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Support vector machine (SVM) is one of the most powerful technologies of machine learning, which has been widely concerned because of its remarkable performance. However, when dealing with the classification problem of large-scale datasets, the high complexity of SVM model leads to low efficiency and become impractical. Due to the sparsity of SVM in the sample space, this paper presents a new parallel data geometry analysis (PDGA) algorithm to reduce the training set of SVM, which helps to improve the efficiency of SVM training. The PDGA introduce Mahalanobis distance to measure the distance from each sample to its centroid. And based on this, proposes a method that can identify non support vectors and outliers at the same time to help remove redundant data. When the training set is further reduced, cosine angle distance analysis method is proposed to determine whether the samples are redundant data, ensure that the valuable data are not removed. Different from the previous data geometry analysis methods, the PDGA algorithm is implemented in parallel, which greatly saving the computational cost. Experimental results on artificial dataset and 6 real datasets show that the algorithm can adapt to different sample distributions. Which significantly reduce the training time and memory requirements without sacrificing the classification accuracy, and its performance is obviously better than the other five competitive algorithms.

Ramalingam Shanmugam,1 Karan P Singh2 1School of Health Administration, Texas State University, San Marcos, TX, 78666, USA; 2Department of Epidemiology and Biostatistics, School of Community and Rural Health, The University of Texas Health Sciences Center at Tyler, Tyler, TX, 75708, USACorrespondence: Karan P SinghDepartment of Epidemiology and Biostatistics, School of Community and Rural Health, The University of Texas Health Sciences Center at Tyler, Tyler, TX, 75708, USAEmail karan.singh@uthct.eduBackground: Challenges to manage, mitigate, or prevent the COVID-19’s pandemics are felt by medical, healthcare professionals and governing agencies. Health researchers conduct survey among the citizens to capture their opinion on COVID-19. In such surveys like in Hanafiah and Wan (2020), structural-zero (different from sampling zero) category occurs as they question about perception, knowledge, and communication regarding COVID-19.Materials: The data were collected in a survey conducted among Malaysians by Hanafiah and Wan regarding COVID-19. The survey focused on people’s response about the public communication, knowledge, and perception.Methods: One of the four question categories in the survey is mutually exclusive with the other three questions. Consequently, there will be no entry in that category. Such group is called structurally zero category in the literature. The literature never probed the migrative split to other categories of the unknown proportion belonging to the structural zero category. In this article, the probability-based new and innovative method configures what proportion in that mutually exclusive category and it is the essence of our method.Results: The mutually exclusive nature of subquestions manufactured structural zero in their data. A careful analysis of the data has created so far unknown probability concepts in the literature, which we named as “Exodus probabilities” in this article. Its discovery and utility are illustrated and elaborated with application in COVID-19. This methodology is also useful in applications in engineering, epidemiology, marketing, communication networking, etc.Conclusion: What is quite novel about the discovery of the exodus probability in this article is the evolution of the concepts from the structural-zero category. In such situation, when a category is eliminated, the proportions of the sample might have uncommunicatively transited to other viable categories and our research question is all about configuring their proportions. This is an innovative approach.Keywords: public knowledge, perception, communication, sample space, dependent probabilities, Venn layout, odds, odds ratio, survey outcomes

This paper proposes an approach to predicting fatigue crack growth under mixed-mode loading based on improved Gaussian process. In terms of analyzing the theoretical background for fatigue crack growth, a corresponding finite element model is built to generate sufficient simulation data, which is utilized to obtain the key parameters (e.g., stress intensity factor) for the fatigue crack growth process. And then, a Gaussian process model is achieved to meet the condition that the stress intensity factor is a nonlinear continuous change in crack growth, especially for mixed-mode loading. Following, an idea of local sample densification method is implemented to improve Gaussian sample generation process according to the simplified model of the crack growth path. Based on the above investigation, a fatigue crack growth prediction model using the improved Gaussian process is finished, which is subsequently verified through the test data of lower bainite steel (SCM435) material. The results show that the proposed approach has better computational accuracy and efficiency than the traditional finite element method in predicting fatigue crack growth under mixed-mode loading.

Granular computing is a method of studying human intelligent information processing, which has advantage of knowledge discovery. In this paper, we convert a classification problem of sample space into a classification problem of fuzzy clustering granular space and propose a random fuzzy clustering granular hyperplane classifier (RFCGHC) from the perspective of granular computing. Most classifiers are only used to process numerical data, RFCGHC can process not only non-numerical data, such as information granules, but also numerical data. The classic granulation method is generally serial granulation, which has high time complexity. We design a parallel distributed granulation method to enhance efficiency. First, a clustering algorithm with adaptive cluster center number is proposed, where the ratio of standard deviation between categories and standard deviation within categories is as evaluation criterion. The clusters and the optimal amount of cluster centers can be achieved by the method. On the basis of these, sample set can be divided into many subsets and each sample can be granulated by these cluster centers. Then, a fuzzy clustering granular space can be formed, where fuzzy clustering granules, fuzzy clustering granular vectors, and their operators can be defined. In order to get the optimal hyperplane in the fuzzy clustering granular space to classify these samples, we design a loss function and evaluate each category with probability by fuzzy clustering granular hyperplane. In solving the loss function, genetic algorithm based on fuzzy clustering granules is adopted. Experimental results and theoretical analysis show that RFCGHC has good performance.

Dynamic networks imply those states of which change over time and such changes are generally associated with the topology of a network. Dynamic models are currently needed for numerous systems which could be defined as a network model. Those related to the propagation of living organisms are also a typical example. the study has examined a sample space which has been defined in the network topology of human population as the way in which it will spread with population growth and correlated with various variables in the modeled dynamic network., Dinamik ağlar, zaman içinde değişiklik gösteren durumları belirtmekte ve bu değişiklikler genellikle bir ağın topolojisi ile ilişkilendirilmektedir. Ağ modeli olarak tanımlanabilecek birçok sistem için dinamik modellere ihtiyaç duyulmaktadır. Canlı organizmaların yayılması ile ilgili olanlar da bu duruma bir örnektir. Çalışmada insan nüfusunun ağ topolojisi tanımlanarak ile bir örnek uzay oluşturulmuş, nüfus artışı ile içerisinde nasıl bir yayılma görüleceği araştırılmış ve nüfus büyümesinin modellenen dinamik ağdaki çeşitli değişkenler ile aralarındaki korelasyonlar incelenmiştir.

To improve the classification results of high-resolution remote sensing images (RSIs), it is necessary to use feature transfer methods to mine the relevant information between high-resolution RSIs and low-resolution RSIs to train the classifiers together. Most of the existing feature transfer methods can only handle homogeneous data (i.e., data with the same dimension) and are susceptible to the quality of the RSIs, while RSIs with different resolutions present different feature dimensions and samples obtained from illumination conditions. To obtain effective classification results, unlike existing methods that focus only on the projection transformation in feature space, a joint feature-space and sample-space heterogeneous feature transfer (JFSSS-HFT) method is proposed to simultaneously process heterogeneous multi-resolution images in feature space using projection matrices of different dimensions and reduce the impact of outliers by adaptive weight factors in the sample space simultaneously to reduce the occurrence of negative transfer. Moreover, the maximum interclass variance term is embedded to improve the discriminant ability of the transferred features. To solve the optimization problem of JFSSS-HFT, the alternating-direction method of multipliers (ADMM) is introduced to alternatively optimize the parameters of JFSSS-HFT. Using different types of ship patches and airplane patches with different resolutions, the experimental results show that the proposed JFSSS-HFT obtains better classification results than the typical feature transferred methods.

The classroom environment is of great significance for the health of primary and secondary school students, but a comfortable indoor environment often requires higher energy consumption. This paper presents a multi-objective optimization method based on an artificial neural network (ANN) model, which can help designers efficiently optimize the design of primary and secondary school classrooms in southern China. In this optimization method, first, the optimization objectives and variables are determined according to building characteristics, and the physical model is established through simulation software (EnergyPlus) to generate the sample space. Second, sensitivity analysis is carried out for each optimization variable, and the physical model is modified according to the results to regenerate the sample space. Third, the ANN model is trained by using the regenerated sample space, and the Pareto optimal solution is generated through the use of the non-dominated sorting genetic algorithm II (NSGA-II). Finally, the effectiveness of the multi-objective optimization method is proven through a typical case of primary and secondary school classrooms in Nanjing, China. The results show that, compared with the benchmark scheme, TES decreased by 810.8 kWh at most, PT increased by 47.8% at most and DI increased by 4.2% at most.

National audience; The mass transportation approach to multivariate quantiles in Chernozhukov et al. (2017) was modified in Faugeras and Rüschendorf (2017) by a two steps procedure. In the first step, a mass transportation problem from a spherical reference measure to the copula is solved and combined in the second step with a marginal quantile transformation in the sample space. Also, generalized quantiles given by suitable Markov morphisms are introduced there.In the present paper, this approach is further extended by a functional approach in terms of membership functions, and by the introduction of randomized quantile regions. In addition, in the case of continuous marginals, a smoothed version of the empirical quantile regions is obtained by smoothing the empirical copula. All three extended approaches give empirical quantile ares of exact level and improved stability. The resulting depth areas give a valid representation of the central quantile areas of a multivariate distribution and provide a valuable tool for their analysis.

To systematically and quantitatively analyze the influence factors on billet gas consumption (BGC) in reheating furnace, a novelty data mining approach for multi-influence factors BGC analysis was proposed in this paper. This multi-influence factors data mining model mainly includes four steps: Firstly, the BGC apportionment model was established based on energy apportionment model in reheating furnace; Secondly, the BGC data set could be achieved according to the division of billet sample space (BSS); Thirdly, the data interpolation calculation method of various BSS subsets (BSSSs) was put forward; Lastly, the influence degree analysis method of various factors on BGC was described in detail. Especially, contribution degree model, which could quantitatively describe the influence degree of each factor on BGC, was established. Case study showed that working groups (WGs) should be eliminated because of weak influence on BGC. Then the order of contribution degree on BGC from weak to strong was working shifts (WSs) (1.61%), residence time (9.7%), loading temperature (88.68%). Therefore, residence time and loading temperature should be highlighted in all factors. Finally, some measures and suggestions, which could improve the residence time and loading temperature, were put forward.

The steel industry is one of the pillar industries in China. The physical and mental health of steel workers is related to the development of China's steel industry. Steel workers have long been working in shifts, high temperatures, noise, highly stressed, and first-line environments. These occupational related factors have an impact on the health of steel workers. At present, the existing hypertension risk scoring models do not include occupational related factors, so they are not applicable to the risk score of hypertension in steel workers. It is necessary to establish a risk scoring model for hypertension in steel workers. In this study, the learning vector quantization (LVQ) neural network algorithm and the FisherSVM coupling algorithm are applied to estimate the hypertension risk of steel workers, and the microscopic laws of the "tailing" phenomenon of the two algorithms are analyzed by means of graphics analysis, which can describe the influence trend of sample size change in different intervals on the classification effect. The results show that the classification accuracy of the algorithm depends on the size of the sample space. When the sample size n ≤ 30 * (k + 1), the Fisher-SVM coupling intelligent algorithm is more applicable. Because its average accuracy rate is 90.00%, the average accuracy of the LVQ algorithm is only 63.34%. When the sample size is n > 30 * (k + 1), the LVQ algorithm is more applicable. Because its average accuracy rate is 93.33%, the average accuracy of the Fisher-SVM coupling intelligent algorithm is only 76.67%. The sample size of this paper is 4422, and the prediction of LVQ neural network model is more accurate. Therefore, based on the relative importance of each risk factor obtained by this model and to establish a steel worker hypertension risk rating scale, the score greater than 18 is considered as the high risk, 12-18 is considered as the medium risk, and less than 12 is considered as the low risk. Through the example's verification, the accuracy rate of the scale is 90.50% and the effect is very good. It shows that the established scoring system can effectively assess the risk of hypertension in steel workers and provide an effective basis for primary prevention of hypertension in steel workers.

Oversampling is an efficient technique in dealing with class-imbalance problem. It addresses the problem by reduplicating or generating the minority class samples to balance the distribution between the samples of the majority and the minority class. Synthetic minority oversampling technique (SMOTE) is one of the typical representatives. During the past decade, researchers have proposed many variants of SMOTE. However, the existing oversampling methods may generate wrong minority class samples in some scenarios. Furthermore, how to effectively mine the inherent complex characteristics of imbalanced data remains a challenge. To this end, this paper proposes a parameter-free data cleaning method to improve SMOTE based on constructive covering algorithm. The dataset generated by SMOTE is first partitioned into a group of covers, then the hard-to-learn samples can be detected based on the characteristics of sample space distribution. Finally, a pair-wise deletion strategy is proposed to remove the hard-to-learn samples. The experimental results on 25 imbalanced datasets show that our proposed method is superior to the comparison methods in terms of various metrics, such as ${F}$ -measure, ${G}$ -mean, and Recall. Our method not only can reduce the complexity of the dataset but also can improve the performance of the classification model.

An optimized neural network classification method based on kernel holistic learning and division (KHLD) is presented. The proposed method is based on the learned radial basis function (RBF) kernel as the research object. The kernel proposed here can be considered a subspace region consisting of the same pattern category in the training sample space. By extending the region of the sample space of the original instances, relevant information between instances can be obtained from the subspace, and the classifier’s boundary can be far from the original instances; thus, the robustness and generalization performance of the classifier are enhanced. In concrete implementation, a new pattern vector is generated within each RBF kernel according to the instance optimization and screening method to characterize KHLD. Experiments on artificial datasets and several UCI benchmark datasets show the effectiveness of our method.

We investigate the possibility of completing financial markets in a model with no exogenous probability measure, with market imperfections and with an arbitrary sample space. We also consider whether such an extension may be possible in a competitive environment. Our conclusions highlight the economic role of complexity.

KNN classification is an improvisational learning mode, in which they are carried out only when a test data is predicted that set a suitable K value and search the K nearest neighbors from the whole training sample space, referred them to the lazy part of KNN classification. This lazy part has been the bottleneck problem of applying KNN classification due to the complete search of K nearest neighbors. In this paper, a one-step computation is proposed to replace the lazy part of KNN classification. The one-step computation actually transforms the lazy part to a matrix computation as follows. Given a test data, training samples are first applied to fit the test data with the least squares loss function. And then, a relationship matrix is generated by weighting all training samples according to their influence on the test data. Finally, a group lasso is employed to perform sparse learning of the relationship matrix. In this way, setting K value and searching K nearest neighbors are both integrated to a unified computation. In addition, a new classification rule is proposed for improving the performance of one-step KNN classification. The proposed approach is experimentally evaluated, and demonstrated that the one-step KNN classification is efficient and promising, 13 pages. in IEEE Transactions on Knowledge and Data Engineering

In causal set theory the gravitational path integral is replaced by a path-sum over a sample space $\Omega_n$ of $n$-element causal sets. The contribution from non-manifold-like orders dominates $\Omega_n$ for large $n$ and therefore must be tamed by a suitable action in the low energy limit of the theory. We extend the work of Loomis and Carlip on the contribution of sub-dominant bilayer orders to the causal set path-sum and show that the "link action" suppresses the dominant Kleitman-Rothschild orders for the same range of parameters., Comment: 14 pages, 10 figures. Section 2 revised and more figures added. Some editing in the introduction and conclusion section, section 3.1 renamed and references added

The paper discusses very general extensions to existing inflation models for discrete random variables, allowing an arbitrary set of points in the sample space to be either inflated or deflated relative to a baseline distribution. The term flation is introduced to cover either inflation or deflation of counts. Examples include one-inflated count models where the baseline distribution is zero-truncated and count models for data with a few unusual large values. The main result is that inference about the baseline distribution can be based solely on the truncated distribution which arises when the entire set of flation points is truncated. A major application of this result relates to estimating the size of a hidden target population, and examples are provided to illustrate our findings.

Statistical inference of evolutionary parameters from molecular sequence data relies on coalescent models to account for the shared genealogical ancestry of the samples. However, inferential algorithms do not scale to available data sets. A strategy to improve computational efficiency is to rely on simpler coalescent and mutation models, resulting in smaller hidden state spaces. An estimate of the cardinality of the state space of genealogical trees at different resolutions is essential to decide the best modeling strategy for a given dataset. To our knowledge, there is neither an exact nor approximate method to determine these cardinalities. We propose a sequential importance sampling algorithm to estimate the cardinality of the sample space of genealogical trees under different coalescent resolutions. Our sampling scheme proceeds sequentially across the set of combinatorial constraints imposed by the data which, in this work, are completely linked sequences of DNA at a nonrecombining segment. We analyze the cardinality of different genealogical tree spaces on simulations to study the settings that favor coarser resolutions. We apply our method to estimate the cardinality of genealogical tree spaces from mtDNA data from the 1000 genomes and a sample from a Melanesian population at the $\beta $-globin locus.

Random number generator (RNG) is a fundamental and important cryptographic element, which has made an outstanding contribution to guaranteeing the network and communication security of cryptographic applications in the Internet age. In reality, if the random number used cannot provide sufficient randomness (unpredictability) as expected, these cryptographic applications are vulnerable to security threats and cause system crashes. Min-entropy is one of the approaches that are usually employed to quantify the unpredictability. The NIST Special Publication 800-90B adopts the concept of min-entropy in the design of its statistical entropy estimation methods, and the predictive model-based estimators added in the second draft of this standard effectively improve the overall capability of the test suite. However, these predictors have problems on limited application scope and high computational complexity, e.g., they have shortfalls in evaluating random numbers with long dependence and multivariate due to the huge time complexity (i.e., high-order polynomial time complexity). Fortunately, there has been increasing attention to using neural networks to model and forecast time series, and random numbers are also a type of time series. In our work, we propose several new and efficient approaches for min-entropy estimation by using neural network technologies and design a novel execution strategy for the proposed entropy estimation to make it applicable to the validation of both stationary and nonstationary sources. Compared with the 90B’s predictors officially published in 2018, the experimental results on various simulated and real-world data sources demonstrate that our predictors have a better performance on the accuracy, scope of applicability, and execution efficiency. The average execution efficiency of our predictors can be up to 10 times higher than that of the 90B’s for 10 6 sample size with different sample spaces. Furthermore, when the sample space is over 2 2 and the sample size is over 10 8 , the 90B’s predictors cannot give estimated results. Instead, our predictors can still provide accurate results. Copyright© 2019 John Wiley & Sons, Ltd.

The study of the structure of compositional changes characterizing a geochemical system in time or space could be the key to understand its dynamics and resilience to environmental and anthropic perturbations. Variables characterizing the composition of an aqueous system (river or ground waters) constitute a multivariate system that moves as a whole due to multiple interrelationships and feed-back mechanisms. If the goal of the research is to understand how the whole moves, the Compositional Data Analysis (CoDA) theory offers the correct statistical framework since aqueous geochemical data pertaining to the simplex sample space. Cases of a compositional matrix can be ranked by using some criterium (e.g. increasing runoff or conductivity values), and the differences between subsequent rows calculated by using the perturbation operator that measures the change in the simplex geometry. The obtained perturbation matrix can be then analyzed by using robust Principal Component Analysis (robust-PCA) to discover the association between variables subjected to proportional perturbations during geochemical processes. The calculus of the robust Mahalanobis distance from the barycenter of this matrix appears to be also useful to reveal presence of intermittency in time or space. Intermittency is highly related to the fractal nature of variability representing an emergent property of self-organized complex dissipative systems since it optimizes the dissipation energy gradients and maximize entropy production. Application examples for the surficial waters of the Alps region and the Arno river basin (Tuscany, Central Italy) reveal that the methodology is powerful and able to discover complex dynamics moving on the boundary between different sample spaces, from the Euclidean one to the fractal one. The proposed approach allows us to shift the perspective to the nature of the dynamic interactions and transitions affecting a geochemical landscape revealing how variability moves and how presence of intermittency and resilient behavior affects evolution and prediction.

Identification of characteristic genes associated with specific biological processes of different cancers could provide insights into the underlying cancer genetics and cancer prognostic assessment. It is of critical importance to select such characteristic genes effectively. In this paper, a novel unsupervised characteristic gene selection method based on sample learning and sparse filtering, Sample Learning based on Deep Sparse Filtering (SLDSF), is proposed. With sample learning, the proposed SLDSF can better represent the gene expression level by the transformed sample space. Most unsupervised characteristic gene selection methods did not consider deep structures, while a multilayer structure may learn more meaningful representations than a single layer, therefore deep sparse filtering is investigated here to implement sample learning in the proposed SLDSF. Experimental studies on several microarray and RNA-Seq datasets demonstrate that the proposed SLDSF is more effective than several representative characteristic gene selection methods (e.g., RGNMF, GNMF, RPCA and PMD) for selecting cancer characteristic genes.

The permanent magnet apparatus described herein is based upon the C-shaped permanent magnet. It is designed to maximise field strength while increasing the pole gap to 5 mm, providing a sample volume large enough for wide applicability. The production of this equipment aims to provide a homogeneous, high field (∼2.5 T) magnetic sample environment with a volume large enough to accommodate solution crystallisation experiments in sample chambers such as NMR tubes and cuvettes whilst simultaneously allowing direct observation of the sample from a wide angle. Although the resulting rig is not lightweight at 26.5 kg it is eminently more portable than an equivalent electromagnet system (of the order of 625 kg), and provides a max field strength of 2.468 T with relatively low stray field. Keywords: Permanent magnet, Sample environment, Horse-shoe magnet

Principal component analysis (PCA) and linear discriminant analysis (LDA) have been extended to be a group of classical methods in dimensionality reduction for unsupervised and supervised learning, respectively. However, compared with the PCA, the LDA loses several advantages because of the singularity of its between-class scatter, resulting in singular mapping and restriction of reduced dimension. In this paper, we propose a dimensionality reduction method by defining a full-rank between-class scatter, called reversible discriminant analysis (RDA). Based on the new defined between-class scatter matrix, our RDA obtains a nonsingular mapping. Thus, RDA can reduce the sample space to arbitrary dimension and the mapped sample can be recovered. RDA is also extended to kernel based dimensionality reduction. In addition, PCA and LDA are the special cases of our RDA. Experiments on the benchmark and real problems confirm the effectiveness of the proposed method.

Betweenness centrality and k-path centrality are two important indices that are widely used to analyze social, technological and information networks. In the current paper, first given a directed network G and a vertex $r\in V(G)$, we present a novel adaptive algorithm for estimating betweenness score of r. Our algorithm first computes two subsets of the vertex set of G, called $\mathcalRF (r)$ and $\mathcalRT (r)$. They define the sample spaces of the start-points and the end-points of the samples. Then, it adaptively samples from $\mathcalRF (r)$ and $\mathcalRT (r)$ and stops as soon as some condition is satisfied. The stopping condition depends on the samples met so far, $|\mathcalRF (r)|$ and $|\mathcalRT (r)|$. We show that compared to the well-known existing algorithms, our algorithm gives a better $(lambda,δ)$-approximation. Then, we propose a novel algorithm for estimating k-path centrality of r. Our algorithm is based on computing two sets $\mathcalRF (r)$ and $\mathcalD (r)$. While $\mathcalRF (r)$ defines the sample space of the source vertices of the sampled paths, $\mathcalD (r)$ defines the sample space of the other vertices of the paths. We show that in order to give a $(lambda,δ)$-approximation of the k-path score of r, our algorithm requires considerably less samples. Moreover, it processes each sample faster and with less memory. Finally, we empirically evaluate our proposed algorithms and show their superior performance. Also, we show that they can be used to efficiently compute centrality scores of a set of vertices.