Artificial Datasets Research Articles

Physics-informed boundary integral networks (PIBI-Nets): A data-driven approach for solving partial differential equations

Partial differential equations (PDEs) are widely used to describe relevant phenomena in dynamical systems. In real-world applications, we commonly need to combine formal PDE models with (potentially noisy) observations. This is especially relevant in settings where we lack information about boundary or initial conditions, or where we need to identify unknown model parameters. In recent years, Physics-Informed Neural Networks (PINNs) have become a popular tool for this kind of problems. In high-dimensional settings, however, PINNs often suffer from computational problems because they usually require dense collocation points over the entire computational domain. To address this problem, we present Physics-Informed Boundary Integral Networks (PIBI-Nets) as a data-driven approach for solving PDEs in one dimension less than the original problem space. PIBI-Nets only require points at the computational domain boundary, while still achieving highly accurate results. Moreover, PIBI-Nets clearly outperform PINNs in several practical settings. Exploiting elementary properties of fundamental solutions of linear differential operators, we present a principled and simple way to handle point sources in inverse problems. We demonstrate the excellent performance of PIBI-Nets for the Laplace and Poisson equations, both on artificial datasets and within a real-world application concerning the reconstruction of groundwater flows.

Predicting Microbiome Growth Dynamics under Environmental Perturbations

MicroGrowthPredictor is a model that leverages Long Short-Term Memory (LSTM) networks to predict dynamic changes in microbiome growth in response to varying environmental perturbations. In this article, we present the innovative capabilities of MicroGrowthPredictor, which include the integration of LSTM modeling with a novel confidence interval estimation technique. The LSTM network captures the complex temporal dynamics of microbiome systems, while the novel confidence intervals provide a robust measure of prediction uncertainty. We include two examples—one illustrating the human gut microbiota composition and diversity due to recurrent antibiotic treatment and the other demonstrating the application of MicroGrowthPredictor on an artificial gut dataset. The results demonstrate the enhanced accuracy and reliability of the LSTM-based predictions facilitated by MicroGrowthPredictor. The inclusion of specific metrics, such as the mean square error, validates the model’s predictive performance. Our model holds immense potential for applications in environmental sciences, healthcare, and biotechnology, fostering advancements in microbiome research and analysis. Moreover, it is noteworthy that MicroGrowthPredictor is applicable to real data with small sample sizes and temporal observations under environmental perturbations, thus ensuring its practical utility across various domains.

A self-organization reconstruction method of ESN reservoir structure based on reinforcement learning

The dynamic reservoir of the randomly generated Echo State Network (ESN) contains numerous redundant neurons, resulting in collinearity in the high-dimensional state space matrix. This collinearity impacts the prediction performance of the network. In order to address this issue, this paper introduces a self-organizing ESN structure optimization model that is based on reinforcement learning, called SR-ESN. The SR-ESN model employs pruning methods to reconstruct the reservoir using contribution and decision mechanisms. To mitigate potential instability caused by high coupling among neurons in a single reservoir, the concept of ensemble learning is applied to create multiple initial reservoir pools, thereby enhancing screening diversity. Simultaneously, the model utilizes reinforcement learning's decision mechanism to identify effective neurons. Neurons with low contribution are pruned, while those with high contribution are retained for self-organizing reconstruction. This optimization of the network structure enhances its prediction performance. Based on both artificial and real datasets, the proposed SR-ESN model demonstrates superior prediction performance with minimal structural complexity compared to other prediction models.

Ratio-type estimator of the population mean in stratified sampling based on the calibration approach

An improved ratio-type calibrated estimator was developed using the logarithmic mean in the calibration constraint for the stratified random sampling scheme. The proposed estimator was extended in the case of stratified double sampling and compared with the estimators given by Tracy et al. (2003) together its ratio-type estimators, as well as Nidhi et al. (2017) and Khare et al. (2022). A simulation study was also carried out on both a real and artificial dataset in order to evaluate the performance of the proposed estimator compared to the existing estimators.

Semi-supervised spectral clustering using shared nearest neighbour for data with different shape and density

<p>In the absence of supervisory information in spectral clustering algorithms, it is difficult to construct suitable similarity graphs for data with complex shapes and varying densities. To address this issue, this paper proposes a Semi-supervised Spectral Clustering algorithm based on shared nearest neighbor. The proposed algorithm combines the idea of semi-supervised clustering, adding Shared Nearest Neighbor information to the calculation of the distance matrix, and using pairwise constraint information to find the relationship between two data points, while providing a portion of supervised information. Comparative experiments were conducted on artificial data sets and University of California Irvine machine learning repository datasets. The experimental results show that the proposed algorithm achieves better clustering results compared to traditional K-means and spectral clustering algorithms.</p>

A New Sufficient & Necessary Condition for Testing Linear Separability Between Two Sets.

As a fundamental mathematical problem in the field of machine learning, the linear separability test still lacks a theoretically complete and computationally efficient method. This paper proposes and proves a sufficient and necessary condition for linear separability test based on a sphere model. The advantage of this test method is two-fold: (1) it provides not only a qualitative test of linear separability but also a quantitative analysis of the separability of linear separable instances; (2) it has low time cost and is more efficient than existing test methods. The proposed method is validated through a large number of experiments on benchmark datasets and artificial datasets, demonstrating both its correctness and efficiency.

A safe screening rule with bi-level optimization of [formula omitted] support vector machine

Support vector machine (SVM) has achieved many successes in machine learning, especially for a small sample problem. As a famous extension of the traditional SVM, the ν support vector machine (ν-SVM) has shown outstanding performance due to its great model interpretability. However, it still faces challenges in training overhead for large-scale problems. To address this issue, we propose a safe screening rule with bi-level optimization for ν-SVM (SRBO-ν-SVM) which can screen out inactive samples before training and reduce the computational cost without sacrificing the prediction accuracy. Our SRBO-ν-SVM is strictly deduced by integrating the Karush–Kuhn–Tucker (KKT) conditions, the variational inequalities of convex problems and the ν-property. Furthermore, we develop an efficient dual coordinate descent method (DCDM) to further improve computational speed. Finally, a unified framework for SRBO is proposed to accelerate many SVM-type models, and it is successfully applied to one-class SVM. Experimental results on 6 artificial data sets and 30 benchmark data sets have verified the effectiveness and safety of our proposed methods in supervised and unsupervised tasks.

Settling Time vs. Accuracy Tradeoffs for Clustering Big Data

We study the theoretical and practical runtime limits of k-means and k-median clustering on large datasets. Since effectively all clustering methods are slower than the time it takes to read the dataset, the fastest approach is to quickly compress the data and perform the clustering on the compressed representation. Unfortunately, there is no universal best choice for compressing the number of points -- while random sampling runs in sublinear time and coresets provide theoretical guarantees, the former does not enforce accuracy while the latter is too slow as the numbers of points and clusters grow. Indeed, it has been conjectured that any sensitivity-based coreset construction requires super-linear time in the datase size. We examine this relationship by first showing that there does exist an algorithm that obtains coresets via sensitivity sampling in effectively linear time -- within log-factors of the time it takes to read the data. Any approach that significantly improves on this must then resort to practical heuristics, leading us to consider the spectrum of sampling strategies across both real and artificial datasets in the static and streaming settings. Through this, we show the conditions in which coresets are necessary for preserving cluster validity as well as the settings in which faster, cruder sampling strategies are sufficient. As a result, we provide a comprehensive theoretical and practical blueprint for effective clustering regardless of data size. Our code is publicly available at https://github.com/Andrew-Draganov/Fast-Coreset-Generation and has scripts to recreate the experiments.

Multi-Objective Automatic Clustering Algorithm Based on Evolutionary Multi-Tasking Optimization

Data mining technology is the process of extracting hidden knowledge and potentially useful information from a large number of incomplete, noisy, and random practical application data. The clustering algorithm based on multi-objective evolution has obvious advantages compared with the traditional single-objective method. In order to further improve the performance of evolutionary multi-objective clustering algorithms, this paper proposes a multi-objective automatic clustering model based on evolutionary multi-task optimization. Based on the multi-objective clustering algorithm that automatically determines the value of k, evolutionary multi-task optimization is introduced to deal with multiple clustering tasks simultaneously. A set of non-dominated solutions for clustering results is obtained by concurrently optimizing the overall deviation and connectivity index. Multi-task adjacency coding based on a locus adjacency graph was designed to encode the clustered data. Additionally, an evolutionary operator based on relevance learning was designed to facilitate the evolution of individuals within the population. It also facilitates information transfer between individuals with different tasks, effectively avoiding negative transfer. Finally, the proposed algorithm was applied to both artificial datasets and UCI datasets for testing. It was then compared with traditional clustering algorithms and other multi-objective clustering algorithms. The results verify the advantages of the proposed algorithm in clustering accuracy and algorithm convergence.

Generative Adversarial Networks for Synthetic Data Generation in Finance: Evaluating Statistical Similarities and Quality Assessment

Generating synthetic data is a complex task that necessitates accurately replicating the statistical and mathematical properties of the original data elements. In sectors such as finance, utilizing and disseminating real data for research or model development can pose substantial privacy risks owing to the inclusion of sensitive information. Additionally, authentic data may be scarce, particularly in specialized domains where acquiring ample, varied, and high-quality data is difficult or costly. This scarcity or limited data availability can limit the training and testing of machine-learning models. In this paper, we address this challenge. In particular, our task is to synthesize a dataset with similar properties to an input dataset about the stock market. The input dataset is anonymized and consists of very few columns and rows, contains many inconsistencies, such as missing rows and duplicates, and its values are not normalized, scaled, or balanced. We explore the utilization of generative adversarial networks, a deep-learning technique, to generate synthetic data and evaluate its quality compared to the input stock dataset. Our innovation involves generating artificial datasets that mimic the statistical properties of the input elements without revealing complete information. For example, synthetic datasets can capture the distribution of stock prices, trading volumes, and market trends observed in the original dataset. The generated datasets cover a wider range of scenarios and variations, enabling researchers and practitioners to explore different market conditions and investment strategies. This diversity can enhance the robustness and generalization of machine-learning models. We evaluate our synthetic data in terms of the mean, similarities, and correlations.

The contrasting trend of global urbanization-induced impacts on day and night land surface temperature from a time-series perspective

Understanding the warming effect of the impervious surface area (ISA) quantitively is crucial to alleviate the urban heat island effect. However, the quantitative analyses of urbanization-induced land surface temperature (LST) change globally remain to be determined during the global warming hiatus. Here, we first characterized the response of LST to ISA (i.e., δLST) in 369 global cities using MODIS LST product (1 km) and the global artificial impervious area dataset (30 m). We then investigated the spatiotemporal changes of δLST and its associated driving factors, including enhanced vegetation index (1 km), albedo (ALB, 500 m), population (100 m), air temperature (AT, 0.1°), and precipitation (0.1°). The analysis was conducted using linear regression models from 2000 to 2010 at the pixel level. The results illustrate that (1) the daytime δLST in urban areas shows a negative trend with –0.2971 °C/% and –0.0870 °C/% in arid and temperate regions, and the nighttime δLSTs were 0.0938 °C/% and 0.0048 °C/%, respectively. In tropical regions, the δLST remains positive throughout the day, while it exhibits an opposite trend in snow regions. (2) The magnitude of nighttime δLST is stronger compared to daytime globally, which is more significant in arid regions with the largest ΔδLST values (i.e., diurnal variations) in urban (0.3909 °C/%) and rural (0.3262 °C/%) areas. (3) In temperate regions, the response of ALB to ISA (δALB, negative effect) and the response of AT to ISA (δAT, positive effect) are dominant factors in regulating δLST during daytime and nighttime, respectively However, in arid regions, the daytime and nighttime δLSTs are negatively correlated by urban population and vegetation, respectively. These findings provide a quantitative understanding on long-term LST variations and driving factors behind at the pixel level, suggesting that urban greening and increasing surface albedo are effective strategies to mitigate the urbanization-induced surface warming.

Integrated approach to generate artificial samples with low tumor fraction for somatic variant calling benchmarking

BackgroundHigh-throughput sequencing (HTS) has become the gold standard approach for variant analysis in cancer research. However, somatic variants may occur at low fractions due to contamination from normal cells or tumor heterogeneity; this poses a significant challenge for standard HTS analysis pipelines. The problem is exacerbated in scenarios with minimal tumor DNA, such as circulating tumor DNA in plasma. Assessing sensitivity and detection of HTS approaches in such cases is paramount, but time-consuming and expensive: specialized experimental protocols and a sufficient quantity of samples are required for processing and analysis. To overcome these limitations, we propose a new computational approach specifically designed for the generation of artificial datasets suitable for this task, simulating ultra-deep targeted sequencing data with low-fraction variants and demonstrating their effectiveness in benchmarking low-fraction variant calling.ResultsOur approach enables the generation of artificial raw reads that mimic real data without relying on pre-existing data by using NEAT, a fine-grained read simulator that generates artificial datasets using models learned from multiple different datasets. Then, it incorporates low-fraction variants to simulate somatic mutations in samples with minimal tumor DNA content. To prove the suitability of the created artificial datasets for low-fraction variant calling benchmarking, we used them as ground truth to evaluate the performance of widely-used variant calling algorithms: they allowed us to define tuned parameter values of major variant callers, considerably improving their detection of very low-fraction variants.ConclusionsOur findings highlight both the pivotal role of our approach in creating adequate artificial datasets with low tumor fraction, facilitating rapid prototyping and benchmarking of algorithms for such dataset type, as well as the important need of advancing low-fraction variant calling techniques.

Knowledge-based system and expectation-maximization to discovering causes of imperfect labels in vehicular networks clustering

This paper focuses on the development of a knowledge-based system for automatically diagnosing issues in Vehicular ad hoc networks (VANETs). VANETs enable communication between vehicles and infrastructure, enhancing road safety and efficiency through timely information exchange. The proposed system aims to efficiently maintain and ensure the continuity of network service by leveraging innovative pattern recognition methods tailored to VANETs. The automatic diagnosis problem in VANETs involves estimating the operating class of network components based on sensor observations. This entails associating sensor measurements with specific operating modes. By implementing condition-based preventive maintenance procedures, potential component failures can be detected early, mitigating network disruptions. Various approaches, such as expert systems, fault trees, network state models, and statistical learning through pattern recognition, can be employed to address this problem. This paper primarily focuses on the statistical learning approach, where a classification or regression function is learned from a set of examples to assign operation modes to new measurements. It discusses relevant metrics and preprocessing techniques to simplify the decision-making process. The diagnostic system's results are determined based on the formulation of the classification or regression problem. The learning base is constructed, and an appropriate classification method is selected to develop and validate the automatic diagnosis system. While non-parametric models like support vector machines are commonly used, this article emphasizes the significance of considering assumptions and leveraging additional information to enhance performance. It proposes a more specific formalization of the problem, integrating the unique characteristics of VANETs. The contributions of this article revolve around the theory of belief functions, a generative approach, and the utilization of parametric models defined using graphical models. Experimental studies conducted on artificial datasets have demonstrated the benefits of the semi-supervised approach within the context of VANET networks.

Comprehensive Performance Evaluation between Visual SLAM and LiDAR SLAM for Mobile Robots: Theories and Experiments

SLAM (Simultaneous Localization and Mapping), primarily relying on camera or LiDAR (Light Detection and Ranging) sensors, plays a crucial role in robotics for localization and environmental reconstruction. This paper assesses the performance of two leading methods, namely ORB-SLAM3 and SC-LeGO-LOAM, focusing on localization and mapping in both indoor and outdoor environments. The evaluation employs artificial and cost-effective datasets incorporating data from a 3D LiDAR and an RGB-D (color and depth) camera. A practical approach is introduced for calculating ground-truth trajectories and during benchmarking, reconstruction maps based on ground truth are established. To assess the performance, ATE and RPE are utilized to evaluate the accuracy of localization; standard deviation is employed to compare the stability during the localization process for different methods. While both algorithms exhibit satisfactory positioning accuracy, their performance is suboptimal in scenarios with inadequate textures. Furthermore, 3D reconstruction maps established by the two approaches are also provided for direct observation of their differences and the limitations encountered during map construction. Moreover, the research includes a comprehensive comparison of computational performance metrics, encompassing Central Processing Unit (CPU) utilization, memory usage, and an in-depth analysis. This evaluation revealed that Visual SLAM requires more CPU resources than LiDAR SLAM, primarily due to additional data storage requirements, emphasizing the impact of environmental factors on resource requirements. In conclusion, LiDAR SLAM is more suitable for the outdoors due to its comprehensive nature, while Visual SLAM excels indoors, compensating for sparse aspects in LiDAR SLAM. To facilitate further research, a technical guide was also provided for the researchers in related fields.

China’s urbanisation evolution and metropolitan area expansion, based on the Prolonged Artificial Nighttime-light Dataset (PANDA, 1984–2020)

ABSTRACT China’s massive urbanisation development will undoubtedly serve as a global reference. Due to the uncertainty of statistical data, nighttime light (NTL) data have emerged as alternative data for urbanisation evaluation. Here, the application of the Prolonged Artificial NTL Dataset of China (1984–2020) has been newly expanded. Total-value statistical, complex NTL index (CNLI), NTL concentration degree, rank-size rule, and Markov transfer matrix were used to systematically mine information about urban change from multiple perspectives. China’s urbanisation exhibited rapid growth and outwards expansion. The total percentage increase in NTL brightness and NTL area was 409.38% and 302.58%, respectively. The Yangtze River Delta urban agglomeration of East China had the fastest urbanisation (CNLI Trend = 0.0057/a, p < 0.01). Low NTL areas transitioned to medium NTL areas, and high and extremely-high NTL areas diffused to medium NTL areas. The cities in Eastern China and Southern China typically exhibited extremely-high type NTL areas, whereas other cities primarily exhibited medium NTL areas. The gaps between city sizes decreased over time (q Trend = – 0.0200/a, p < 0.01). Lowest-ranked cities exhibited the highest stability (>95%) in city size type transition. The spatiotemporal changes in NTL obtained were of great significance for monitoring urban expansion patterns, making government decisions, and quantifying China’s sustainable development.

Parametric and nonparametric versions of adaptive CUSUM charts for monitoring the location of individual measurements

Control charts are customarily developed under the assumption of normal quality characteristics to be monitored. However, in many real dataset applications, the normality assumption is not easy to hold. The in-control (IC) robustness of the charting schemes has significant importance for the valid out-of-control (OOC) performance. This article intends to investigate the IC robustness of the unbiased-function-based adaptive cumulative sum (ACUSUM) chart and nonparametric ACUSUM (NPACUSUM) chart against the non-normal process distributions including symmetrical, skewed, and contaminated normal distributions. The OOC run length profiles of the ACUSUM and the proposed NPACUSUM charts for the individual measurements against the non-normal distributions are also a part of this study. The run length profiles of the proposed charting schemes have been computed using the Monte Carlo simulation method. The artificial datasets have been taken from some symmetric and skewed distributions to implement the proposals. An electrical engineering dataset has also been taken for the implementation of the proposal on a real dataset.

Natural local density-based adaptive oversampling algorithm for imbalanced classification

Oversampling-based methods achieve impressive performance for classifying imbalanced data. However, many existing oversampling algorithms are still very sensitive to noise. Besides, these algorithms also require one or more parameters, how to set these parameters is very challenging. Furthermore, the generated samples by these algorithms are meaningless or unsafe. To solve these problems, a novel oversampling algorithm for unbalanced classification is presented, named Natural Local Density-based Adaptive Oversampling algorithm (NLDAO). NLDAO has four main advantages: (a) it does not need any parameter due to the use of natural neighbors to calculate local density; (b) it applies a noisy filter to remove noises, which makes the sample boundary cleaner so that the proposed method is robust to noise; (c) it unevenly distributes the generated samples to the minority class, which maintains the original characteristics and enhances the boundary classification ability; (d) it determines the generated region by tracking the sample proportion drop that declines the randomness of the synthesized and reduces the noisy generation. Finally, in experiments, we apply the NLDAO algorithm to artificial datasets to visually demonstrate its effectiveness. Moreover, intensive experiments on real datasets show that NLDAO can achieve better performance than state-of-the-art methods.

DEA-based internal validity index for clustering

Internal validity indices are crucial in evaluating the quality of clustering results, serving as valuable tools for comparing various clustering algorithms and determining the optimal number of clusters for datasets. Most existing internal validity indices use the worst-case scenario to represent the overall validity. Moreover, some indices assign equal weights to distances among different clusters, even when these distances might have varying degrees of influence on the overall validity. Data envelopment analysis (DEA) is an effective technique for evaluating the performance of decision-making units through the computation of the ratio of the weighted sum of outputs to the weighted sum of inputs. The weight assigned to each indicator signifies its degree of influence on efficiency. Furthermore, DEA can be viewed as a multiple-criteria evaluation methodology, wherein inputs and outputs are two sets of performance criteria. We propose a DEA-based internal validity index (DEAI) to evaluate the validity of the clustering results. In this approach, intra-cluster compactness and inter-cluster separation are employed for determining the input(s) and output(s). The DEAI is then applied to the artificial datasets and empirical examples. Experimental results illustrate that DEAI outperforms six classic internal validity indices in accurately identifying the optimal cluster across all 10 datasets.

Feature selection by Universum embedding

Feature selection in classification is an important task in machine learning. Inspired by the success of Universum support vector machine proposed by Weston et al. on improving the classification ability of classical support vector machine, this paper considers a special type of Universum and further lets it play its role in both useful feature identification and separating hyperplane construction, aiming to improve both the feature selection ability and classification performance of Universum support vector machine. By introducing this special Universum, a redundant feature can be identified by observing whether some Universum sample is useful. In fact, we prove that by observing the dual solution of the optimization problem, useful features can be selected from a set satisfying some properties. Due to the introduction of these extra Universum samples, it needs to cope with a large-scale optimization problem. To improve the training efficiency, we modify the sequential minimal optimization algorithm and further combine it with the coordinate descent technique to solve the proposed model. Experimental results on artificial datasets, benchmark datasets, and text classification datasets demonstrate that the proposed method improves the classification performance of support vector machine and Universum support vector machine, and also has good feature selection ability.

A Prolonged Artificial Nighttime-light Dataset of China (1984-2020)

Nighttime light remote sensing has been an increasingly important proxy for human activities. Despite an urgent need for long-term products and pilot explorations in synthesizing them, the publicly available long-term products are limited. A Night-Time Light convolutional LSTM network is proposed and applied the network to produce a 1-km annual Prolonged Artificial Nighttime-light DAtaset of China (PANDA-China) from 1984 to 2020. Assessments between modeled and original images show that on average the RMSE reaches 0.73, the coefficient of determination (R2) reaches 0.95, and the linear slope is 0.99 at the pixel level, indicating a high confidence in the quality of generated data products. Quantitative and visual comparisons witness PANDA-China’s superiority against other NTL datasets in its significantly longer NTL dynamics, higher temporal consistency, and better correlations with socioeconomics (built-up areas, gross domestic product, population) characterizing the most relevant indicator in different development phases. The PANDA-China product provides an unprecedented opportunity to trace nighttime light dynamics in the past four decades.