Dimensional Vector Research Articles

Conic cancellation laws and some applications in set optimization

We discuss, on finite and infinite dimensional normed vector spaces, some versions of Rådström cancellation law (or lemma) that are suited for applications to set optimization problems. In this sense, we call our results ‘conic’ variants of the celebrated result of Rådström, since they involve the presence of an ordering cone on the underlying space. Several adaptations to this context of some topological properties of sets are studied and some applications to subdifferential calculus associated to set-valued maps and to necessary optimality conditions for constrained set optimization problems are given. Finally, a stability problem is considered.

Modal synthesis of observers of state variables of ship dynamical systems

The purpose of the work is to increase the information content of ship control systems through the use of dynamic observers, which are, in essence, mathematical information sensors and allow you to fully restore the vector of state variables of the object model with high accuracy by measuring the output vector of a smaller dimension. An algorithm for the synthesis of observers based on the modal method of parametric evaluation of their model is proposed. It provides obtaining the parameters of the regulator according to the given spectra of the matrices of the state of the observed system and the object by means of the Control Toolbox of the MATLAB computing environment. The use of the modal method (subject to the conditions of observability and controllability) guarantees the stability of observers, which allows them to be used for stable and unstable observed objects and systems. The algorithm of modal synthesis of observers is suitable for increasing the information content of a wide range of ship dynamic systems and, above all, control systems for ship energy complexes and their components. These include autopilots, control systems for ship power plants and their elements, dynamic complexes of satellite and inertial navigation systems and positioning of moving objects in remote control conditions, monitoring and safety tools, identifiers, etc. It has been shown that in the conditions of digital transformation, the use of observers dramatically improves the quality and reduces the time for modeling the dynamics of ship systems and energy complexes operated under conditions of external disturbances, which makes it possible to improve the algorithms for estimating state variables of a class of autonomous objects modeled by nonlinear equations that allow the transition in the working area to quasi linear models with time-invariant parameters. The proposed algorithm is demonstrated by the example of the synthesis of a three-dimensional observer for the control system of a supertanker with deadweight of 150 thousand tons. The simulation of the control object is performed with an input signal of triangular shape, which most fully corresponds to the real control signal, and it is implemented in the form of a program compiled in MATLAB codes. The obtained values of state variables and errors of their recovery correspond to the specified speed and the required stability of the control system.

Content-based image retrieval for medical diagnosis using fuzzy clustering and deep learning

Brain tumors are one of the most threatening causes of death worldwide. Neuroradiologists widely use Magnetic Resonance Imaging as a golden standard non-invasive imaging method for diagnosing Glioma grades. Brain tumor diagnosis based on radiology images is tedious and highly subjective to intra and inter-observer variability; it adversely affects therapeutic planning. Better medical treatment can be provided relating to similar past cases if relevant images are retrieved from an extensive medical image database. Content-Based Image Retrieval systems are potent image tools for dealing with such massive datasets. In a CBIR system, accurate classification and retrieval of similar pathological images can be effectively automated by utilising Convolutional Neural Network-based feature extraction methods. This paper presents a Content-Based Medical Image Retrieval pipeline on a medical domain using the CNN model for feature extraction and the clustering method used to index the feature map database. The proposed system applies a Multi-level Gain-based feature selection to reduce the dimensionality of the feature vectors obtained from the pre-trained CNN models. The experiment follows five-fold cross-validation on BraTS 2018 and 2020 datasets. The proposed system achieves state-of-the-art MRI brain image retrieval performance with a mean Average Precision and Precision@10 of 98.15% and 97.62%, respectively. The results prove the proposed method’s effectiveness and validate its clinical application.

On inference in high-dimensional logistic regression models with separated data

Summary Direct use of the likelihood function typically produces severely biased estimates when the dimension of the parameter vector is large relative to the effective sample size. With linearly separable data generated from a logistic regression model, the loglikelihood function asymptotes and the maximum likelihood estimator does not exist. We show that an exact analysis for each regression coefficient produces half-infinite confidence sets for some parameters when the data are separable. Such conclusions are not vacuous, but an honest portrayal of the limitations of the data. Finite confidence sets are only achievable when additional, perhaps implicit, assumptions are made. Under a notional double-asymptotic regime in which the dimension of the logistic coefficient vector increases with the sample size, the present paper considers the implications of enforcing a natural constraint on the vector of logistic transformed probabilities. We derive a relationship between the logistic coefficients and a notional parameter obtained as a probability limit of an ordinary least-squares estimator. The latter exists even when the data are separable. Consistency is ascertained under weak conditions on the design matrix.

Dynamic Shrinkage Priors for Large Time-Varying Parameter Regressions Using Scalable Markov Chain Monte Carlo Methods.

Time-varying parameter (TVP) regression models can involve a huge number of coefficients. Careful prior elicitation is required to yield sensible posterior and predictive inferences. In addition, the computational demands of Markov Chain Monte Carlo (MCMC) methods mean their use is limited to the case where the number of predictors is not too large. In light of these two concerns, this paper proposes a new dynamic shrinkage prior which reflects the empirical regularity that TVPs are typically sparse (i.e. time variation may occur only episodically and only for some of the coefficients). A scalable MCMC algorithm is developed which is capable of handling very high dimensional TVP regressions or TVP Vector Autoregressions. In an exercise using artificial data we demonstrate the accuracy and computational efficiency of our methods. In an application involving the term structure of interest rates in the eurozone, we find our dynamic shrinkage prior to effectively pick out small amounts of parameter change and our methods to forecast well.

GE-DDRL: Graph Embedding and Deep Distributional Reinforcement Learning for Reliable Shortest Path: A Universal and Scale Free Solution

This paper studies the reliable shortest path (RSP) problem in stochastic transportation networks. State-of-the-art RSP solutions usually target one specific RSP problem; moreover, the corresponding algorithm’s computational complexity scales at least linearly with the size of the underlying transportation network. While in this paper, we propose a graph embedding and deep distributional reinforcement learning (GE-DDRL) method, which serves as a universal and scale-free solution to the RSP problem. GE-DDRL uses deep distributional reinforcement learning (DDRL) to estimate the full travel-time distribution of a given routing policy, and improves the given routing policy with the generalized policy iteration (GPI) scheme. Further, in order to achieve the generalization ability to new destination nodes, we employ one of the canonical graph embedding techniques (Skip-Gram) to compress the nodes’ representation into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$</tex-math> </inline-formula> -dimensional real-valued vectors. With the properly compressed node features, GE-DDRL is able to generalize its estimation of the routing policy’s travel-time distribution to untrained destination nodes, and hence achieve the ‘all-to-all’ navigation functionality. To the best of our knowledge, GE-DDRL serves as the first RSP planner, which applies simultaneously to almost all RSP objectives and in the meanwhile, is scale free with the size of the transportation network in terms of the online decision-making time and memory complexity. Experimental results and comparisons with state of the arts show the efficacy and efficiency of GE-DDRL in a range of transportation networks.

Research on Feature Extraction of Underwater Acoustic Target Radiation Noise Based on Machine Learning Algorithm

Underwater acoustic target recognition is a very important technology in the field of underwater acoustics, with great economic and military value. Feature extraction technology for underwater acoustic target radiation noise signals is the key to achieving acoustic target recognition. This study aims at the feature extraction task of acoustic targets and extracts 10 types of 252-dimensional feature vectors from three domains: time domain, frequency domain, and auditory domain. Through 7 machine learning algorithms for classification and recognition experiments, the experimental results show that the recognition performance of the ensemble classifier is much better than that of a single classifier. For different types of features, this study combines three ensemble learning algorithms and feature selection algorithms to select the original 252-dimensional features. The feature selection experiment shows that the wrapper feature selection algorithm has the best effect, and the feature vector dimension can be reduced to 40 dimensions. The recognition accuracy rate is not less than 92.8%, which provides feature extraction guidance for acoustic target recognition based on feature extraction.

Research on tool condition monitoring (TCM) using a novel unsupervised deep neural network (DNN)

In order to improve the recognition precision and accuracy of tool wear monitoring, an unsupervised deep neural network (DNN) based on stack denoising autoencoder (SDA) is proposed. After feature extraction and selection, the stack denoising automatic coding network reduces the dimensionality of the feature vector. On this basis, principal component analysis (PCA) and T-distributed random neighbor embedding (t-SNE) are used to reduce the dimensionality of the features twice, and finally a simple two-dimensional feature matrix is obtained. Finally, the deep neural network model of SDA is established by adding SoftMax regression layer, and the tool wear monitoring results are taken as new labeled data, and the deep neural network parameters are fine-tuned by secondary backpropagation. The experimental results show that the proposed method can learn adaptively and obtain effective feature expression, and the tool wear state recognition results are highly accurate. The proposed method can effectively identify the tool wear state.

Application of Artificial Neural Networks for Identification of Lithofacies by Processing of Core Drilling Data

Identifying lithofacies types from core drilling data presents significant challenges, especially given the limited number of physical drilling characteristics available for analysis. Traditional machine learning methods often face issues with poor training and testing due to these limitations. Addressing this, we propose a new method for processing core drilling data to improve the accuracy of deep artificial neural networks (DANNs) in lithofacies recognition. Our approach transforms torque, weight on bit (WOB), and rotational speed data into three square matrices, creating a novel three-channel lithofacies image. This method allows for the application of DANNs by converting the complex lithofacies recognition task into a more standard image recognition problem. The developed method dramatically increases the input vector dimensions, enhancing the richness of the data input. The validation of results revealed that the DANN model trained for merely 3000 iterations successfully predicted lithofacies types of all eight testing samples in a mere 2.85 ms, showcasing superior accuracy. The innovative drilling data processing method proposed in this study enables DANNs to identify lithofacies with increased speed and accuracy. This offers a new direction for other DANNs utilizing drilling data.

Test for diagonal symmetry in high dimension

Utilizing the energy distance and energy statistics, Sang and Dang (2020) proposed a test statistic as a difference of two U-statistics for the diagonal symmetry test of a p-vector X. Under the regular setting where the dimensionality of the random vector is fixed, the test statistic is a degenerate U-statistic and hence converges to a mixture of chi-squared distributions. In this paper, we test the diagonal symmetry of X in a more realistic setting where both the sample size and the dimensionality are diverging to infinity. Our theoretical results reveal that the degenerate U-statistic admits a central limit theorem in the high dimensional setting and the accuracy of normal approximation can increase with dimensionality. We then construct a powerful and consistent test for the diagonal symmetry problem based on the asymptotic normality. Simulation studies are conducted to illustrate the performances of the test.

The application of fault diagnosis techniques and monitoring methods in building electrical systems – based on ELM algorithm

The reliability of modern building electrical systems are receiving increasing attention as they become more intelligent and complex. As the majority of building electrical systems use neutral point grounding, earth faults or short circuits can get worse over time and damage both the distribution system and the electrical equipment. To this end, the corresponding three phases and four categories, namely three-phase voltage, three-phase current after fault, three-phase voltage distortion rate, three-phase current distortion rate, a total of 12 dimensional fault feature vectors and 10 fault simulation types, were summarised and extracted in conjunction with the actual operating conditions of the system. Using traditional fault identification ideas and neural network algorithm as reference, a 12-dimensional fault feature vector is used as the model input to construct a building electrical fault diagnosis and detection model based on ELM algorithm. Results showed that the ELM-based model’s classification accuracy for this experimental sample was 97.56 %, its AUC was 0.92, and its RMSE was 0.3521. These figures were higher than the classification accuracy and performance of the BP algorithm and GA-BP algorithm fault diagnosis models, and they also demonstrate better robustness and generalizability. The model also has a 97.27 % correct rate in fault discrimination, while the computation time is only 0.201 s, and its fault identification and diagnosis speed is faster than other algorithmic models. At the same time, this research model has a good fault monitoring accuracy of up to 98.6 % for building electrical systems. The research can provide a more sensitive, accurate and rapid fault monitoring method for the current building electrical system. It also improves the reliability of the building electrical system in a complex environment and achieves better protection of the system. This has a certain significance for the development of the building electrical industry.

Disentangling the latent space of GANs for semantic face editing.

Disentanglement research is a critical and important issue in the field of image editing. In order to perform disentangled editing on images generated by generative models, this paper presents an unsupervised, model-agnostic, two-stage trained editing framework. This work addresses the problem of discovering interpretable, disentangled directions of edited image attributes in the latent space of generative models. This effort's primary objective was to address the limitations discovered in previous research, mainly (a) the discovered editing directions are interpretable but significantly entangled, i.e., changes to one attribute affect the others and (b) Prior research has utilized direction discovery and direction disentanglement separately, and they can't work synergistically. More specifically, this paper proposes a two-stage training method that discovers the editing direction with semantics, perturbs the dimension of the direction vector, adjusts it with a penalty mechanism, and makes the editing direction more disentangled. This allows easy distinguishable image editing, such as age and facial expressions in facial images. Experimentally compared to other methods, the proposed method outperforms them both qualitatively and quantitatively in terms of interpretability, disentanglement, and distinguishability of the generated images. The implementation of our method is available at https://github.com/ydniuyongjie/twoStageForFaceEdit.

Hybrid generative model for grading the severity of diabetic retinopathy images

ABSTRACT One of the common eye conditions affecting patients with diabetes is diabetic retinopathy (DR). It is characterised by the progressive impairment to the blood vessels with the increase of glucose level in the blood. The grading efficiency still finds challenging because of the existence of intra-class variations and imbalanced data distributions on the retinal images. Traditional machine learning techniques utilise hand-engineered features for classification of the affected retinal images. As convolutional neural network produces better image classification accuracy in many medical images, this work utilises the CNN-based feature extraction method. This feature has been used to build Gaussian mixture model (GMM) for each class that maps the CNN features to log-likelihood dimensional vector spaces. Since the Gaussian mixture model can be realised as a mixture of both parametric and nonparametric density models and has their flexibility in capturing different data distributions, probabilistic outputs, interpretability, efficient parameter estimation, and robustness to outliers, the proposed model aimed to obtain and provide a smooth approximation of the underlying distribution of features for training the model. Then these vector spaces are trained by the SVM classifier. Experimental results illustrate the efficacy of the proposed model with accuracy 86.3% and 89.1%, respectively.

Computer assisted proof of homoclinic chaos in the spatial equilateral restricted four-body problem

We develop constructive, computer assisted arguments for proving the existence of transverse homoclinic connections for hyperbolic periodic orbits in Hamiltonian systems. These arguments are applied at a number of non-perturbative parameter and energy values in the spatial equilateral circular restricted four-body problem: a six dimensional vector field. The idea is to formulate the desired connecting orbits as solutions of certain two point boundary value problems for orbit segments which originate and terminate on the local stable/unstable manifolds attached to a periodic orbit. These boundary value problems are studied via a Newton-Kantorovich argument in an appropriate Cartesian product of Banach algebras of rapidly decaying sequences of Chebyshev coefficients. Perhaps the most delicate part of the problem is controlling the boundary conditions, which must lie on the local stable/unstable manifolds of the periodic orbit. For this portion of the problem we use a parameterization method to develop Fourier-Taylor approximations equipped with mathematically rigorous a-posteriori error bounds. This requires validated computation of a finite number of Fourier-Taylor coefficients via Newton-Kantorovich arguments in appropriate Cartesian product of rapidly decaying sequences of Fourier coefficients, followed by a fixed point argument to bound the tail terms of the Taylor expansion. After some geometric considerations in the energy manifold, transversality of the connection follows as a direct consequence of the Newton-Kantorovich argument.

Positional difference and Frequency (PdF) based alignment-free technique for genome sequence comparison

In the field of computational biology, genome sequence comparison among different species is essential and has applications in both the research and scientific fields. Owing to the lengthy processing time and large number of data sets, the alignment-based approaches are unsuitable and ineffective. Therefore, alignment-free techniques have obtained popularity for acquiring proper sequence clustering and evolutionary relationship among species. In this paper, a complete bipartite graph based Positional difference and Frequency (PdF) vector descriptor is introduced. Positional difference and Frequency, two parameters, are applied to the genome sequence to create a 16- dimensional vector descriptor using the di-nucleotide representation of genome sequence. Subsequently, a distance matrix is calculated to construct the phylogenetic trees for different data sets of mammals and viruses. The achieved outcomes are compared with the phylogenetic trees of the earlier methods viz. the FFP method, the ClustalW method, the MEV method, the PCNV method and the FIS method. In most instances, the proposed method produces more precise outcomes than the preceding techniques and has potential for genome sequence comparison on both the equal and unequal length of data-sets. Communicated by Ramaswamy H. Sarma

Dual incidences and t‐designs in vector spaces

AbstractLet be an ‐dimensional vector space over and is any set of ‐dimensional subspaces of . We construct two incidence structures and using subspaces from . The points are subspaces from . The blocks of are indexed by all hyperplanes of , while the blocks of are indexed by all subspaces of dimension 1. We show that and are dual in the sense that their incidence matrices are dependent, one can be calculated from the other. Additionally, if is a ‐design we prove new matrix equations for incidence matrices of and .

Machine learning models and methods for human gait recognition

The paper explores the challenge of human identification through gait recognition within biometric identification systems. Itoutlines the essential criteria for human biometric features, discusses primary biometric characteristics, and their application in biometric identification systems. The paper also examines the feasibility of utilizing gait as a biometric identifier, emphasizing its advantages, such as not requiring the upfront provision of personal biometric information and specialized equipment.The authors conduct an analysis of existing scientific literature in the field of gait recognition, categorizing gait recognition methodsinto template-based and non-template-based approaches. Throughout their research, they identify the key issues and challenges that researchers face in this domain, along with the prevailing trends in human gait recognition within biometric identification systems.Additionally, the paper introduces a method for person identification based on gait, utilizing the Histogram of Oriented Gradients and the Sum Variance Haralick texture features. It involves transforming input video into a series of images depicting the gait silhouette, creating a Gait Energy Image (GEI) by combining these gait silhouettes throughout a gait cycle, and translating the GEI into the Gait Gradient Magnitude Image (GGMI). The subsequent step involves extracting recommended gait characteristics from the GGMIs of participants included in a dataset.To preprocess the collected characteristics, Principal Component Analysis (PCA) is applied, reducing the dimensions that may negatively impact classification robustness, thereby enhancing overall performance. In the final step, a K-Nearest Neighbors (KNN) classifier is employed to categorize the characteristics obtained from a specific dataset.The proposed novel feature vector in the paper demonstrates increased reliability and effectively captures spatial variations in gait patterns. Notably, it reduces the dimensionality of the feature vector from 3780×1 to 63×1, resulting in decreased computational complexity in the gait recognition system. Experimental evaluations on the CASIA A and CASIA B datasets reveal that the proposed approach outperforms other HOG-based methods in most scenarios, with the exception of situations involving frontal images.

Disambiguation of company names via deep recurrent networks

Name Entity Disambiguation is the Natural Language Processing task of identifying textual records corresponding to the same Named Entity, i.e., real-world entities represented as a list of attributes (names, places, organisations, etc.). In this work, we face the task of disambiguating companies on the basis of their written names. We propose a Siamese LSTM Network approach to extract – via supervised learning – an embedding of company name strings in a (relatively) low dimensional vector space and use this representation to identify pairs of company names that actually represent the same company (i.e., the same Entity).Given that the manual labelling of string pairs is a rather onerous task, we analyse how an Active Learning approach to prioritise the samples to be labelled leads to a more efficient overall learning pipeline.The contributions of this work are: with empirical investigations on real-world industrial data, we show that our proposed Siamese Network outperforms several benchmark approaches based on standard string matching algorithms when enough labelled data are available; moreover, we show that Active Learning prioritisation is indeed helpful when labelling resources are limited, and let the learning models reach the out-of-sample performance saturation with less labelled data with respect to standard (random) data labelling approaches.

GSCtool: A Novel Descriptor that Characterizes the Genome for Applying Machine Learning in Genomics

Machine learning (ML) is one of the core driving forces for the next breeding stage, and Breeding 4.0. Genotype matrix based on single‐nucleotide polymorphisms (SNPs) is often used in ML for genome‐to‐phenotype prediction. Genotype matrix has an inherent defect, as the feature spaces it generates across different individuals or groups are inconsistent, and this hinders the application of ML. To overcome the challenge, a genome descriptor, Genic SNPs Composition Tool (GSCtool) is developed, which counts the number of SNPs in each gene of the genome so the dimension of the feature vectors equals the number of annotated genes in a species. Compared to using the genotype matrix, using GSCtool significantly decreases the model training time and has a higher accuracy of phenotype prediction. GSCtool also achieves good performance in variety identification, which is useful in crop variety protection. In general, GSCtool will help facilitate the application and study of genomic ML. The source code and test data of GSCtool are freely available at https://github.com/SZJhacker/GSCtool and https://gitee.com/shenzijie/GSCtool.

GSQAS: Graph Self-supervised Quantum Architecture Search

Quantum Architecture Search (QAS) is a promising approach for designing quantum circuits specifically tailored for variational quantum algorithms (VQAs). However, existing QAS algorithms require calculating the ground-truth performances of a substantial number of quantum circuits during the search process, rendering them computationally demanding and limiting their applicability to large-scale quantum circuits. Recently, a predictor-based QAS has been proposed to address this challenge by estimating circuit performance directly based on their structures using a predictor trained on a set of labeled quantum circuits. However, the predictor is trained by purely supervised learning, which suffers from poor generalization ability when labeled training circuits are scarce. It is highly time-consuming to obtain a substantial number of labeled quantum circuits because the gate parameters of quantum circuits need to be optimized until convergence to obtain their ground-truth performances. To overcome these limitations, we propose GSQAS, a graph self-supervised QAS that trains a predictor by self-supervised learning. Specifically, we first pre-train a graph encoder using a well-designed pretext task on a large number of unlabeled quantum circuits, aiming to generate meaningful representations of quantum circuits. Subsequently, the downstream predictor is trained on a small set of quantum circuits’ representations and their corresponding labels. Once the encoder is trained, it becomes applicable to various downstream tasks. To effectively encode spatial topology information and avoid huge dimensions of feature vectors for large-scale quantum circuits, we propose a graph-based encoding scheme for quantum circuits. Simulation results on QAS for variational quantum eigensolver and quantum state classification demonstrate that GSQAS outperforms the state-of-the-art predictor-based QAS, yielding superior performance with fewer labeled circuits.