Spectral Partitioning Research Articles

Palm vein template protection scheme for resisting similarity attack

Palm vein recognition technology has rapidly developed due to its high confidentiality and the advantages of liveness detection. Various palm vein template protection methods have emerged to safeguard palm vein data from theft and attack. To fulfill the performance loss requirement of the ideal biometric template protection scheme, these methods make the distribution of the original palm vein data and the palm vein protection templates have a strong distance preserving property (similarity preserving), making it difficult to defend against similarity attack (SA). To address these risks and prevent palm vein data leakage, we propose a Nonlinear Spectral Hashing (NSH) method for palm vein template protection. To obtain palm vein templates with both performance and security, the method first performs random projection on palm vein data to obtain revocable and unlinkable palm vein features. Subsequently, through spectral graph partitioning, it achieves mapping with a preserved similarity structure for palm veins, avoiding excessive performance loss. The method then employs a nonlinear activation function to alter the distribution of palm vein templates with large post-mapping differences, resulting in a uniform distribution of inter-class distances for palm vein data. By reducing the distance-preserving properties, the method enhances protection against similarity attacks. Finally, a sign function is applied to obtain non-invertible binary palm vein templates. Experimental evaluations on the public Tongji University palm vein database assess the method's non-invertibility, revocability, unlinkability, resistance to similarity attack, and recognition performance. The results indicate an Equal Error Rate (EER) of 0.50 %, demonstrating the method's ability to maintain good recognition performance while ensuring high security.

Spectral Partition Problems with Volume and Inclusion Constraints

Spectral Partition Problems with Volume and Inclusion Constraints

Partial recovery and weak consistency in the non-uniform hypergraph stochastic block model

Abstract We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions. When the random hypergraph has bounded expected degrees, we provide a spectral algorithm that outputs a partition with at least a $\gamma$ fraction of the vertices classified correctly, where $\gamma \in (0.5,1)$ depends on the signal-to-noise ratio (SNR) of the model. When the SNR grows slowly as the number of vertices goes to infinity, our algorithm achieves weak consistency, which improves the previous results in Ghoshdastidar and Dukkipati ((2017) Ann. Stat.45(1) 289–315.) for non-uniform HSBMs. Our spectral algorithm consists of three major steps: (1) Hyperedge selection: select hyperedges of certain sizes to provide the maximal signal-to-noise ratio for the induced sub-hypergraph; (2) Spectral partition: construct a regularised adjacency matrix and obtain an approximate partition based on singular vectors; (3) Correction and merging: incorporate the hyperedge information from adjacency tensors to upgrade the error rate guarantee. The theoretical analysis of our algorithm relies on the concentration and regularisation of the adjacency matrix for sparse non-uniform random hypergraphs, which can be of independent interest.

Spectral Bipartition via Gap Cut on DNA Sequences

Deoxyribonucleic Acid (DNA) and graph partitioning are two distinct fields of study which can be linked in the structure of biological networks. Graph partitioning has been extensively studied but not its application in the biological field. This research explored on the application of spectral graph partitioning in DNA splicing, aiming to simulate the cleavage of DNA by performing spectral bipartition on DNA sequences in a DNA splicing system. This research incorporates Fiedler theory and algebraic graph theory, which are commonly utilized in network analysis and the analysis of graph connectivity. Some DNA sequences of even length are selected and expressed in graphical representations. The adjacency matrix, Laplacian matrix, and degree matrix are computed from the graphs, as well as the Fiedler value and Fiedler vector associated with the graphs. Gap cut is used as a method of spectral bipartition which produces two partitions of DNA sequence of unequal lengths. The generalizations of gap cut on DNA sequences of even length are provided as lemmas and theorem.

Co-Clustering by Directly Solving Bipartite Spectral Graph Partitioning.

Bipartite spectral graph partitioning (BSGP) method as a co-clustering method, has been widely used in document clustering, which simultaneously clusters documents and words by making full use of the duality between documents and words. It consists of two steps: 1) graph construction and 2) singular value decomposition on the bipartite graph to compute a continuous cluster assignment matrix, followed by post-processing to get the discrete solution. However, the generated graph is unstructured and fixed. It heavily relies on the quality of the graph construction. Moreover, the two-stage process may deviate from directly solving the primal problem. In order to tackle these defects, a novel bipartite graph partitioning method is proposed to learn a bipartite graph with exactly c connected components (c is the number of clusters), which can obtain clustering results directly. Furthermore, it is experimentally and theoretically proved that the solution of the proposed model is the discrete solution of the primal BSGP problem for a special situation. Experimental results on synthetic and real-world datasets exhibit the superiority of the proposed method.

Wind-Sea and Swell Climate in the Black and Azov Seas, Based on 42-Year Spectral Wave Hindcast

Long-term wave climates of the Black and Azov Seas are widely assessed based on the bulk wave parameters of the mixed sea. However, studies based on spectral wave partitions are rarely documented. Assessment of the wave climate based on the individual wave systems provides a more reliable description of the sea states' characteristics and the variability in the long-term wave climate. For instance, the wind-sea climate may reflect a real change in the local climate. However, local change in swell characteristics may not necessarily reflect a change in the local climate, and it can locally influence the mixed sea climate variability. This study assessed the spatial distributions of the long-term averages and maxima of mixed seas, wind-sea, and swell partitions at annual and seasonal scales. The contributions of wind-sea and swell partitions to the mixed-sea were computed, and their spatial and temporal variability was also assessed for overall and extreme sea state conditions. Finally, the occurrence in main wave systems' directions and occurrence of crossing, opposing, and following wind-sea and swell interactions were computed. The wind-sea contribution to the mixed-sea exceeds 70 % in all Black Sea and >95 % in the Azov Sea. The swells are more dominant on the Northeastern and Northwestern Black Sea basins. Thus, the results show spatial and temporal variability in the wind-sea climate close to the mixed sea but largely different compared to the swell climate. The inter-annual trends in the swell partitions and wind-sea are inversed at some locations.

A Novel Sample Generation Method for Deep Learning Lithological Mapping with Airborne TASI Hyperspectral Data in Northern Liuyuan, Gansu, China

High-resolution and thermal infrared hyperspectral data acquired from the Thermal Infrared Airborne Spectrographic Imager (TASI) have been recognized as efficient tools in geology, demonstrating significant potential for rock discernment. Deep learning (DL), as an advanced technology, has driven substantial advancements in lithological mapping by automatically extracting high-level semantic features from images to enhance recognition accuracy. However, gathering sufficient high-quality lithological samples for model training is challenging in many scenarios, posing limitations for data-driven DL approaches. Moreover, existing sample collection approaches are plagued by limited verifiability, subjective bias, and variation in the spectra of the same class at different locations. To tackle these challenges, a novel sample generation method called multi-lithology spectra sample selection (MLS3) is first employed. This method involves multiple steps: multiple spectra extraction, spectra combination and optimization, lithological type identification, and sample selection. In this study, the TASI hyperspectral data collected from the Liuyuan area in Gansu Province, China, were used as experimental data. Samples generated based on MLS3 were fed into five typical DL models, including two-dimensional convolutional neural network (2D-CNN), hybrid spectral CNN (HybridSN), multiscale residual network (MSRN), spectral-spatial residual network (SSRN), and spectral partitioning residual network (SPRN) for lithological mapping. Among these models, the accuracy of the SPRN reaches 84.03%, outperforming the other algorithms. Furthermore, MLS3 demonstrates superior performance, achieving an overall accuracy of 2.25–6.96% higher than other sample collection methods when SPRN is used as the DL framework. In general, MLS3 enables both the quantity and quality of samples, providing inspiration for the application of DL to hyperspectral lithological mapping.

Wave spectral partitioning for the SWIM spectrometer based on the wave age and parameter optimization method

The paper proposes a wave spectral partitioning method for the surface waves investigation and monitoring (SWIM) spectrometer based on the wave age and parameter optimization (WA-PO) method. The wave age criterion is a way to identify waves as wind waves or swells, and parameter optimization methods enable the modeling of wave spectra. The combination of the two can use the spectrum models to fit the SWIM spectra based on clarifying whether the spectrum models belong to wind waves or swells, which achieves spectral partitioning. The WA-PO method consists of four steps: peaks region dividing, spectral peaks searching, objective function constructing, and model parameters optimizing. The results show that compared with the partition products provided by the SWIM, the partition parameters obtained from the WA-PO method are closer to those of the Integrated Ocean Waves for Geophysical and other Applications (IOWAGA) numerical hindcast dataset developed from the WAVEWATCH III (WW3). The WA-PO method can prevent over-partitioning of the wave spectra and detect wind-wave components hidden in the swell partition.

Acoustic fish community in the Madeira Archipelago (North Atlantic Ocean): Characterization of sound diversity and daily patterns

Marine ecosystems are increasingly subjected to anthropogenic pressures, which demands urgent monitoring plans. Understanding soundscapes can offer unique insights into the ocean status providing important information and revealing different sounds and their sources. Fishes can be prominent soundscape contributors, making passive acoustic monitoring (PAM) a potential tool to detect the presence of vocal fish species and to monitor changes in biodiversity. The major goal of this research was to provide a first reference of the marine soundscapes of the Madeira Archipelago focusing on fish sounds, as a basis for a long-term PAM program. Based on the literature, 102 potentially vocal and 35 vocal fish species were identified. Additionally 43 putative fish sound types were detected in audio recordings from two marine protected areas (MPAs) in the Archipelago: the Garajau MPA and the Desertas MPA. The Garajau MPA exhibited higher fish vocal activity, a greater variety of putative fish sound types and higher fish sound diversity. Lower abundance of sounds was found at night at both MPAs. Acoustic activity revealed a clear distinction between diurnal and nocturnal fish groups and demonstrated daily patterns of fish sound activity, suggesting temporal and spectral partitioning of the acoustic space. Pomacentridae species were proposed as candidates for some of the dominant sound types detected during the day, while scorpionfishes (Scorpaena spp.) were proposed as sources for some of the dominant nocturnal fish sounds. This study provides an important baseline about this community acoustic behaviour and is a valuable steppingstone for future non-invasive and cost-effective monitoring programs in Madeira.

The equivalences of community detection methods for bipartite networks

Investigating the community structures of bipartite networks is a frequent topic of discussion in the ecological and social fields. The most widely used methods, as proposed by numerous academics from varying perspectives, include spectral graph partitioning, modularity, non-negative matrix factorization, and stochastic block model. In this paper, we demonstrate three equivalences among these four methods. i) Both Dhillon spectral graph partitioning and Barber modularity clustering are equivalent to solving for the matrix's left and right singular vectors after relaxing the discrete constraints. ii) The non-negative matrix factorization clustering is equivalent to the Dhillon spectral graph partitioning. iii) The bipartite stochastic block model is equivalent to the constraint-based NMF that uses K-L divergence as its cost function. These equivalences, obtained through rigorous mathematical derivations, will aid in the future development of efficient algorithms for community detection in bipartite networks.

A worldwide coastal analysis of the climate wave systems

Wind generated waves of a sea state are generally the result of the superposition of wind sea and swells, making the frequency-direction wave energy distribution crucial for comprehending this behavior. Wave spectral partitioning methods provide groups of waves with similar characteristics, thus they have been usually applied to identify wind sea and swell. In addition, several swells can coexist in a sea state. This study develops a method to estimate the wave systems and analyze their characteristics over the coast worldwide using 32year (1989-2020) historical information and more than 10.000 locations. A wave system is considered as the long-term climate conditions prevailing over a frequency-direction wave energy area collecting similar environmental and physical characteristics. The method is applied for the hourly time series of the directional wave spectra. First, the watershed clustering algorithm is used and the partitions found are classified as wind sea or swells based on a wave age criterion. The information obtained from the swell spectral partitions is then used to estimate the probability of their occurrence within specific frequency-direction bins and the clustering algorithm is applied anew to this population in order to identify the number of significant long-term climate wave systems locally and their characteristics. Outcomes reveal that on average swells coexist with wind sea in approximately 70% of the global coast, whereas about 25% is predominantly dominated by pure swells and the wind sea dominates only in the 5%. Only the 2% of the global coast line presents one swell wave system. About 50% of the global coastal locations exhibit three and four, whereas the 15% presents two swell wave systems. The analysis shows that about 30% of the coastal locations present at least five swell wave systems, mostly on Pacific islands and enclosed seas.

Satellite wave 2D spectrum partition based on the PI-vit-GAN(physically-informed ViT-GAN) method

The abundant spectral data provided by satellite technology are crucial for interpreting the complex marine environment, and the effective and accurate analysis of these data is particularly important for coastal engineering. In this regard, this study proposes a Physically Informed ViT-GAN (PI-ViT-GAN) automatic partitioning method, based on CFOSAT satellite wave spectrum data. Specifically, the model consists of a generator and discriminator. The generator utilizes a contrastive learning strategy as pretraining and through the self-attention mechanism of the ViT model, it focuses on key parts of the spectrum to extract wave group features and wave element parameters. Partitioning-head joint training realizes the output of wave group partition element indices. Subsequently, the discriminator uses the wave group features and a parametric model for spectrum reconstruction and computes the error with the original observed spectrum to evaluate the partition and reconstruction effects. Additionally, this model incorporates two physically corrected functions, wave system classification loss and merging loss, based on the wave age criterion, thereby guiding the training process, and enhancing model efficiency. The results indicate that the reconstructed theoretical spectrum, obtained through the utilization of this method, aligns well with the original sea wave spectrum, demonstrating a precision superior to the spectral partitioning product of CFOSAT's own SWIM. Combining the robust learning capability of the transformer and the regularization of physical prior knowledge, this model can achieve precise, low-cost automated analysis of satellite wave spectra, providing a new scalable method for big data analysis in marine and coastal engineering.

Historical change and variability of spectral wind wave climate in the New York Bight

AbstractThe sea surface is a complex superposition of various wave systems, thus, analysing their characteristics provides more meaningful and accurate information compared to conventional integrated wave parameter approaches. The concept of wave family—a population of wave systems within a specific region in spectral space—provides the foundation for investigating the long‐term climatology of wave systems. This study adopts a wave family approach to investigate the climatology of wave systems and their long‐term climate controllers at the location of a coastal buoy in the western North Atlantic Ocean. The frequency‐direction wave spectrum is constructed for a historical 20‐year period by applying the Maximum Entropy Method on directional buoy measurements acquired from the National Data Buoy Center station 44025, located in the New York Bight. The two‐dimensional wave spectrum is partitioned, using the watershed partitioning algorithm, and the occurrence distribution of spectral partitions is calculated to identify predominant wave families. Each of the four identified wave families carries unique characteristics based on spatial formation and duration of propagation prior to arrival at the study site. The study quantifies long‐term trends and variability in wave height of each wave family on a monthly, seasonal and annual level, and their relative importance to the bulk sea‐state climatology. The nexus between the bulk or wave family seasonal wave heights and the climate indices is quantified to identify the wave climate controllers in the study area.

A bivariate spectral linear partition method for solving nonlinear evolution equations

This work develops a method for solving nonlinear evolution equations. The method, termed a bivariate spectral linear partition method (BSLPM), combines the Chebyshev spectral collocation method, bivariate Lagrange interpolation, and a linear partition technique as an underlying linearization method. It is developed for an th‐order nonlinear differential equation and then used to solve three known evolution problems. The results are compared with known exact solutions from literature. The method's applicability, reliability, and accuracy are confirmed by the congruence between the numerical and exact solutions. Tables, error graphs, and convergence graphs were generated using MATLAB (R2015a), to confirm the order of accuracy of the method and verify its convergence. The performance of the method is also observed against other methods performing well in these types of differential equations and is found to be comparable in terms of accuracy. The proposed method is also efficient as it uses minimal computation time.

DiGRASS: Di rected Gra ph S pectral S parsification via Spectrum-Preserving Symmetrization

Recent spectral graph sparsification research aims to construct ultra-sparse subgraphs for preserving the original graph spectral (structural) properties, such as the first few Laplacian eigenvalues and eigenvectors, which has led to the development of a variety of nearly-linear time numerical and graph algorithms. However, there is very limited progress for spectral sparsification of directed graphs. In this work, we prove the existence of nearly-linear-sized spectral sparsifiers for directed graphs under certain conditions. Furthermore, we introduce a practically-efficient spectral algorithm (diGRASS) for sparsifying real-world, large-scale directed graphs leveraging spectral matrix perturbation analysis. The proposed method has been evaluated using a variety of directed graphs obtained from real-world applications, showing promising results for solving directed graph Laplacians, spectral partitioning of directed graphs, and approximately computing (personalized) PageRank vectors.

Deep Spectral Meshes: Multi-Frequency Facial Mesh Processing with Graph Neural Networks

With the rising popularity of virtual worlds, the importance of data-driven parametric models of 3D meshes has grown rapidly. Numerous applications, such as computer vision, procedural generation, and mesh editing, vastly rely on these models. However, current approaches do not allow for independent editing of deformations at different frequency levels. They also do not benefit from representing deformations at different frequencies with dedicated representations, which would better expose their properties and improve the generated meshes’ geometric and perceptual quality. In this work, spectral meshes are introduced as a method to decompose mesh deformations into low-frequency and high-frequency deformations. These features of low- and high-frequency deformations are used for representation learning with graph convolutional networks. A parametric model for 3D facial mesh synthesis is built upon the proposed framework, exposing user parameters that control disentangled high- and low-frequency deformations. Independent control of deformations at different frequencies and generation of plausible synthetic examples are mutually exclusive objectives. A Conditioning Factor is introduced to leverage these objectives. Our model takes further advantage of spectral partitioning by representing different frequency levels with disparate, more suitable representations. Low frequencies are represented with standardised Euclidean coordinates, and high frequencies with a normalised deformation representation (DR). This paper investigates applications of our proposed approach in mesh reconstruction, mesh interpolation, and multi-frequency editing. It is demonstrated that our method improves the overall quality of generated meshes on most datasets when considering both the L1 norm and perceptual Dihedral Angle Mesh Error (DAME) metrics.

Investigation of multimodal wave climate using spectral partitioning and wave system tracking algorithms

Typically, ocean waves comprise both wind sea and swell systems, each exhibiting different characteristics in terms of decay, propagation, and their impact on engineering. Distinguishing between wind sea and short/long swell systems is critical for both scientific research and engineering applications, such as climate assessment, harbor agitation, and structural design, which has led to a growing interest in studies of multimodal wave climate.This study investigates the origin and characteristics of multimodal waves based on spectral partitioning and wave system tracking, taking Sri Lanka in the North Indian Ocean as a case study. The data is generated from the spectral wave model WAVEWATCH III. Results show that the wave systems mainly originate from the southwest monsoon, northeast monsoon, southeast trade winds, and southern storm belt. Tropical cyclones can occasionally contribute to multimodal waves. Subsequently, four spectral zones of wave origins are defined according to the joint probability density distribution of partitioned mean wave directions and peak periods estimated by a kernel function. Storm belt waves are responsible for over 36 % of the total wave systems. Finally, two ways of describing wave climate based on the partitioned bulk wave parameters are compared. One offers a thorough understanding of the wave climate from the perspective of wave origin; however, it loses the combined information of wave systems. The other method, while lacking a guaranteed coherence between the wave systems over time, preserves the crucial combined information of wave systems, which is useful in generating a reduced dataset comprising representative cases.

A parallel computing framework for large-scale microscopic traffic simulation based on spectral partitioning

This paper introduces a parallel computing framework based on the Spectral Partitioning (SP) method designed to enhance the computational efficiency of large-scale microscopic traffic simulation (LSMTS). The framework employs the SP method to partition road networks, taking into account vehicle information and road information as constitutive components for node weight determination. Micro-simulation relies on vehicle information from both preceding and following vehicles to accurately infer the operational states of a vehicle. However, network partitioning can disrupt the flow of vehicle information, resulting in its loss. To address this, the proposed framework incorporates a boundary transmission method to ensure simulation accuracy and precision. This study presents an improved SP (iSP) method tailored for LSMTS, further enhancing the partitioning results achieved through the SP method. Lastly, the framework's validity is confirmed through road network experiments of varying scales and densities, with comparisons made to existing parallel simulation methods. The results demonstrate that the framework significantly reduces the execution time of simulation tasks while maintaining a high level of load balance and minimizing communication overhead.

“Intelligent Heuristics Are the Future of Computing”

Back in 1988, the partial game trees explored by computer chess programs were among the largest search structures in real-world computing. Because the game tree is too large to be fully evaluated, chess programs must make heuristic strategic decisions based on partial information, making it an illustrative subject for teaching AI search. In one of his lectures that year on AI search for games and puzzles, Professor Hans Berliner—a pioneer of computer chess programs 1 —stated: As a student in the field of the theory of computation, I was naturally perplexed but fascinated by this perspective. I had been trained to believe that “Algorithms and computational complexity theory are the foundation of computer science.” However, as it happens, my attempts to understand heuristics in computing have subsequently played a significant role in my career as a theoretical computer scientist. I have come to realize that Berliner’s postulation is a far-reaching worldview, particularly in the age of big, rich, complex, and multifaceted data and models, when computing has ubiquitous interactions with science, engineering, humanity, and society. In this article, 2 I will share some of my experiences on the subject of heuristics in computing, presenting examples of theoretical attempts to understand the behavior of heuristics on real data, as well as efforts to design practical heuristics with desirable theoretical characterizations. My hope is that these theoretical insights from past heuristics—such as spectral partitioning, multilevel methods, evolutionary algorithms, and simplex methods—can shed light on and further inspire a deeper understanding of the current and future techniques in AI and data mining.

Numerical Investigation of Hydrodynamic Responses of a Moored Liquefied Natural Gas Ship under Multimodal Waves

Ocean waves typically consist of wind, sea, and swell trains. Conventionally, the treatment of multimodal waves has been to conceptualize them as a unified wave system and employ a single set of aggregate wave parameters for the representation of their collective characteristics. Nevertheless, a better understanding of multimodal waves is important when analyzing the interactions between waves and moored vessels, considering the pronounced sensitivity of a ship’s responses to wave periods and directions. Many spectral partitioning methodologies have been proposed to discern and segregate multimodal waves into two or more distinct wave systems, providing fundamental information for investigating moored ship responses to multimodal waves. Utilizing the wave spectra data acquired from a specific water region in South America, a comprehensive numerical study was undertaken by employing the specialized ocean engineering software ORCAFLEX 11.2e. The primary objective of this investigation is to analyze the dynamic response of a moored liquefied natural gas (LNG) vessel in ballast conditions subjected to waves defined by distinct wave identification methods (i.e., overall method and spectral partition method). Furthermore, the waves are categorized into two groups: beam waves and head waves. Results show that beam waves induce a substantial ship response, whereas head waves pose a comparatively lower risk to maritime vessels. Furthermore, the conventional overall wave approach tends to neglect the roll motion generated by multimodal waves when they propagate as head waves. Nevertheless, when the wave direction aligns with beam waves, the overall wave approach tends to produce the roll motion. These findings indicate the importance of considering multimodal waves in quay layout and mooring configuration design.