Hyperspherical Model Research Articles

Network Based Feature Extraction Method for Fraud Detection Using Label Propagation

Abstract: Nowadays, judging the current transaction based on user history transactions is an important detection method. However, different users have different transaction behaviors, when all users use the same limit to judge whether the transaction is abnormal, it will result in higher misjudgment for some users. Aiming at the above problems, this paper proposes an individual behavior transaction detection method based on hypersphere model. In this model, considering multiple dimensions of normal historical transaction records, the characteristics of user’s transaction behavior is generated with the trend of transaction. Then, the user optimal risk threshold algorithm is proposed to determine the optimal risk threshold for each user. Finally combining the transaction behavior and the optimal risk threshold, the user behavior benchmark is formed, which is used to construct the multidimensional hypersphere model. On this basis, a mapping method for transforming transaction detection into midpoint in multidimensional space is proposed. The experiment proves that the proposed method is superior to other models, and it is found that the characterization effect of user behavior is related to the frequency of users’ transactions. Applied computing → Secure online transactions; Digital cash; Computing methodologies → Instance-based learning; Rule learning

Dynamic Hypersphere Embedding Scale Against Adversarial Attacks

Learning robust features against adversarial attacks is a challenging task that requires highly complex models, especially on aerial images, because they are subject to environmental and adversarial changes. Embedding hypersphere normalization, along with adversarial settings, causes performance degradation and enables the feature to overlap. To address this, in this article, we propose a dynamic hypersphere embedding scale (DHS) method that remaps the normalized features to a relative scale to learn robust features. The proposed method combines the benefits of hypersphere embedding without scarifying softmax advantages. The DHS aggregates the normalized features and the non-normalized ones. It uses a hypersphere embedding to enforce maximum-margin to the features that yield shorter magnitude and utilizes a dynamic scale to avoid features overlapping in the case of adversarial attacks. We validate the DHS's effectiveness by embedding the adversarial training attacks such as Projected Gradient Descent (PGD), CW, and DeepFool. Empirical experiments revealed that the DHS improves the model performance by 12% when using the PGD attack, with less computation than legacy hypersphere models. Another set of experiments showed that the DHS does not obfuscate the gradient.

Controlled graph neural networks with denoising diffusion for anomaly detection

Leveraging labels in a supervised learning framework as prior knowledge to enhance network anomaly detection has become a trend. Unfortunately, just a few labels are typically available due to the expensive labeling cost. The limited labeled data might not adequately represent the underlying distribution of the data, making the trained model fail to accurately detect anomalies in test data that fall outside the labeled data’s distribution. Recently, data augmentation has been widely used to address this issue. However, general graph data augmentation methods might lead to suboptimal performance when directly applying to network anomaly detection as they might alter graph semantics. In this paper, we provide a denoising diffusion probabilistic model (DDPM)-based Controlled Graph Neural Networks (ConGNN) that can address the problem of insufficient labeled data. In particular, we propose a graph-specific diffusion model-based generator which can inject the characteristics of a reference node into another source node. This generator is adopted to steer the procedure of neighborhood aggregation in GNN to build a controlled GNN for generating augmented data. Based on these augmented data, we present a data-enclosing hypersphere model with our designed consistency regularization term to perform anomaly detection. Extensive experiments demonstrate the superior performance of our model compared to the state-of-the-art baselines.

Solving the geometric reliability index for a case involving multivariate random variables in the original physical space

AbstractAn effective interpretation of the complex reliability theory will promote its application in engineering practice. Based on an algorithm for solving the geometric reliability index for cases involving two or three random variables in the original physical space, an advanced algorithm for multivariate random variables is further developed by using a hypersphere model and inverse Nataf transformation. The main components of the algorithm include the definition of limit state surface, the construction of a hypersphere model, the determination of probability density iso‐contour points, the identification of limit state of these points, and the definition of an actual reliability index. Several typical practical problems associated with two to five variables are analyzed, and the results are compared with those obtained using the first‐order reliability method (FORM) and the copula‐based sampling method (CBSM), thus validating the accuracy of the proposed algorithm. With the help of the powerful and open‐source R language platform, the visualization of a reliability index in low dimensions and the solvability in high dimensions are implemented, which makes the interpretation of reliability theory more intuitive.

Multichannel hyperspherical model for Efimov physics with van der Waals interactions controlled by a Feshbach resonance

Here we present a four-channel model that incorporates a magnetically tunable Feshbach resonance in a system of three atoms that interact via pairwise van der Waals interactions. Our method is designed to model recent experiments where the tunability of the scattering length has been used to study three-body Efimov states, which appear in the limit of a diverging two-body scattering length. Using this model, we calculate three-body adiabatic and effective potential curves and study how the strength (or width) of the Feshbach resonance affects the three-body potential that is connected to the Efimov effect. We find that the position of the repulsive barrier, which has been used to explain the so-called van der Waals universality in broad resonances, is slightly shifted as the narrow resonance limit is approached and that this shift is correlated to the appearance of two avoided crossings in the adiabatic energy landscape. More importantly, the attractive well is markedly shifted upward in energy and is extremely shallow for the narrowest resonance. We argue that this behavior is connected to the breakdown of van der Waals universality for weak (narrow) resonances.

TSI-based hierarchical clustering method and regular-hypersphere model for product quality detection

In modern industry, the production process is always accompanied by a large amount of high-dimensional data, which is always too sparse to provide sufficient information for quality detection. Moreover, traditional quality detection methods show the ambiguity and uncertainty in the clustering process. To overcome these difficulties, an improved hierarchical clustering method and a hypersphere model are proposed respectively in this paper. First, the weights of the minimum spanning tree in each cluster are used to calculate the intra-cluster dispersion and the inter-cluster expansion. Next, to enhance the effectiveness of the clustering process, a threshold-based scheduling index is designed to determine whether the merging process for different clusters continues or not, by which the optimal clustering results can be obtained eventually. Then, the obtained clustering results can be used to calculate the centroid of each cluster, thereby to train the judgment boundary to form a hypersphere. Finally, the hypersphere can be used to detect the product quality. The simulation and experimental results show that, the clustering accuracy is close to 100%, and the accuracy of detection model is superior to 91.83%. Those results are competitive with existing state-of-the-art detection methods in terms of clustering effectiveness and the real-time performance.

An anti-interference method and system for detecting shallow-ground metal based on hyper-sphere model

Based on the research background of shallow-ground metal detection under the environment with the interference of steeling structure,a metal detection method based on the transient electromagnetic method is studied. The test platform is built and verified by experiments. Firstly, the loos model of the coil system is established, and the transfer function with the excitation voltage source as the input signal and the induced voltage of the metal conductor as the output signal is derived. The system design of metal detection based on pulse electromagnetic induction is carried out, and a simple and feasible experimental platform is built according to the demand. Aiming at the signal processing problem of metal detection in a complex environment such as steel structure, a detection algorithm based on a hypersphere model and confidence interval is applied. Finally, the experimental verification is carried out. The results show that the designed system is feasible for metal detection, and the applied signal processing algorithm is effective although interfering by steeling structure inthe environment.

From anomaly detection to open set recognition: Bridging the gap

The classifiers that return compact acceptance regions are crucial for the success in anomaly detection and open set recognition settings since we have to determine and reject the anomalies and samples coming from the unknown classes. This paper introduces novel methods that approximate the class acceptance regions with compact hypersphere models for anomaly detection and open set recognition. As opposed to the other deep hypersphere classifiers, we treat the hypersphere centers as learnable parameters and update them based on the changing deep feature representations. In addition, we propose novel loss terms that are more robust to the noisy labels within the outlier exposure and background datasets. The proposed methods bear similarity to the deep distance metric learning classifiers using the triplet loss function with the exception that the anchors are set to the hypersphere centers which are updated dynamically. The experimental results show that the proposed methods achieve the state-of-the-art accuracies on the majority of the tested datasets in the context of anomaly detection and open set recognition.

A novel fault classification method using reconstructed distance‐based discriminant locality preserving projection for industrial processes

AbstractFault detection and classification is a crucial issue in modern industrial processes for ensuring steady operation and high product quality. The process data collected and stored fully reflect the equipment running state and the production process. Moreover, the extracted nonlinear features can directly affect the effectiveness of the data‐driven fault classification model. In this paper, a novel fault classification method based on nonlinear feature extraction using reconstructed distance‐based discriminant locality preserving projection (RD‐DLPP) is proposed. First, a hypersphere model for each class of data is developed according to the spatial structures and classes information in high‐dimensional space. The hyperspheres are used as indicators to evaluate the discriminatory difficulty of samples. Second, the constraints of the correlations between the k‐nearest neighbour points of the sample and the hypersphere are introduced, which can efficiently reconstruct new measure metrics between the sample and its k‐nearest neighbour points. Finally, an improved fault classification model based on RD‐DLPP is established for the construction of the highly discriminant subspace. The Bayesian decision is then used to classify the samples. The feasibility and efficiency of the proposed method are verified by the Tennessee Eastman process as a case study.

A novel approach to improve network validity using various soft computing techniques

Mobile Adhoc Networks (MANET) in modern research have many optimal energy conservation mechanisms that can be deployed easily and in a faster manner. The routing approaches associated with energy consumption play a dominant role in routing the data packets between the mobile sensor nodes within the range of optimization. However, major challenges associated with energy consumption in MANETs include reduced lifetime of sensor nodes, poor coverage, and throughput. Most methods tend to reduce the interference of data while traversing between the sensor nodes and increase the capacity of the network. This results in delays while transmitting the packets across the network, and this may result in failure of packets being transmitted. To resolve this issue, in this paper, we propose an ant colony optimization combined with a flower pollination algorithm for minimal energy consumption and throughput maximisation in MANETs. This hybrid meta-heuristic model resolves the issues, including delays, poor coverage, and reduced network lifetime. This hybrid model uses the estimation of neighbourhood distance among the nodes for optimal placement of nodes for effective location. The estimation of location is found using a flower pollination algorithm with a levy flight mechanism. The estimation is carried out in a hyper sphere model that helps in finding the coverage area of the sensor nodes. Depending upon the estimation of neighbourhood distance among the sensor nodes, the consumption of energy among the sensor nodes in MANETs is reduced. The simulation was conducted between the proposed hybrid approach and conventional soft computing heuristics, where the results show that the proposed model achieves a higher rate of energy conservation and reduces delay than other methods.

Multiscale One-Class Classification Network for Machine Health Monitoring

Currently, most machine health monitoring methods require labeled abnormal or faulty samples to build a supervised classification model. However, it is difficult and expensive to collect enough faulty samples for accurate and reliable fault detection and diagnosis. To address this issue, we formulate machine health monitoring as a one-class classification problem and propose a new unsupervised health monitoring model named multiscale one-class classification network (MOCN) only relying on normal data without any label information. It consists of two sequential learning modules: a multiscale feature representation learning module to extract effective features from raw one-dimensional vibration signals and a one-classifier training module to build a hypersphere model to contain all normal samples with a minimum radius. Unlike traditional two-step one-class classification methods, both modules in our proposed MOCN are jointly optimized, and therefore it can simultaneously learn compact representations and train a deep one-class classifier. Our proposed MOCN method is evaluated through experiments on three datasets, and experimental results have proved the superiority of our proposed MOCN model compared with several existing methods.

Stellar spectra classification with twin hypersphere model

With the increase of stellar spectra, how to automatically classify these spectra have attracted astronomer's attention. Support Vector Machine (SVM), as a typical classifier, has widely used in stellar spectra classification. Due to its limited performance in various classification problems and higher training time, a model with a pair of hyperspheres named Twin Hypersphere Model (THM), proposed by Peng and Xu, is utilized for stellar spectra classification in this paper. In THM, the samples in one hypersphere is far from another according to the Euclidean distance. The comparative experiments with SVM and Twin Support Vector Machine (TWSVM) on the SDSS datasets shows that the THM model gives the best classification accuracy of 0.8836 for type F, 0.9446 for type G, and 0.9509 for type K, which are better than the classification accuracies of 0.8000, 0.8484, 0.8911 obtained by SVM and 0.8413, 0.8699, 0.9109 obtained by TWSVM. It can be concluded that THM perform better than traditional techniques such as SVM and TWSVM on the K-, F-, G- type stellar spectra classification.

Quick detection of product quality based on clustering hypersphere model

• A k -means clustering method is used to segment the original data for reducing false detection rate. • A mirror sphere is designed as the reference point for speeding up the detection process. • Proposed method based on the clustering hypersphere model can adapt to various shape distributions of the process data. With the rapid development of industry 4.0, intelligent methods for detecting product quality have attached considerable interests. In traditional quality control methods, the process data is required to meet the requirements of independent and identical distribution, which limits the industrial applications. In this paper, a fast product quality detection method based on a clustering hypersphere model is proposed. First, to make the detection boundary more flexible, a simplified classification method based on k -means clustering is designed. Next, the smallest closed hypersphere is built for each subset, and its radius and center are calculated by a sequence minimum optimization algorithm. Then, by exploring the data distribution in the feature space, the accurate original image of the mirror sphere center can be obtained. Finally, compared with the traditional methods, the proposed method can achieve lower false-detection rate and faster detection speed according to the simulation and experimental results.

Preload state detection for precision spindle bearings based on multi-level classification

In this study, a multi-level state classification method based on support vector data description (SVDD) is proposed to detect bearing preload state. Firstly, a three-category classification support vector data description algorithm is proposed to establish the three-state non-aliasing hypersphere model, which can combine the kernel principal component analysis (KPCA) and membership degree. Then, by classifying the first-level training sample model of uniform and non-uniform preload states, the second-level training sample model of non-uniform preload states is established based on SVDD algorithm. Moreover, the balanced multi-label propagation classification criterion is defined that can be used to identify the preload state level based on the training sample model. Finally, a preload state detection system is developed, which can accurately simulate uniform/non-uniform preload states for spindle bearings. The experimental results demonstrate that the proposed algorithm can effectively classify the preload states of spindle bearings with average accuracy higher than 94%.

Face Recognition Based on Videos by Using Convex Hulls

A wide range of face appearance variations can be modeled by using set-based recognition approaches effectively, but computational complexity of current methods is highly dependent on the set and class sizes. This paper introduces new video-based classification methods designed for reducing the required disk space of data samples and speed up the testing process in large-scale face recognition systems. In the proposed method, image sets collected from videos are approximated with kernelized convex hulls and it was shown that it is sufficient to use only the samples that participate in shaping the image set boundaries in this setting. The kernelized support vector data description (SVDD) is used to extract those important samples that form the image set boundaries. Moreover, we show that these kernelized hypersphere models can also be used to approximate image sets for classification purposes. Then, we propose a binary hierarchical decision tree approach to improve the speed of the classification system even more. At last, we introduce a new video database that includes 285 people with 8 videos of each person, since the most popular video data sets used for set-based recognition methods include either a few people, or small number of videos per person. The experimental results on varying sized databases show that the proposed methods greatly improve the testing times of the classification system (we obtained speed-ups to a factor of 20) without a significant drop in accuracies.

Accurate ROI localization and hierarchical hyper-sphere model for finger-vein recognition

Abstract Recently, the finger-vein (FV) trait has attracted substantial attentions for personal recognition in biometric community, and some FV-based biometric systems have been well developed in real applications. However, improving the efficiency of FV recognition over a large-scale database remains a big practical problem. Moreover, unreliable finger-vein region of interest (ROI) localization and venous region enhancement can also heavily degrade the performance of a finger-vein based recognition system in practical scenario. In this paper, we first propose some new methods in FV ROI extraction and enhancement, and then an efficient and powerful hierarchical hyper-sphere model (HHsM) is developed based on granular computing (GrC). For HHsM construction, FV image samples from a given FV database are first converted into atomic granules for primary hyper-sphere granule set generation, and then some coarsened granule sets with different granularity levels are born by hyper-sphere granulation. Considering recognition efficiency improvement, a new hierarchical relationship among the coarsened granule sets is established to structure them level-wisely. Experimental results demonstrate that the proposed methods perform very well in handling ROI extraction, venous region enhancement and FV recognition.

Feature Extraction Based on Support Vector Data Description

Motivated by the improvement of performance and reduction of complexity, feature extraction is referred to one manner of dimensionality reduction. This paper presents a new feature extraction method based on support vector data description (FE-SVDD). First, the proposed method establishes hyper-sphere models for each category of the given data using support vector data description. Second, FE-SVDD calculates the distances between data points and the centers of the hyper-spheres. Finally, the ratios of the distances to the radii of the hyper-spheres are treated as new extracted features. Experimental results on different data sets indicate that FE-SVDD can speed up the procedure of feature extraction and extract the distinctive information of original data.

Multimode Process Fault Detection Based on Local Density Ratio-Weighted Support Vector Data Description

Industrial process fault detection plays an important role for process security, and data-based process monitoring is an effective way to detect fault. Industrial processes typically have multiple operating modes with different data distribution and outliers. This paper proposes a novel multimode process fault detection method based on local density ratio-weighted support vector data description (LDR-wSVDD) to address the multimodal process monitoring with different density and outliers in training samples. By considering both global density distribution and local data structure, this method provides a weight for each training sample based on its density information to make sure that the outliers with lower weight have less influence on the normal sample model. Meanwhile, it maintains the efficiency of SVDD single hypersphere model for multimode processes. The feasibility and validity of the LDR-wSVDD approach for multimode multidensity process monitoring are demonstrated through a numerical example and T...

A label embedding kernel method for multi-view canonical correlation analysis

In this paper, we propose a novel label embedding kernel method (LEKM), which is capable of well capturing intrinsic discriminating structure of samples with the help of class label information. LEKM can efficiently project training samples into a label kernel space according to a label-based unit hypersphere model. However, it is difficult for LEKM to map out-of-sample data into the label kernel space due to the lack of out-of-sample class label information. To solve the problem, we give a simple but effective fuzzy projection strategy (FPS) that can approximately project out-of-sample data into the label kernel space according to similarity principle of sample distribution. With LEKM and FPS, we present a label embedding kernel multi-view canonical correlation analysis (LEKMCCA) algorithm, which can extract nonlinear canonical features with well discriminating power. The algorithm is applied to object, face and handwritten image recognition. Extensive experiments on several real-world image datasets have demonstrated the superior performance of the algorithm.

Hyperspherical three-body model calculation for the bound 3,1S-states of Coulombic systems

In this paper, hyperspherical three-body model formalism has been applied for the calculation of energies of the low-lying bound [Formula: see text]-states of neutral helium and helium like Coulombic three-body systems having nuclear charge (z) in the range [Formula: see text]. Energies of [Formula: see text]-states are also calculated for those having nuclear charge in the range [Formula: see text]. The calculation of the coupling potential matrix elements of the two-body potentials has been simplified by the use of Raynal–Revai Coefficients (RRC). The three-body wave function in the Schrödinger equation when expanded in terms of hyperspherical harmonics (HH), leads to an infinite set of coupled differential equation (CDE) which for practical purposes is truncated to a finite set and the truncated set of CDE’s are solved by renormalized Numerov method (RNM) to get the energy (E). The calculated energy is compared with the ones of the literature.