusoidal transforms can be used in data compression, digital filtering, spectral analysis and pattern recognition. Short-time transforms based on discrete sinusoidal transforms are suitable for the adaptive processing and time–frequency analysis of quasi-stationary data. The generalized sliding discrete transform is a type of short-time transform, that is, a fixed-length windowed transform that slides over a signal with an arbitrary integer step. In this paper, eight fast algorithms for calculating various sliding sinusoidal transforms based on a generalized solution of a second-order linear nonhomogeneous difference equation and pruned discrete sine transforms are proposed. The performances of the algorithms in terms of computational complexity and execution time were compared with those of recursive sliding and fast discrete sinusoidal algorithms. The low complexity of the proposed algorithms resulted in significant time savings. Full article

(This article belongs to the Special Issue Deep Learning Algorithms in Computational Intelligence: Advances and Applications)

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14 pages, 1247 KiB

Open AccessFeature PaperArticle

EvolveNet: Evolving Networks by Learning Scale of Depth and Width

by Athul Shibu and Dong-Gyu Lee

Mathematics 2023, 11(16), 3611; https://doi.org/10.3390/math11163611 - 21 Aug 2023

Cited by 1 | Viewed by 1198

Abstract

Convolutional neural networks (CNNs) have shown decent performance in a variety of computer vision tasks. However, these network configurations are largely hand-crafted, which leads to inefficiency in the constructed network. Various other algorithms have been proposed to address this issue, but the inefficiencies [...] Read more.

Convolutional neural networks (CNNs) have shown decent performance in a variety of computer vision tasks. However, these network configurations are largely hand-crafted, which leads to inefficiency in the constructed network. Various other algorithms have been proposed to address this issue, but the inefficiencies resulting from human intervention have not been addressed. Our proposed EvolveNet algorithm is a task-agnostic evolutionary search algorithm that can find optimal depth and width scales automatically in an efficient way. The optimal configurations are not found using grid search, and are instead evolved from an existing network. This eliminates inefficiencies that emanate from hand-crafting, thus reducing the drop in accuracy. The proposed algorithm is a framework to search through a large search space of subnetworks until a suitable configuration is found. Extensive experiments on the ImageNet dataset demonstrate the superiority of the proposed method by outperforming the state-of-the-art methods. Full article

(This article belongs to the Special Issue Deep Learning Algorithms in Computational Intelligence: Advances and Applications)

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20 pages, 2898 KiB

Open AccessArticle

Research on Real-Time Detection Algorithm for Pavement Cracks Based on SparseInst-CDSM

by Shao-Jie Wang, Ji-Kai Zhang and Xiao-Qi Lu

Mathematics 2023, 11(15), 3277; https://doi.org/10.3390/math11153277 - 26 Jul 2023

Cited by 3 | Viewed by 1241

Abstract

This paper proposes a road crack detection algorithm based on an improved SparseInst network, called the SparseInst-CDSM algorithm, aimed at solving the problems of low recognition accuracy and poor real-time detection of existing algorithms. The algorithm introduces the CBAM module, DCNv2 convolution, SPM [...] Read more.

This paper proposes a road crack detection algorithm based on an improved SparseInst network, called the SparseInst-CDSM algorithm, aimed at solving the problems of low recognition accuracy and poor real-time detection of existing algorithms. The algorithm introduces the CBAM module, DCNv2 convolution, SPM strip pooling module, MPM mixed pooling module, etc., effectively improving the integrity and accuracy of crack recognition. At the same time, the central axis skeleton of the crack is extracted using the central axis method, and the length and maximum width of the crack are calculated. In the experimental comparison under the self-built crack dataset, SparseInst-CDSM has an accuracy of 93.66%, a precision of 67.35%, a recall of 66.72%, and an IoU of 84.74%, all higher than mainstream segmentation models such as Mask-RCNN and SOLO that were compared, reflecting the superiority of the algorithm proposed in this paper. The comparison results of actual measurements show that the algorithm error is within 10%, indicating that it has high effectiveness and practicality. Full article

(This article belongs to the Special Issue Deep Learning Algorithms in Computational Intelligence: Advances and Applications)

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16 pages, 2737 KiB

Open AccessArticle

Constrained Self-Adaptive Physics-Informed Neural Networks with ResNet Block-Enhanced Network Architecture

by Guangtao Zhang, Huiyu Yang, Guanyu Pan, Yiting Duan, Fang Zhu and Yang Chen

Mathematics 2023, 11(5), 1109; https://doi.org/10.3390/math11051109 - 22 Feb 2023

Cited by 1 | Viewed by 3134

Abstract

Physics-informed neural networks (PINNs) have been widely adopted to solve partial differential equations (PDEs), which could be used to simulate physical systems. However, the accuracy of PINNs does not meet the needs of the industry, and severely degrades, especially when the PDE solution [...] Read more.

Physics-informed neural networks (PINNs) have been widely adopted to solve partial differential equations (PDEs), which could be used to simulate physical systems. However, the accuracy of PINNs does not meet the needs of the industry, and severely degrades, especially when the PDE solution has sharp transitions. In this paper, we propose a ResNet block-enhanced network architecture to better capture the transition. Meanwhile, a constrained self-adaptive PINN (cSPINN) scheme is developed to move PINN’s objective to the areas of the physical domain, which are difficult to learn. To demonstrate the performance of our method, we present the results of numerical experiments on the Allen–Cahn equation, the Burgers equation, and the Helmholtz equation. We also show the results of solving the Poisson equation using cSPINNs on different geometries to show the strong geometric adaptivity of cSPINNs. Finally, we provide the performance of cSPINNs on a high-dimensional Poisson equation to further demonstrate the ability of our method. Full article

(This article belongs to the Special Issue Deep Learning Algorithms in Computational Intelligence: Advances and Applications)

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18 pages, 802 KiB

Open AccessArticle

Learning Heterogeneous Graph Embedding with Metapath-Based Aggregation for Link Prediction

by Chengdong Zhang, Keke Li, Shaoqing Wang, Bin Zhou, Lei Wang and Fuzhen Sun

Mathematics 2023, 11(3), 578; https://doi.org/10.3390/math11030578 - 21 Jan 2023

Cited by 1 | Viewed by 3619

Abstract

Along with the growth of graph neural networks (GNNs), many researchers have adopted metapath-based GNNs to handle complex heterogeneous graph embedding. The conventional definition of a metapath only distinguishes whether there is a connection between nodes in the network schema, where the type [...] Read more.

Along with the growth of graph neural networks (GNNs), many researchers have adopted metapath-based GNNs to handle complex heterogeneous graph embedding. The conventional definition of a metapath only distinguishes whether there is a connection between nodes in the network schema, where the type of edge is ignored. This leads to inaccurate node representation and subsequently results in suboptimal prediction performance. In heterogeneous graphs, a node can be connected by multiple types of edges. In fact, each type of edge represents one kind of scene. The intuition is that if the embedding of nodes is trained under different scenes, the complete representation of nodes can be obtained by organically combining them. In this paper, we propose a novel definition of a metapath whereby the edge type, i.e., the relation between nodes, is integrated into it. A heterogeneous graph can be considered as the compound of multiple relation subgraphs from the view of a novel metapath. In different subgraphs, the embeddings of a node are separately trained by encoding and aggregating the neighbors of the intrapaths, which are the instance levels of a novel metapath. Then, the final embedding of the node is obtained by the use of the attention mechanism which aggregates nodes from the interpaths, which is the semantic level of the novel metapaths. Link prediction is a downstream task by which to evaluate the effectiveness of the learned embeddings. We conduct extensive experiments on three real-world heterogeneous graph datasets for link prediction. The empirical results show that the proposed model outperforms the state-of-the-art baselines; in particular, when comparing it to the best baseline, the F1 metric is increased by 10.35% over an Alibaba dataset. Full article

(This article belongs to the Special Issue Deep Learning Algorithms in Computational Intelligence: Advances and Applications)

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16 pages, 48353 KiB

Open AccessArticle

MedDeblur: Medical Image Deblurring with Residual Dense Spatial-Asymmetric Attention

by S. M. A. Sharif, Rizwan Ali Naqvi, Zahid Mehmood, Jamil Hussain, Ahsan Ali and Seung-Won Lee

Mathematics 2023, 11(1), 115; https://doi.org/10.3390/math11010115 - 27 Dec 2022

Cited by 10 | Viewed by 2633

Abstract

Medical image acquisition devices are susceptible to producing blurry images due to respiratory and patient movement. Despite having a notable impact on such blind-motion deblurring, medical image deblurring is still underexposed. This study proposes an end-to-end scale-recurrent deep network to learn the deblurring [...] Read more.

Medical image acquisition devices are susceptible to producing blurry images due to respiratory and patient movement. Despite having a notable impact on such blind-motion deblurring, medical image deblurring is still underexposed. This study proposes an end-to-end scale-recurrent deep network to learn the deblurring from multi-modal medical images. The proposed network comprises a novel residual dense block with spatial-asymmetric attention to recover salient information while learning medical image deblurring. The performance of the proposed methods has been densely evaluated and compared with the existing deblurring methods. The experimental results demonstrate that the proposed method can remove blur from medical images without illustrating visually disturbing artifacts. Furthermore, it outperforms the deep deblurring methods in qualitative and quantitative evaluation by a noticeable margin. The applicability of the proposed method has also been verified by incorporating it into various medical image analysis tasks such as segmentation and detection. The proposed deblurring method helps accelerate the performance of such medical image analysis tasks by removing blur from blurry medical inputs. Full article

(This article belongs to the Special Issue Deep Learning Algorithms in Computational Intelligence: Advances and Applications)

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25 pages, 8898 KiB

Open AccessArticle

Coarse Point Cloud Registration Based on Variational Functionals

by Artyom Makovetskii, Sergei Voronin, Vitaly Kober and Alexei Voronin

Mathematics 2023, 11(1), 35; https://doi.org/10.3390/math11010035 - 22 Dec 2022

Cited by 10 | Viewed by 1834

Abstract

Point cloud collection forming a 3D scene typically uses information from multiple data scans. The common approach is to register the point cloud pairs consequentially using a variant of the iterative closest point (ICP) algorithm, but most versions of the ICP algorithm only [...] Read more.

Point cloud collection forming a 3D scene typically uses information from multiple data scans. The common approach is to register the point cloud pairs consequentially using a variant of the iterative closest point (ICP) algorithm, but most versions of the ICP algorithm only work correctly for a small movement between two point clouds. This makes it difficult to accumulate multiple scans. Global registration algorithms are also known, which theoretically process point clouds at arbitrary initial positions. Recently, a multiparameter variational functional was described and used in the ICP variant to register point clouds at arbitrary initial positions. The disadvantage of this algorithm was the need for manual selection of parameters. In this paper, a modified version of the algorithm with automatic selection of the model parameters is proposed. The proposed algorithm is a fusion of the ICP and RANSAC concepts. Moreover, the algorithm can be parallelized. The performance of the proposed algorithm is compared with that of known global registration algorithms. Full article

(This article belongs to the Special Issue Deep Learning Algorithms in Computational Intelligence: Advances and Applications)

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14 pages, 1262 KiB

Open AccessArticle

Improving Motor Imagery EEG Classification Based on Channel Selection Using a Deep Learning Architecture

by Tat’y Mwata-Velu, Juan Gabriel Avina-Cervantes, Jose Ruiz-Pinales, Tomas Alberto Garcia-Calva, Erick-Alejandro González-Barbosa, Juan B. Hurtado-Ramos and José-Joel González-Barbosa

Mathematics 2022, 10(13), 2302; https://doi.org/10.3390/math10132302 - 1 Jul 2022

Cited by 15 | Viewed by 3504

Abstract

Recently, motor imagery EEG signals have been widely applied in Brain–Computer Interfaces (BCI). These signals are typically observed in the first motor cortex of the brain, resulting from the imagination of body limb movements. For non-invasive BCI systems, it is not apparent how [...] Read more.

Recently, motor imagery EEG signals have been widely applied in Brain–Computer Interfaces (BCI). These signals are typically observed in the first motor cortex of the brain, resulting from the imagination of body limb movements. For non-invasive BCI systems, it is not apparent how to locate the electrodes, optimizing the accuracy for a given task. This study proposes a comparative analysis of channel signals exploiting the Deep Learning (DL) technique and a public dataset to locate the most discriminant channels. EEG channels are usually selected based on the function and nomenclature of electrode location from international standards. Instead, the most suitable configuration for a given paradigm must be determined by analyzing the proper selection of the channels. Therefore, an EEGNet network was implemented to classify signals from different channel location using the accuracy metric. Achieved results were then contrasted with results from the state-of-the-art. As a result, the proposed method improved BCI classification accuracy. Full article

(This article belongs to the Special Issue Deep Learning Algorithms in Computational Intelligence: Advances and Applications)

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