Journal articles: 'Graph wavelets'

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Wu, Jiasong, Fuzhi Wu, Qihan Yang, et al. "Fractional Spectral Graph Wavelets and Their Applications." Mathematical Problems in Engineering 2020 (November 6, 2020): 1–18. http://dx.doi.org/10.1155/2020/2568179.

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One of the key challenges in the area of signal processing on graphs is to design transforms and dictionary methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier transform (GFT) to spectral graph fractional Fourier transform (SGFRFT), which is then used to define a novel transform named spectral graph fractional wavelet transform (SGFRWT), which is a generalized and extended version of spectral graph wavelet transform (SGWT). A fast algorithm for SGFRWT is also derived and implemented based on Fourier series approximation. Some potential applications of SGFRWT are also presented.

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Hammond, David K., Pierre Vandergheynst, and Rémi Gribonval. "Wavelets on graphs via spectral graph theory." Applied and Computational Harmonic Analysis 30, no. 2 (2011): 129–50. http://dx.doi.org/10.1016/j.acha.2010.04.005.

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Bastos, Anson, Abhishek Nadgeri, Kuldeep Singh, Toyotaro Suzumura, and Manish Singh. "Learnable Spectral Wavelets on Dynamic Graphs to Capture Global Interactions." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 6 (2023): 6779–87. http://dx.doi.org/10.1609/aaai.v37i6.25831.

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Learning on evolving(dynamic) graphs has caught the attention of researchers as static methods exhibit limited performance in this setting. The existing methods for dynamic graphs learn spatial features by local neighborhood aggregation, which essentially only captures the low pass signals and local interactions. In this work, we go beyond current approaches to incorporate global features for effectively learning representations of a dynamically evolving graph. We propose to do so by capturing the spectrum of the dynamic graph. Since static methods to learn the graph spectrum would not consider the history of the evolution of the spectrum as the graph evolves with time, we propose an approach to learn the graph wavelets to capture this evolving spectra. Further, we propose a framework that integrates the dynamically captured spectra in the form of these learnable wavelets into spatial features for incorporating local and global interactions. Experiments on eight standard datasets show that our method significantly outperforms related methods on various tasks for dynamic graphs.

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Paul, Okuwobi Idowu, and Yong Hua Lu. "Facial Prediction and Recognition Using Wavelets Transform Algorithm and Technique." Applied Mechanics and Materials 666 (October 2014): 251–55. http://dx.doi.org/10.4028/www.scientific.net/amm.666.251.

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An efficient facial representation is a crucial step for successful and effective performance of cognitive tasks such as object recognition, fixation, facial recognition system, etc. This paper demonstrates the use of Gabor wavelets transform for efficient facial representation and recognition. Facial recognition is influenced by several factors such as shape, reflectance, pose, occlusion and illumination which make it even more difficult. Gabor wavelet transform is used for facial features vector construction due to its powerful representation of the behavior of receptive fields in human visual system (HVS). The method is based on selecting peaks (high-energized points) of the Gabor wavelet responses as feature points. This paper work introduces the use of Gabor wavelets transform for efficient facial representation and recognition. Compare to predefined graph nodes of elastic graph matching, the approach used in this paper has better representative capability for Gabor wavelets transform. The feature points are automatically extracted using the local characteristics of each individual face in order to decrease the effect of occluded features. Based on the experiment, the proposed method performs better compared to the graph matching and eigenface based methods. The feature points are automatically extracted using the local characteristics of each individual face in order to decrease the effect of occluded features. The proposed system is validated using four different face databases of ORL, FERRET, Purdue and Stirling database.

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Xu, Mingxing, Wenrui Dai, Chenglin Li, Junni Zou, Hongkai Xiong, and Pascal Frossard. "Graph Neural Networks With Lifting-Based Adaptive Graph Wavelets." IEEE Transactions on Signal and Information Processing over Networks 8 (2022): 63–77. http://dx.doi.org/10.1109/tsipn.2022.3140477.

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Tay, D. B. H., and Z. Lin. "Highly localised near orthogonal graph wavelets." Electronics Letters 52, no. 11 (2016): 966–68. http://dx.doi.org/10.1049/el.2016.0482.

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Tremblay, Nicolas, and Pierre Borgnat. "Graph Wavelets for Multiscale Community Mining." IEEE Transactions on Signal Processing 62, no. 20 (2014): 5227–39. http://dx.doi.org/10.1109/tsp.2014.2345355.

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Masoumi, Majid, and A. Ben Hamza. "Shape classification using spectral graph wavelets." Applied Intelligence 47, no. 4 (2017): 1256–69. http://dx.doi.org/10.1007/s10489-017-0955-7.

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Yang, Zhirui, Yulan Hu, Sheng Ouyang, et al. "WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 8 (2024): 9287–95. http://dx.doi.org/10.1609/aaai.v38i8.28781.

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In the existing spectral GNNs, polynomial-based methods occupy the mainstream in designing a filter through the Laplacian matrix. However, polynomial combinations factored by the Laplacian matrix naturally have limitations in message passing (e.g., over-smoothing). Furthermore, most existing spectral GNNs are based on polynomial bases, which struggle to capture the high-frequency parts of the graph spectral signal. Additionally, we also find that even increasing the polynomial order does not change this situation, which means polynomial-based models have a natural deficiency when facing high-frequency signals. To tackle these problems, we propose WaveNet, which aims to effectively capture the high-frequency part of the graph spectral signal from the perspective of wavelet bases through reconstructing the message propagation matrix. We utilize Multi-Resolution Analysis (MRA) to model this question, and our proposed method can reconstruct arbitrary filters theoretically. We also conduct node classification experiments on real-world graph benchmarks and achieve superior performance on most datasets. Our code is available at https://github.com/Bufordyang/WaveNet

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Sun, Qingyun, Jianxin Li, Beining Yang, Xingcheng Fu, Hao Peng, and Philip S. Yu. "Self-Organization Preserved Graph Structure Learning with Principle of Relevant Information." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 4 (2023): 4643–51. http://dx.doi.org/10.1609/aaai.v37i4.25587.

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Most Graph Neural Networks follow the message-passing paradigm, assuming the observed structure depicts the ground-truth node relationships. However, this fundamental assumption cannot always be satisfied, as real-world graphs are always incomplete, noisy, or redundant. How to reveal the inherent graph structure in a unified way remains under-explored. We proposed PRI-GSL, a Graph Structure Learning framework guided by the Principle of Relevant Information, providing a simple and unified framework for identifying the self-organization and revealing the hidden structure. PRI-GSL learns a structure that contains the most relevant yet least redundant information quantified by von Neumann entropy and Quantum Jensen Shannon divergence. PRI-GSL incorporates the evolution of quantum continuous walk with graph wavelets to encode node structural roles, showing in which way the nodes interplay and self-organize with the graph structure. Extensive experiments demonstrate the superior effectiveness and robustness of PRI-GSL.

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Chen, Lianggangxu, Youqi Song, Shaohui Lin, Changbo Wang, and Gaoqi He. "Kumaraswamy Wavelet for Heterophilic Scene Graph Generation." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 2 (2024): 1138–46. http://dx.doi.org/10.1609/aaai.v38i2.27875.

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Graph neural networks (GNNs) has demonstrated its capabilities in the field of scene graph generation (SGG) by updating node representations from neighboring nodes. Actually it can be viewed as a form of low-pass filter in the spatial domain, which smooths node feature representation and retains commonalities among nodes. However, spatial GNNs does not work well in the case of heterophilic SGG in which fine-grained predicates are always connected to a large number of coarse-grained predicates. Blind smoothing undermines the discriminative information of the fine-grained predicates, resulting in failure to predict them accurately. To address the heterophily, our key idea is to design tailored filters by wavelet transform from the spectral domain. First, we prove rigorously that when the heterophily on the scene graph increases, the spectral energy gradually shifts towards the high-frequency part. Inspired by this observation, we subsequently propose the Kumaraswamy Wavelet Graph Neural Network (KWGNN). KWGNN leverages complementary multi-group Kumaraswamy wavelets to cover all frequency bands. Finally, KWGNN adaptively generates band-pass filters and then integrates the filtering results to better accommodate varying levels of smoothness on the graph. Comprehensive experiments on the Visual Genome and Open Images datasets show that our method achieves state-of-the-art performance.

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Gong, Bo, Benjamin Schullcke, Sabine Krueger-Ziolek, et al. "EIT Imaging Regularization Based on Spectral Graph Wavelets." IEEE Transactions on Medical Imaging 36, no. 9 (2017): 1832–44. http://dx.doi.org/10.1109/tmi.2017.2716825.

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Tay, David B. H., Yuichi Tanaka, and Akie Sakiyama. "Almost Tight Spectral Graph Wavelets With Polynomial Filters." IEEE Journal of Selected Topics in Signal Processing 11, no. 6 (2017): 812–24. http://dx.doi.org/10.1109/jstsp.2017.2726972.

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Manoharan, Samuel. "STUDY ON HERMITIAN GRAPH WAVELETS IN FEATURE DETECTION." Journal of Soft Computing Paradigm 2019, no. 1 (2019): 24–32. http://dx.doi.org/10.36548/jscp.2019.1.003.

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The enormous information flow in our day today life, initiates the necessitates of the identifying the valuable data that are to be concentrated. In case of image segmentation and signal processing, the feature detection takes up the role of fixating to the data that are to be focused. Thus directing to the pixels or information that are to be concentrated eliminating the time and the energy wastage in examining the pixels or the information’s that are of least important. The paper is the study, focusing on the advantages of utilizing the Hermitian wavelet transform incorporated with the graph wavelet in the feature detection, leading to an accurate identification of the information to be processed further.

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Wang, Qingzheng, Huixin Wu, Hua Yang, Yue Liu, Chenming Zhang, and Bin Li. "Data-Specific Anisotropic Mexican Hat Wavelets for Structure-Preserving Image Processing." Scientific Programming 2022 (April 13, 2022): 1–13. http://dx.doi.org/10.1155/2022/4455871.

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This paper proposes a novel approach for structure-sensitive image processing based on the rigorous mathematical derivation of data-specific anisotropic Mexican hat wavelets (DAM). Our DAM is derived from the negative first-order derivative of the fundamental solution of heat diffusion equation with respect to time, which not only shares similar properties with Mexican hat wavelet but also intrinsically embeds the image-specific properties. Through the scale-aware DAM transform and its inverse transform, we are capable of conducting structure-sensitive image processing. Our key idea is to represent the images as undirected graphs, whose edge weights are governed by the normalized intensity/color differences within the local neighboring pixel window. Based on the rigorous theory of global graph Laplacian and heat diffusion, our original DAM can also encode the local/global structure of images. We employ the Krylov subspace technique to reduce the computational cost of our DAM transform. Furthermore, aiming at various structure-preserving image processing applications such as filtering, detail enhancement, tone manipulation, and stylization, we conduct comprehensive experiments and make quantitative comparisons with other state-of-the-art methods, which demonstrate the versatility and superiority of our method.

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Prakash, Anurag, and Subrat Kar. "Graph wavelets for fault localization in optical mesh networks." Optical Fiber Technology 72 (September 2022): 103006. http://dx.doi.org/10.1016/j.yofte.2022.103006.

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Zhong, Ming, and Hong Qin. "Sparse approximation of 3D shapes via spectral graph wavelets." Visual Computer 30, no. 6-8 (2014): 751–61. http://dx.doi.org/10.1007/s00371-014-0971-0.

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Cui, Beibei, and Jean-Charles Créput. "NCC Based Correspondence Problem for First- and Second-Order Graph Matching." Sensors 20, no. 18 (2020): 5117. http://dx.doi.org/10.3390/s20185117.

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Automatically finding correspondences between object features in images is of main interest for several applications, as object detection and tracking, identification, registration, and many derived tasks. In this paper, we address feature correspondence within the general framework of graph matching optimization and with the principal aim to contribute. We proposed two optimized algorithms: first-order and second-order for graph matching. On the one hand, a first-order normalized cross-correlation (NCC) based graph matching algorithm using entropy and response through Marr wavelets within the scale-interaction method is proposed. First, we proposed a new automatic feature detection processing by using Marr wavelets within the scale-interaction method. Second, feature extraction is executed under the mesh division strategy and entropy algorithm, accompanied by the assessment of the distribution criterion. Image matching is achieved by the nearest neighbor search with normalized cross-correlation similarity measurement to perform coarse matching on feature points set. As to the matching points filtering part, the Random Sample Consensus Algorithm (RANSAC) removes outliers correspondences. One the other hand, a second-order NCC based graph matching algorithm is presented. This algorithm is an integer quadratic programming (IQP) graph matching problem, which is implemented in Matlab. It allows developing and comparing many algorithms based on a common evaluation platform, sharing input data, and a customizable affinity matrix and matching list of candidate solution pairs as input data. Experimental results demonstrate the improvements of these algorithms concerning matching recall and accuracy compared with other algorithms.

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Bala, B. Kiran, and S. Audithan. "Identification of Spectral Graph Wavelets for Microcalcifications in Mammogram Images." Indian Journal of Public Health Research & Development 9, no. 5 (2018): 251. http://dx.doi.org/10.5958/0976-5506.2018.00448.5.

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Farouk, R. M. "Iris recognition based on elastic graph matching and Gabor wavelets." Computer Vision and Image Understanding 115, no. 8 (2011): 1239–44. http://dx.doi.org/10.1016/j.cviu.2011.04.002.

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Sakiyama, Akie, Kana Watanabe, and Yuichi Tanaka. "Spectral Graph Wavelets and Filter Banks With Low Approximation Error." IEEE Transactions on Signal and Information Processing over Networks 2, no. 3 (2016): 230–45. http://dx.doi.org/10.1109/tsipn.2016.2581303.

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BOURBAKIS, N., P. YUAN, and P. KAKUMANU. "A GRAPH BASED OBJECT DESCRIPTION AND RECOGNITION METHODOLOGY." International Journal on Artificial Intelligence Tools 17, no. 06 (2008): 1161–94. http://dx.doi.org/10.1142/s0218213008004345.

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This paper presents a methodology for recognizing 3D objects using synthesis of 2D views. In particular, the methodology uses wavelets for rearranging the shape of the perceived 2D view of an object for attaining a desirable size, local-global (LG) graphs for representing the shape, color and location of each image object's region obtained by an image segmentation method and the synthesis of these regions that compose that particular object. The synthesis of the regions is obtained by composing their local graph representations under certain neighborhood criteria. The LG graph representation of the extracted object is compared against a set of LG based object-models stored in a Database (DB). The methodology is accurate for recognizing objects existed in the DB and it has the capability of "learning" the LG patterns of new objects by associating them with attributes from existing LG patterns in the DB. Note that for each object-model stored in the database there are only six views, since all the intermediate views can be generated by appropriately synthesizing these six views. Illustrative examples are also provided.

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Irfan, Muhammad Abeer, and Enrico Magli. "Joint Geometry and Color Point Cloud Denoising Based on Graph Wavelets." IEEE Access 9 (2021): 21149–66. http://dx.doi.org/10.1109/access.2021.3054171.

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Li, Nannan, Shengfa Wang, Ming Zhong, Zhixun Su, and Hong Qin. "Generalized Local-to-Global Shape Feature Detection Based on Graph Wavelets." IEEE Transactions on Visualization and Computer Graphics 22, no. 9 (2016): 2094–106. http://dx.doi.org/10.1109/tvcg.2015.2498557.

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Behjat, Hamid, Nora Leonardi, Leif Sörnmo, and Dimitri Van De Ville. "Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping." NeuroImage 123 (December 2015): 185–99. http://dx.doi.org/10.1016/j.neuroimage.2015.06.010.

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Petrovic, Miljan, Thomas A. W. Bolton, Maria Giulia Preti, Raphaël Liégeois, and Dimitri Van De Ville. "Guided graph spectral embedding: Application to the C. elegans connectome." Network Neuroscience 3, no. 3 (2019): 807–26. http://dx.doi.org/10.1162/netn_a_00084.

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Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions—for example, based on wavelets and Slepians—that can be applied to filter signals defined on the graph. In this work, we take inspiration from these constructions to define a new guided spectral embedding that combines maximizing energy concentration with minimizing modified embedded distance for a given importance weighting of the nodes. We show that these optimization goals are intrinsically opposite, leading to a well-defined and stable spectral decomposition. The importance weighting allows us to put the focus on particular nodes and tune the trade-off between global and local effects. Following the derivation of our new optimization criterion, we exemplify the methodology on the C. elegans structural connectome. The results of our analyses confirm known observations on the nematode’s neural network in terms of functionality and importance of cells. Compared with Laplacian embedding, the guided approach, focused on a certain class of cells (sensory neurons, interneurons, or motoneurons), provides more biological insights, such as the distinction between somatic positions of cells, and their involvement in low- or high-order processing functions.

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Shigeta, Hironori, Tomohiro Mashita, Junichi Kikuta, et al. "Bone marrow cavity segmentation using graph-cuts with wavelet-based texture feature." Journal of Bioinformatics and Computational Biology 15, no. 05 (2017): 1740004. http://dx.doi.org/10.1142/s0219720017400042.

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Emerging bioimaging technologies enable us to capture various dynamic cellular activities [Formula: see text]. As large amounts of data are obtained these days and it is becoming unrealistic to manually process massive number of images, automatic analysis methods are required. One of the issues for automatic image segmentation is that image-taking conditions are variable. Thus, commonly, many manual inputs are required according to each image. In this paper, we propose a bone marrow cavity (BMC) segmentation method for bone images as BMC is considered to be related to the mechanism of bone remodeling, osteoporosis, and so on. To reduce manual inputs to segment BMC, we classified the texture pattern using wavelet transformation and support vector machine. We also integrated the result of texture pattern classification into the graph-cuts-based image segmentation method because texture analysis does not consider spatial continuity. Our method is applicable to a particular frame in an image sequence in which the condition of fluorescent material is variable. In the experiment, we evaluated our method with nine types of mother wavelets and several sets of scale parameters. The proposed method with graph-cuts and texture pattern classification performs well without manual inputs by a user.

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Venkat, Aarthi, Martina Damo, Nikhil S. Joshi, and Smita Krishnaswamy. "Mapping the gene space at single-cell resolution with gene signal pattern analysis." Journal of Immunology 210, no. 1_Supplement (2023): 251.03. http://dx.doi.org/10.4049/jimmunol.210.supp.251.03.

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Abstract In single-cell RNA sequencing analysis, several computational methods have been developed to map the cellular state space, but little has been done to map the gene space. A mapping that preserves gene-gene relationships within the dataset is particularly useful for characterizing cellular heterogeneity within cell types, where boundaries between cell subpopulations are often unclear or even arbitrary. Here, we present gene signal pattern analysis, a new paradigm for analyzing single cells. We build a cell-cell graph and design a dictionary of diffusion wavelets, capturing a multiscale view of the cell space. We then transform genes by the dictionary and learn a reduced gene representation. Given the gap in prior research for this problem, we design nine alternative strategies and three benchmarks for evaluating preservation of gene-gene relationships, all of which are outperformed by diffusion wavelet-transformed signals. We also define, calculate, and evaluate localization, a key property of a gene signal on the cellular graph. We demonstrate the utility of gene signal pattern analysis on T cells from a mouse model of peripheral tolerance in skin. The gene space mapping reveals a continuum of gene signals characterized by T cell subtypes and transcriptional programs related to effector function and proliferation. Furthermore, we built a multiscale manifold of 48 melanoma patient samples, demonstrating the ability of our method to characterize differences between responders and non-responders to checkpoint immunotherapy. Together, we show gene signal pattern analysis, through methodology from graph signal processing, spectral graph theory, and machine learning, represents an avenue for future research in scRNA-seq analysis. Gruber Foundation

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CHENG, Hao, Hao YAN, Li-jun BAI, and Bao-guo WANG. "Exploration of whole brain networks modulated by acupuncture at analgesia acupoint ST36 using scale-specific wavelet correlation analysis." Chinese Medical Journal 126, no. 13 (2013): 2459–64. http://dx.doi.org/10.3760/cma.j.issn.0366-6999.20122681.

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Background Previous studies have demonstrated that acupuncture could modulate various brain systems in the resting brain networks. Graph theoretical analysis offers a novel way to investigate the functional organization of the large-scale cortical networks modulated by acupuncture at whole brain level. In this study, we used wavelets correlation analysis to estimate the pairwise correlations between 90 cortical and subcortical human brain regions in normal human volunteers scanned during the post-stimulus resting state. Methods Thirty-two college students, all right-handed and acupuncture naïve, participated in this study. Every participant received only one acupoint stimulation, resulting in 16 subjects in one group. Both structural functional magnetic resonance imaging (fMRI) data (3D sequence with a voxel size of 1 mm3 for anatomical localization) and functional fMRI data (TR=1500 ms, TE=30 ms, flip angle=90°) were collected for each subject. After thresholding the resulting scale-specific wavelet correlation matrices to generate undirected binary graphs, we compared graph metrics of brain organization following verum manual acupuncture (ACU) and sham acupuncture (SHAM) groups. Results The topological parameters of the large-scale brain networks in ACU group were different from those of the SHAM group at multiple scales. There existed distinct modularity functional brain networks during the post-stimulus resting state following ACU and SHAM at multiple scales. Conclusions The distinct modulation patterns of the resting brain attributed to the specific effects evoked by acupuncture. In addition, we also identified that there existed frequency-specific modulation in the post-stimulus resting brain following ACU and SHAM. The modulation may be related to the effects of verum acupuncture on modulating special disorder treatment. This preliminary finding may provide a new clue to understand the relatively function-oriented specificity of acupuncture effects.

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Lakshmi, K. Sai Prasanna. "HAAR Wavelets and Graph based Model for Content Based Image Retrieval in MNIST." International Journal for Research in Applied Science and Engineering Technology 6, no. 4 (2018): 90–98. http://dx.doi.org/10.22214/ijraset.2018.4020.

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Watson, James R., Zach Gelbaum, Mathew Titus, Grant Zoch, and David Wrathall. "Identifying multiscale spatio-temporal patterns in human mobility using manifold learning." PeerJ Computer Science 6 (June 15, 2020): e276. http://dx.doi.org/10.7717/peerj-cs.276.

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When, where and how people move is a fundamental part of how human societies organize around every-day needs as well as how people adapt to risks, such as economic scarcity or instability, and natural disasters. Our ability to characterize and predict the diversity of human mobility patterns has been greatly expanded by the availability of Call Detail Records (CDR) from mobile phone cellular networks. The size and richness of these datasets is at the same time a blessing and a curse: while there is great opportunity to extract useful information from these datasets, it remains a challenge to do so in a meaningful way. In particular, human mobility is multiscale, meaning a diversity of patterns of mobility occur simultaneously, which vary according to timing, magnitude and spatial extent. To identify and characterize the main spatio-temporal scales and patterns of human mobility we examined CDR data from the Orange mobile network in Senegal using a new form of spectral graph wavelets, an approach from manifold learning. This unsupervised analysis reduces the dimensionality of the data to reveal seasonal changes in human mobility, as well as mobility patterns associated with large-scale but short-term religious events. The novel insight into human mobility patterns afforded by manifold learning methods like spectral graph wavelets have clear applications for urban planning, infrastructure design as well as hazard risk management, especially as climate change alters the biophysical landscape on which people work and live, leading to new patterns of human migration around the world.

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Li, Yong Mei, Bing Zhou, Guo Fu Sun, and Bo Yan Yang. "Study on Damage Location of Spatial Structures Based on Wavelet Analysis of Model Strain Energy." Advanced Materials Research 639-640 (January 2013): 1033–37. http://dx.doi.org/10.4028/www.scientific.net/amr.639-640.1033.

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The research to identify and locate the damage to the engineering structure mainly aimed at some simple structure forms before, such as beam and framework. Damage shows changes of local characteristics of the signal, while wavelet analysis can reflect local damage traits of the signal in time domain and frequency domain. For confirming the validity and applicability of structural damage identification methods, wavelet analysis is used to spatial structural damage detection. The wavelet analysis technique provides new ideas and methods of spatial steel structural damage detection. Based on the theory of wavelet singularity detection，with the injury signal of modal strain energy as structural damage index，the mixing of the modal strain energy and wavelet method to identify and locate the damage to the spatial structure is considered. The multiplicity of the bars and nodes can be taken into account, and take the destructive and nondestructive modal strain energy of Kiewitt-type reticulated shell with 40m span as an example of numerical simulation，the original damage signal and the damage signal after wavelet transformation is compared. The location of the declining stiffness identified by the maximum of wavelet coefficients，analyzed as signal by db1 wavelet，and calculate the graph relation between coefficients of the wavelets and the damage to the structure by discrete or continuous wavelet transform, and also check the accuracy degree of this method with every damage case. Finally，the conclusion is drawn that the modal strain energy and wavelet method to identify and locate the damage to the long span reticulated shell is practical, effective and accurate, that the present method as a reliable and practical way can be adopted to detect the single and several locations of damage in structures.

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Larsen, Nadia S., and Iain Raeburn. "Projective multi-resolution analyses arising from direct limits of Hilbert modules." MATHEMATICA SCANDINAVICA 100, no. 2 (2007): 317. http://dx.doi.org/10.7146/math.scand.a-15026.

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The authors have recently shown how direct limits of Hilbert spaces can be used to construct multi-resolution analyses and wavelets in $L^2(\mathsf R)$. Here they investigate similar constructions in the context of Hilbert modules over $C^*$-algebras. For modules over $C(\mathsf T^n)$, the results shed light on work of Packer and Rieffel on projective multi-resolution analyses for specific Hilbert $C(\mathsf T^n)$-modules of functions on $\mathsf R^n$. There are also new applications to modules over $C(C)$ when $C$ is the infinite path space of a directed graph.

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Gersztenkorn, Adam. "A new approach for detecting topographic and geologic information in seismic data." GEOPHYSICS 77, no. 2 (2012): V81—V90. http://dx.doi.org/10.1190/geo2011-0216.1.

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Interpreting 3D seismic volumes can be an intensive and time-consuming endeavor. Algorithms that provide additional information and expedite this process can therefore be useful tools for the interpreter. To further this goal, an algorithm that gives a topographic perspective of seismic data is described. After applying the continuous wavelet transform to the data, templates having a directional orientation are constructed locally in the complex wavelet domain for a number of scales. For each scale, a complex matrix is formed having real and imaginary parts, which are independently designed for a specific purpose and then combined to produce the final result. Whereas the composition of the real matrix is not well suited for dealing with the topographic aspect of the data, the imaginary matrix is. Using basic concepts from graph theory, the imaginary matrix is constructed to reveal the topographic nature of the underlying data. To a limited extent, dip scans provide similar results. Nonetheless, comparisons with dip scans reveal significant differences in the final results and computational efficiency. Although the general features seem to be similar, detailed features appear to be missing from the dip scan results. For the dip scans, semblance is measured over a number of dips and the highest value is used to determine the dip. The computational cost can vary, depending on factors such as the number of dips tested and implementation, but a comparison indicates that dip scans can be computationally more costly. In contrast, the algorithm to be described uses a single suite of wavelets convolved with the data to produce a number of scale-dependent complex matrices that are summed in a specific way. Furthermore, convolutions may be performed in the frequency domain. This reduces the computational cost, making this algorithm an effective and relatively fast interpretation tool.

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Khushi, Bhoj, Choksi Kuldeep, Kitawat Rishi, and Rana Manish. "Review on various face recognition databases." i-manager’s Journal on Pattern Recognition 9, no. 2 (2022): 17. http://dx.doi.org/10.26634/jpr.9.2.19189.

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Face recognition is one of the multimedia items that has seen a remarkable increase in popularity in recent years. Face continues to be the most difficult study topic for experts in the field of computer vision and image processing since it is an item with different properties for detection. We have attempted to handle the most challenging facial aspects in this survey work, including posture invariance, aging, illuminations, and partial occlusion. When applied to facial photographs, they are regarded as essential components of face recognition systems. The most recent face detection methods and techniques are also examined in this paper, including Eigenface, Artificial Neural Networks (ANN), Support Vector Machines (SVM), Principal Component Analysis (PCA), Independent Component Analysis (ICA), Gabor Wavelets, Elastic Bunch Graph Matching, 3D Morphable Models, and Hidden Markov Models. Many testing face databases, such as AT & T (ORL), AR, FERET, LFW, YTF, and Yale, also reviewed. However, the purpose of this study is to present a thorough literature assessment on face recognition and its applications.

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SMALTER, AARON, JUN HUAN, and GERALD LUSHINGTON. "GRAPH WAVELET ALIGNMENT KERNELS FOR DRUG VIRTUAL SCREENING." Journal of Bioinformatics and Computational Biology 07, no. 03 (2009): 473–97. http://dx.doi.org/10.1142/s0219720009004187.

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In this paper, we introduce a novel statistical modeling technique for target property prediction, with applications to virtual screening and drug design. In our method, we use graphs to model chemical structures and apply a wavelet analysis of graphs to summarize features capturing graph local topology. We design a novel graph kernel function to utilize the topology features to build predictive models for chemicals via Support Vector Machine classifier. We call the new graph kernel a graph wavelet-alignment kernel. We have evaluated the efficacy of the wavelet-alignment kernel using a set of chemical structure–activity prediction benchmarks. Our results indicate that the use of the kernel function yields performance profiles comparable to, and sometimes exceeding that of the existing state-of-the-art chemical classification approaches. In addition, our results also show that the use of wavelet functions significantly decreases the computational costs for graph kernel computation with more than ten fold speedup.

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Deb, Swakshar, Sejuti Rahman, and Shafin Rahman. "SEA-GWNN: Simple and Effective Adaptive Graph Wavelet Neural Network." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 10 (2024): 11740–48. http://dx.doi.org/10.1609/aaai.v38i10.29058.

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The utilization of wavelet-based techniques in graph neural networks (GNNs) has gained considerable attention, particularly in the context of node classification. Although existing wavelet-based approaches have shown promise, they are constrained by their reliance on pre-defined wavelet filters, rendering them incapable of effectively adapting to signals that reside on graphs based on tasks at hand. Recent research endeavors address this issue through the introduction of a wavelet lifting transform. However, this technique necessitates the use of bipartite graphs, causing a transformation of the original graph structure into a bipartite configuration. This alteration of graph topology results in the generation of undesirable wavelet filters, thereby undermining the effectiveness of the method. In response to these challenges, we propose a novel simple and effective adaptive graph wavelet neural network (SEA-GWNN) class that employs the lifting scheme on arbitrary graph structures while upholding the original graph topology by leveraging multi-hop computation trees. A noteworthy aspect of the approach is the focus on local substructures represented as acyclic trees, wherein the lifting strategy is applied in a localized manner. This locally defined lifting scheme effectively combines high-pass and low-pass frequency information to enhance node representations. Furthermore, to reduce computing costs, we propose to decouple the higher- order lifting operators and induce them from the lower-order structures. Finally, we benchmark our model on several real- world datasets spanning four distinct categories, including citation networks, webpages, the film industry, and large-scale graphs and the experimental results showcase the efficacy of the proposed SEA-GWNN.

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Cui, Lihong, Qiaoyun Wu, Jiale Liu, and Jianjun Sun. "Dual Wavelet Frame Transforms on Manifolds and Graphs." Journal of Mathematics 2019 (May 28, 2019): 1–12. http://dx.doi.org/10.1155/2019/1637623.

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In this paper, we consider the dual wavelet frames in both continuum setting, i.e., on manifolds, and discrete setting, i.e., on graphs. Firstly, we give sufficient conditions for the existence of dual wavelet frames on manifolds by their corresponding masks. Then, we present the formula of the decomposition and reconstruction for the dual wavelet frame transforms on graphs. Finally, we give a numerical example to illustrate the validity of the dual wavelet frame transformation applied to the graph data.

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Zhou, Jie, and Zeze Zhang. "A Brief Survey of the Graph Wavelet Frame." Complexity 2022 (October 3, 2022): 1–12. http://dx.doi.org/10.1155/2022/8153249.

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In recent years, the research of wavelet frames on the graph has become a hot topic in harmonic analysis. In this paper, we mainly introduce the relevant knowledge of the wavelet frames on the graph, including relevant concepts, construction methods, and related theory. Meanwhile, because the construction of graph tight framelets is closely related to the classical wavelet framelets on ℝ , we give a new construction of tight frames on ℝ . Based on the pseudosplines of type II, we derive an MRA tight wavelet frame with three generators ψ 1 , ψ 2 , and ψ 3 using the oblique extension principle (OEP), which generate a tight wavelet frame in L 2 ℝ . We analyze that three wavelet functions have the highest possible order of vanishing moments, which matches the order of the approximation order of the framelet system provided by the refinable function. Moreover, we introduce the construction of the Haar basis for a chain and analyze the global orthogonal bases on a graph G . Based on the sequence of framelet generators in L 2 ℝ and the Haar basis for a coarse-grained chain, the decimated tight framelets on graphs can be constructed. Finally, we analyze the detailed construction process of the wavelet frame on a graph.

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Babić, Ranko, and Lidija Babić. "A New Type of Bipartite Random Graph as a Transform of Seismogram and Its Potential for Organizing Seismic Databases." Applied Sciences 13, no. 18 (2023): 10303. http://dx.doi.org/10.3390/app131810303.

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This paper proposes a method to reduce seismogram variability as a determining factor in its interpretation, processing, and clustering. By introducing the concept of single fluctuations (SFs), the seismogram can be parsed into a sequence of random impulses with subsequent ordering. This rearrangement of SFs, if they are assigned by positive integers, represents the formal mapping of a regular string of integers into a random one, which can be represented with a bipartite random graph (bigraph). Due to its specific randomness, such a bigraph is considered a new type of random balanced bigraph. The R-envelope and RQ-envelope, its equidistant version, are defined by tracing the peak envelope over ordered SFs. The equivalence and complementariness of the RQ and bigraph are considered and discussed, forming a combined characteristic of the seismogram. The R/RQ provided a considerable reduction in seismogram variability, which was confirmed by creating and analyzing an ensemble of RQ from several seismograms. In the RQ domain, distance is defined as a possible basis for metrics and clustering, but the ensemble variability was quite narrow and not as suitable for this purpose. Otherwise, the ensemble shows high redundancy hidden in the seismogram population. As for the bigraph, the mesh of its edges is structuralized in bundles, forming a skeleton, which reflects the internal structural content of the seismogram. The distance over the domain of bigraphs is proposed to show the possibility of clustering. This means that only a combined RQ and bigraph provides a suitable frame for seismogram representation with reduced variability and, thus, the potential for more effectively organizing seismic databases and a deeper interpretation of seismograms; therefore, RQs and bigraphs can be considered as a transform of a seismogram. Many aspects of these concepts are thoroughly discussed. The similarity between concepts of SF and wavelets is briefly considered. This very complex theme is new and promises broad further research. All issues considered in the paper are abundantly illustrated.

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Ouda, Eman Hassan. "Direct Method for Variational Problems Using Boubaker Wavelets." Ibn AL-Haitham Journal For Pure and Applied Sciences 36, no. 3 (2023): 427–36. http://dx.doi.org/10.30526/36.3.3048.

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The wavelets have many applications in engineering and the sciences, especially mathematics. Recently, in 2021, the wavelet Boubaker (WB) polynomials were used for the first time to study their properties and applications in detail. They were also utilized for solving the Lane-Emden equation. The aim of this paper is to show the truncated Wavelet Boubaker polynomials for solving variation problems. In this research, the direct method using wavelets Boubaker was presented for solving variational problems. The method reduces the problem into a set of linear algebraic equations. The fundamental idea of this method for solving variation problems is to convert the problem of a function into one that involves a finite number of variables. Different numerical examples were given to demonstrate the applicability and validity of this method using the Matlab program. Also, the results of this technique were compared with the exact solution, and graphs were added to these examples to test the convergence of Wavelet Boubaker polynomials using this method.

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Gong, Bo, Benjamin Schullcke, Sabine Krueger-Ziolek, and Knut Moeller. "Regularization of EIT reconstruction based on multi-scales wavelet transforms." Current Directions in Biomedical Engineering 2, no. 1 (2016): 423–26. http://dx.doi.org/10.1515/cdbme-2016-0094.

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AbstractElectrical Impedance Tomography (EIT) intends to obtain the conductivity distribution of a domain from the electrical boundary conditions. This is an ill-posed inverse problem usually solved on finite element meshes. Wavelet transforms are widely used for medical image reconstruction. However, because of the irregular form of the finite element meshes, the canonical wavelet transforms is impossible to perform on meshes. In this article, we present a framework that combines multi-scales wavelet transforms and finite element meshes by viewing meshes as undirected graphs and applying spectral graph wavelet transform on the meshes.

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Arkhipova, O. V., N. N. Dolgikh, S. Yu Dolinger, V. Z. Kovalev, and D. S. Osipov. "Wavelet transform algorithm of daily load graphs for choosing parameters of hybrid energy storage." Omsk Scientific Bulletin, no. 174 (2020): 57–62. http://dx.doi.org/10.25206/1813-8225-2020-174-57-62.

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The paper presents an algorithm for frequency decomposition of daily load graphs based on a discrete wavelet transform. This algorithm makes it possible to choose the optimal type of wavelet function, optimal level and wavelet decomposition tree. The inverse wavelet transform (recovery) along a single branch of the approximating coefficient allows obtaining the lowfrequency component of the power graph for selecting the optimal mode of the hybrid energy storage battery. The detailing branch of the wavelet coefficients determines the operating mode of the supercapacitor. A numerical experiment is built on the basis of data obtained using certified equipment

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Schab, Esteban, Carla Casanova, and Fabiana Piccoli. "Graph Representations for Reinforcement Learning." Journal of Computer Science and Technology 24, no. 1 (2024): e03. http://dx.doi.org/10.24215/16666038.24.e03.

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Graph analysis is becoming increasingly important due to the expressive power of graph models and the efficient algorithms available for processing them. Reinforcement Learning is one domain that could benefit from advancements in graph analysis, given that a learning agent may be integrated into an environment that can be represented as a graph. Nevertheless, the structural irregularity of graphs and the lack of prior labels make it difficult to integrate such a model into modern Reinforcement Learning frameworks that rely on artificial neural networks. Graph embedding enables the learning of low-dimensional vector representations that are more suited for machine learning algorithms, while retaining essential graph features. This paper presents a framework for evaluating graph embedding algorithms and their ability to preserve the structure and relevant features of graphs by means of an internal validation metric, without resorting to subsequent tasks that require labels for training. Based on this framework, three defined algorithms that meet the necessary requirements for solving a specific problem of Reinforcement Learning in graphs are selected, analyzed, and compared. These algorithms are Graph2Vec, GL2Vec, and Wavelet Characteristics, with the latter two demonstrating superior performance.

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Kazantsev, S., A. Pavlov, and O. Chekha. "Wavelet transforms of the time series of small wholesale prices in the agricultural sector." IOP Conference Series: Earth and Environmental Science 937, no. 3 (2021): 032075. http://dx.doi.org/10.1088/1755-1315/937/3/032075.

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Abstract The article provides a wavelet analysis of small wholesale prices for white cabbage in Rostov-on-Don from 2017 to 2020 year. Approximation coefficients show a steady trend, the detailing coefficients reflect seasonal and insignificant temporary price fluctuations. The constituent scaling approximation coefficients and the detailing components are highlighted in the form of separate graphs. The series was decomposed up to the 6th level using the Haar and Daubechies wavelets.

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Srinivasa, Kumbinarasaiah, Haci Mehmet Baskonus, and Yolanda Guerrero Sánchez. "Numerical Solutions of the Mathematical Models on the Digestive System and COVID-19 Pandemic by Hermite Wavelet Technique." Symmetry 13, no. 12 (2021): 2428. http://dx.doi.org/10.3390/sym13122428.

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This article developed a functional integration matrix via the Hermite wavelets and proposed a novel technique called the Hermite wavelet collocation method (HWM). Here, we studied two models: the coupled system of an ordinary differential equation (ODE) is modeled on the digestive system by considering different parameters such as sleep factor, tension, food rate, death rate, and medicine. Here, we discussed how these parameters influence the digestive system and showed them through figures and tables. Another fractional model is used on the COVID-19 pandemic. This model is defined by a system of fractional-ODEs including five variables, called S (susceptible), E (exposed), I (infected), Q (quarantined), and R (recovered). The proposed wavelet technique investigates these two models. Here, we express the modeled equation in terms of the Hermite wavelets along with the collocation scheme. Then, using the properties of wavelets, we convert the modeled equation into a system of algebraic equations. We use the Newton–Raphson method to solve these nonlinear algebraic equations. The obtained results are compared with numerical solutions and the Runge–Kutta method (R–K method), which is expressed through tables and graphs. The HWM computational time (consumes less time) is better than that of the R–K method.

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Liu, Xinlin, Viktor Krylov, Su Jun, et al. "Segmentation and identification of spectral and statistical textures for computer medical diagnostics in dermatology." Mathematical Biosciences and Engineering 19, no. 7 (2022): 6923–39. http://dx.doi.org/10.3934/mbe.2022326.

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<abstract> <p>An important component of the computer systems of medical diagnostics in dermatology is the device for recognition of visual images (DRVI), which includes identification and segmentation procedures to build the image of the object for recognition. In this study, the peculiarities of the application of detection, classification and vector-difference approaches for the segmentation of textures of different types in images of dermatological diseases were considered. To increase the quality of segmented images in dermatologic diagnostic systems using a DRVI, an improved vector-difference method for spectral-statistical texture segmentation has been developed. The method is based on the estimation of the number of features and subsequent calculation of a specific texture feature, and it uses wavelets obtained by transforming the graph of the power function at the stage of contour segmentation. Based on the above, the authors developed a modulus for spectral-statistical texture segmentation, which they applied to segment images of psoriatic disease; the Pratt's criterion was used to assess the quality of segmentation. The reliability of the classification of the spectral-statistical texture images was confirmed by using the True Positive Rate (TPR) and False Positive Rate (FPR) metrics calculated on the basis of the confusion matrix. The results of the experimental research confirmed the advantage of the proposed vector-difference method for the segmentation of spectral-statistical textures. The method enables further supplementation of the vector of features at the stage of identification through the use of the most informative features based on characteristic points for different degrees and types of psoriatic disease.</p> </abstract>

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Leontiev, N. A. "Using of Beylkin Wavelet for Speech Recognition." Journal of Physics: Conference Series 2096, no. 1 (2021): 012080. http://dx.doi.org/10.1088/1742-6596/2096/1/012080.

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Abstract This paper describes the application of the Beylkin wavelet for speech segmentation. The problem of speech segmentation in the Yakut language is that there are segmentation difficulties due to the peculiarities of the language. The use of long vowels and double consonants in the Yakut language complicates the correct segmentation of oral speech. For the analysis, the window method of analyzing the energy of the wavelet signal is used. The experience of using different wavelet functions has shown that it is not always possible to accurately find the segment boundaries in some cases. The Scilab package has a large library of wavelets that allows extensive research into their applications in speech recognition. The results of the study show that there are difficulties due to various reasons, one of which is the presence of double sonorant consonants. The graphs of the analysis of doubled sonorant consonants are given.

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LOURENS, TINO, and ROLF P. WÜRTZ. "EXTRACTION AND MATCHING OF SYMBOLIC CONTOUR GRAPHS." International Journal of Pattern Recognition and Artificial Intelligence 17, no. 07 (2003): 1279–302. http://dx.doi.org/10.1142/s0218001403002848.

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We describe an object recognition system based on symbolic contour graphs. The image to be analyzed is transformed into a graph with object corners as vertices and connecting contours as edges. Image corners are determined using a robust multiscale corner detector. Edges are constructed by line-following between corners based on evidence from the multiscale Gabor wavelet transform. Model matching is done by finding subgraph isomorphisms in the image graph. The complexity of the algorithm is reduced by labeling vertices and edges, whereby the choice of labels also makes the recognition system invariant under translation, rotation and scaling. We provide experimental evidence and theoretical arguments that the matching complexity is below O(#V3), and show that the system is competitive with other graph-based matching systems.

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Yang, Weike, and Zheng Tao. "Wavelet Analysis of Bitcoin Price and Twitter-Based Economic Uncertainty Index." Proceedings of Business and Economic Studies 5, no. 5 (2022): 96–101. http://dx.doi.org/10.26689/pbes.v5i5.4414.

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In this paper, we analyze the time-series graphs of Bitcoin price and Twitter-based economic uncertainty index over the past two years and use a wavelet coherence graph to determine their relationship. We found a causal relationship between Bitcoin (BTC) and Twitter-based economic uncertainty (TEU) index in different frequency bands, which would help predict Bitcoin price movements in the future. Our study provides reference to academics and investors.

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Journal articles on the topic 'Graph wavelets'

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