The kernel density estimator (KDE) is a probability density function (PDF) estimation tool that has found wide application in the fields of data mining and machine learning. The performance of KDE in fitting PDF depends on the selection of the kernel function and the corresponding kernel bandwidth. The previous studies conducted on KDE construction primarily focus on the selection and optimization of the kernel bandwidth. The existing model-driven KDEs ignore the internal distribution characteristics of the multi-modal and mode-proximity data, producing high fitting uncertainty and low estimation accuracy. In this study, we propose a data-driven fused kernel density estimator (DDF-KDE) that constructs a well-performed KDE by partitioning data points into multiple subsets and integrating the base KDEs constructed on these subsets with the model evaluation strategy. The initial number of modes for given dataset is analyzed using the peak observation method used in the I-nice algorithm. Furthermore, we combined Akaike information criterion (AIC) and Bayesian information criterion (BIC) to determine the optimal number of modes required for constructing the final DDF-KDE. We conducted a series of persuasive experiments on 16 representative multi-modal datasets to validate the feasibility, rationality and effectiveness of DDF-KDE. The experimental results demonstrate that DDF-KDE achieves lower estimation error and superior PDF approximation compared with five existing classic KDEs when using the same kernel function and bandwidth selection method. Thus, DDF-KDE exhibits better performance for analyzing the unknown PDF and can be used for multi-modal PDF estimation.

The high volatility of gasoline futures prices challenges producers, investors, and policymakers, as inaccurate forecasts may cause substantial economic losses. Existing forecasting methods often struggle with non-stationarity, noise, and trend sensitivity, limiting accuracy and robustness. To address these issues, we propose a Synergistic Multi-Mechanism Cooperative-Driven (MMCD) forecasting framework. MMCD integrates rolling-window segmentation, Daubechies 4 (Db4) wavelet decomposition, and QuantileTransformer normalization for multi-scale denoising, combined with Bidirectional Gated Recurrent Units (BiGRU), dilated convolutions, and a self-attention mechanism to capture temporal dependencies. A dual-constrained trend loss jointly optimizes numerical precision and directional consistency. Experiments on West Texas Intermediate (WTI) crude oil and Reformulated Blendstock for Oxygenate Blending (RBOB) gasoline futures show that MMCD achieves RMSE values of 1.1970 and 0.0349 respectively, with R & sup2; exceeding 0.9890 on both series and directional accuracy (MDA > 0.833), surpassing benchmark models. Cross-domain validation on the SPLV (S&P 500 Low Volatility) equity ETF further confirms generalizability, yielding an RMSE of 1.3842, R & sup2; of 0.9346, and a Calmar Ratio of 2.8462. Ablation studies verify each component's essential contribution. The proposed framework thus offers a robust forecasting tool for volatile energy markets, with evidence of broader applicability.

In geo-distributed big data computing based on Apache Spark, data skew may cause excessive workloads on certain partitions, thereby delaying the overall execution progress of computing tasks. Existing data skew handling approaches are mainly designed for single data center environments and are insufficient to achieve global partition load balancing in geo-distributed scenarios. To address this issue, this paper proposes a data skew handling method for geo-distributed big data computing, termed Skew Detection and Repartition (SDR), which consists of two key operations: skewed partition detection and balanced repartitioning. Specifically, SDR first collects statistical information, including the frequency and corresponding data size of each key generated during the Map phase across multiple data centers. A key-based pre-aggregation mechanism is introduced to reduce cross-domain communication overhead during statistic collection. Then, a median-driven skew detection strategy is employed to identify globally skewed partitions. Furthermore, a greedy bin-packing-based repartitioning algorithm is designed, where the data size associated with each key is considered as its weight. The algorithm sorts keys in descending order of their weights and iteratively assigns them to the currently maximum load partition that does not exceed the target partition size. While ensuring that records with the same key are not split across different partitions, the proposed algorithm dynamically balances partition workloads and improves subsequent task scheduling efficiency. Experimental results demonstrate that SDR effectively mitigates partition skewness and reduces task execution time across datasets with different skew levels. In highly skewed WordCount workloads, SDR reduces execution time by up to 32.20% compared with the original hash partitioning method. Moreover, across five datasets with varying skew levels, SDR achieves an average reduction of 10.74% in overall execution time.

Time series forecasting is essential in finance, meteorology, healthcare, and industrial process control. Traditional time-domain forecasting methods struggle to capture complex patterns and structures. Frequency-domain analysis offers an alternative perspective for identifying periodic and oscillatory behaviour. However, current frequency-domain methods often lose vital information by excluding high-frequency components, which contain crucial short-term variations and abrupt changes that impact forecasting accuracy. Additionally, existing multilevel analyses inadequately integrate local and global features, making it difficult for forecasting algorithms to capture both detailed local information and broader global trends. To address these issues, this study introduces FreqMLNet, a novel non-transformer architecture that combines frequency-domain reconstruction and multilevel feature representation to enhance time series forecasting. FreqMLNet extracts periodic patterns through a frequency-domain reconstruction module and integrates information from multiple scales using multilevel feature representation, resulting in a more comprehensive time series feature representation. Experimental results demonstrate that the proposed model achieves an average improvement of 14.39% in mean squared error across seven long-term datasets and 11.03% in symmetric mean absolute percentage error across four short-term datasets compared to state-of-the-art models. Moreover, an in-depth analysis reveals that FreqMLNet exhibits greater robustness and prediction accuracy, particularly in complex time series forecasting tasks.

1 Introduction Big data,characterized by its unprecedented volume,velocity,variety,and veracity[1],has revolutionized the way we collect,analyze,and interpret information[2].Modern technologies,from Internet of Things devices to social media platforms,generate massive datasets that capture intricate patterns of human behavior,natural phenomena,and industrial processes.

Existing ensemble-based positive and unlabeled learning (PUL) methods often fail to adequately account for the impact of noise in both positive and unlabeled samples during classifier construction. To address this issue, this paper proposes a naïve Bayesian ensemble-based PUL algorithm (NBEB-PUL), which consists of two stages: label assignment and noise filtering. In the label assignment stage, NBEB-PUL employs naïve Bayesian classifiers as base learners and integrates them using the AdaBoosting ensemble strategy to construct a strong classifier, named Ada-NBC. This strong classifier is then utilized to compute the mean posterior probabilities of a validation set for unlabeled samples, enabling explicit modeling of labeling uncertainty. Based on low-uncertainty predictions a set of reliable positive samples is iteratively identified, along with a residual unlabeled sample set. In the noise filtering stage, NBEB-PUL leverages the ensemble classifier generated in the first stage to reclassify the reliable positive set and the residual unlabeled set, resulting in Ada-NBC-predicted positive and negative sample sets. These sets are then intersected with the first-stage positive and unlabeled sets to extract overlapping high-confidence samples, forming the final positive and negative sample sets. The samples pruned from the dataset during this process are identified as noise. The feasibility, rationality, and effectiveness of NBEB-PUL were validated on 23 benchmark datasets from UCI and KEEL. Experimental results demonstrate that the algorithm exhibits stable convergence during the training process as the number of iterations increases. Moreover, NBEB-PUL outperforms six state-of-the-art PUL algorithms (S-EM, Biased-SVM, Modified-PUL, PU-LP, LP-PUL, and AdaPU) in terms of classification accuracy under varying positive sample proportions of 0.45, 0.40, 0.35, and 0.30. These results confirm that NBEB-PUL provides an effective and robust solution for positive and unlabeled learning in the presence of noise.

Accurate classification and forecasting of renewable energy, such as wind and photovoltaic (PV) power, are critical for effective grid management and stable integration of renewable energy sources. However, existing computational methods-particularly time-series-based approaches-often fail to capture complex, latent relationships in renewable energy data and offer limited interpretability. To address these challenges, we propose HUF4WP (High-Utility Framework for Wind/PV power), a high-utility data fusion framework designed to extract and leverage predictive patterns from wind/PV data. HUF4WP transforms continuous energy data into a discretized format and applies high-utility pattern mining algorithms to discover both ordered and unordered patterns, along with high-utility association rules. These patterns are then utilized for wind and solar power classification/prediction by fusing informative feature interactions across various conditions. We evaluate HUF4WP on eight PV and six wind datasets using seven classification models and seven evaluation metrics. Experimental results demonstrate that HUF4WP achieves better classification performance compared to baseline models trained on the raw features. It also provides faster computational performance than baseline and regression-based forecasting approaches. Moreover, the discovered patterns and rules provide interpretable insights into key features and their contributions to renewable energy dynamics.

The link prediction (LP) for social network is an important research direction of complex network mining, which tries to detect the potential relationship between network nodes. The popular LP algorithms for social networks include thestatic similarity-based indicators, dynamic learning-based predictors and content-based methods. Although the experimental results have reported the good performances in specific application scenarios of these algorithms, some essential defects such as prediction unreliability and detection incapability still exist and cannot be effectively solved up to now. Therefore, a reliability enhancement-based link prediction (RE-LP) algorithm is proposed to make up the above-mentioned shortcomings of existing LP algorithms. There are three main components in RE-LP algorithm, i.e., non-existing link partition, reliable predictor construction, and connection probability calculation. In RE-LP algorithm, the observable non-existing links are sophisticatedly partitioned into highly-reliable non-existing (HRNE) links and possibly-observed existing (POE) links. It then continuously identifies HRNE links from the POE links in an iterative manner, and uses a well-performed Bayesian classifier-based link predictor to calculate the connection probabilities of the POE links, in order to achieve the goal of accurately and reliably predicting unknown links. Through a series of verification experiments, the advantages of RE-LP algorithm in terms of feasibility, rationality and effectiveness are fully demonstrated. The experimental results demonstrate that RE-LP algorithm can obtain the 21.7%~36.1% higher prediction AUC than 5 advanced LP algorithms and meanwhile is able to detect the potential links with high credibility.

We investigate the imaginary-time relaxation critical dynamics of the two-dimensional transverse-field Ising model using infinite projected entangled pair states (iPEPS) with the full-update strategy. Simulating directly in the thermodynamic limit, we explore the relaxation process near the critical point with two types of initial states: a fully polarized state and a product state with a small magnetization. For the fully polarized state, the magnetization shows a power-law scaling M proportional to tau-beta/(nu z) in the imaginary-time evolution, from which both the critical point and critical exponent can be determined with high accuracy. For the nearly paramagnetic state, the relaxation process exhibits a behavior of M proportional to tau theta with theta = 0.1958 being the critical initial-slip exponent, which is in good agreement with that obtained from the dynamic scaling of the self-correlation in the quantum Monte Carlo method. These universal features emerge well before the system converges to the ground state, demonstrating the efficiency of imaginary-time evolution for probing quantum criticality. Our results demonstrate that iPEPS can serve as a robust and scalable method for studying dynamical critical phenomena in two-dimensional quantum many-body systems.

In the Spark distributed computing framework, data skew—especially the hot key issue for large-scale data processing—is one of the main causes of performance bottlenecks. Traditional partitioning methods often overlook effective handling of hot keys, causing key-value pairs to cluster in a few partitions, resulting in imbalanced data partitioning. This paper addresses this issue by introducing an efficient TemporalHash partitioning (THP) algorithm. By extending Spark's partitioner class, THP implements a custom partitioning strategy that incorporates a uniqueHash function and a getPartition function. THP first concatenates the input key with the system's current nanosecond timestamp. The resulting string is then processed using the MurmurHash3 algorithm to blend the key with the times-tamp, yielding the final hash code. The partition index is then determined by applying the modulo operation on this hash code relative to the total number of partitions. To assess THP's effectiveness, experiments were conducted using sorting and word frequency statistics applications, comparing THP against state-of-the-art partitioning algorithms. Results show that THP significantly reduces the coefficient of variation in partition sizes by up to three orders of magnitude, highlighting its effectiveness in high-skew scenarios and large-scale data contexts. Moreover, THP excels at mitigating data skew when generating unique RDD keys in distributed systems, demonstrating its broad applicability and practical advantages. Thanks to its efficient hash calculations, THP does not increase time complexity, effectively mitigates data skew, enhances Spark's data processing efficiency through uniform partitioning, optimizes CPU resource utilization, and circumvents the waste of CPU time slices due to prolonged single job processing times. This represents a significant technological advancement for physical distributed computing framework.

Estimating probability density functions (PDFs) is critical in data analysis, particularly for complex multimodal distributions. traditional kernel density estimator (KDE) methods often face challenges in accurately capturing multimodal structures due to their uniform weighting scheme, leading to mode loss and degraded estimation accuracy. This paper presents the flexible kernel density estimator (F-KDE), a novel nonparametric approach designed to address these limitations. F-KDE introduces the concept of kernel unit inequivalence, assigning adaptive weights to each kernel unit, which better models local density variations in multimodal data. The method optimises an objective function that integrates estimation error and log-likelihood, using a particle swarm optimisation (PSO) algorithm that automatically determines optimal weights and bandwidths. Through extensive experiments on synthetic and real-world datasets, we demonstrated that (1) the weights and bandwidths in F-KDE stabilise as the optimisation algorithm iterates, (2) F-KDE effectively captures the multimodal characteristics and (3) F-KDE outperforms state-of-the-art density estimation methods regarding accuracy and robustness. The results confirm that F-KDE provides a valuable solution for accurately estimating multimodal PDFs.

The utilisation of effective dependent attribute groups (DAGs) can benefit the construction of a high-performance na & iuml;ve Bayesian classifier (NBC), to alleviate the conditional independence assumption of na & iuml;ve Bayes. An NBC with optimised DAGs retains the simple NBC structure and significantly enhances NBC generalisation performance. However, it is extremely difficult to determine the appropriate DAGs for a given dataset when training an NBC with good generalisation capability. Therefore, this study proposes a relaxed NBC (RNBC) based on the maximum DAGs (MDAGs), that relaxes the attribute independence assumption by constructing an NBC with a series of MDAGs generated from the original condition attribute set. To determine the MDAGs, the RNBC includes an effective objective function to determine the degree of membership of conditional attributes belonging to different DAGs. Unlike the regular computation of class-conditional probability in traditional NBCs with whole condition attributes, the RNBC calculates multiple class-conditional probabilities corresponding to non-overlapping MDAGs and their products are utilised to construct the classification system. Exhaustive experiments were conducted to systematically verify the feasibility, rationality, and effectiveness of RNBC. The results demonstrate that (1) the objective function used to determine the MDAGs is convergent, and that MDAGs can be obtained with low time consumption; (2) the RNBC with MDAGs achieves a lower classification risk than traditional NBCs with the independence assumption; and (3) the RNBC achieves statistically higher training/testing accuracy and probability estimation quality with lower classification risk compared with eight representative Bayesian classifiers spanning 22 benchmark datasets. The best average testing accuracy, probability mean square error, and area under the curve for the RNBC were 0.76, 0.35, and 0.85, respectively. These results systematically confirmed that the proposed RNBC is an efficient NBC variant with high structural stability, strong correlation expression, and good generalisability.

Several methods have been developed to alleviate the impact of conditional independence assumption on the performance of naive Bayes classifiers (NBCs). Among these, the attribute-weighted NBC has gained considerable attention in recent years. The existing weighted NBC algorithms primarily determine attribute weights using metrics such as mutual information, entropy, and accuracy ratios. However, they typically ignore the underlying probability and spatial distribution information embedded within attributes and classes. This study proposes a novel multi-source weighted NBC (MS-WNBC) to address this gap and establish a more robust framework for attribute-weighted characterization. The proposed method innovatively computes attribute weights by integrating three sources of information-attribute correlation, probability distribution, and structural characteristics. This multi-source fusion strategy enhances the discriminative quality of attribute weights, thereby systematically reducing classification risk. Experiments to evaluate the performance of MS-WNBC revealed the following: (1) the MS-WNBC improves the classification robustness of NBC by fusing multi-source weights; (2) it significantly reduces the classification risk while exhibiting strong resistance to interference; and (3) it statistically improves the training and testing accuracy, average probability estimation quality, and area under the curve when compared with NBC and its seven variants across 30 benchmark datasets. The study findings indicate that the MS-WNBC, characterized by high structural stability, robust correlation expression capabilities, and excellent generalization performance, is an efficient variant of NBC.

The naive Bayesian classifier (NBC) is a supervised machine learning algorithm having a simple model structure and good theoretical interpretability. However, the generalization performance of NBC is limited to a large extent by the assumption of attribute independence. To address this issue, this paper proposes a novel attribute grouping-based NBC (AG-NBC), which is a variant of the classical NBC trained with different attribute groups. AG-NBC first applies a novel effective objective function to automatically identify optimal dependent attribute groups (DAGs). Condition attributes in the same DAG are strongly dependent on the class attribute, whereas attributes in different DAGs are independent of one another. Then, for each DAG, a random vector functional link network with a SoftMax layer is trained to output posterior probabilities in the form of joint probability density estimation. The NBC is trained using the grouping attributes that correspond to the original condition attributes. Extensive experiments were conducted to validate the rationality, feasibility, and effectiveness of AG-NBC. Our findings showed that the attribute groups chosen for NBC can accurately represent attribute dependencies and reduce overlaps between different posterior probability densities. In addition, the comparative results with NBC, flexible NBC (FNBC), tree augmented Bayes network (TAN), gain ratio-based attribute weighted naive Bayes (GRAWNB), averaged one-dependence estimators (AODE), weighted AODE (WAODE), independent component analysis-based NBC (ICA-NBC), hidden naive Bayesian (HNB) classifier, and correlation-based feature weighting filter for naive Bayes (CFW) show that AG-NBC obtains statistically better testing accuracies, higher area under the receiver operating characteristic curves (AUCs), and fewer probability mean square errors (PMSEs) than other Bayesian classifiers. The experimental results demonstrate that AG-NBC is a valid and efficient approach for alleviating the attribute independence assumption when building NBCs.

Time-series forecasting in electricity markets is crucial for ensuring reliable energy supply and stable grid operations. However, traditional time-domain forecasting models encounter significant challenges in capturing the intricate patterns of electricity demand, particularly in multi-frequency data comprising both long-term and short-term dependencies. While frequency-domain analysis is effective at capturing cyclical patterns and short-term fluctuations, existing models struggle to adapt to the dynamic nature of frequency components. Moreover, accurately capturing both global trends and local variations in time-series data remains a persistent challenge. To address these issues, this study introduces a novel adaptive frequency-domain feature extraction model with large language models (AFDFE-LLM) for time-series forecasting. AFDFE-LLM dynamically segments low-, medium-, and high-frequency components, enabling more precise distinction between long-term trends and short-term fluctuations. This approach enhances the adaptability of AFDFE-LLM to respond to the complex and volatile nature of electricity market time-series data. Furthermore, by dynamically optimising frequency-band processing, AFDFE-LLM effectively retains high-frequency details, thus overcoming the information loss typically associated with excessive smoothing in traditional approaches. Experimental results demonstrate that AFDFE-LLM significantly outperforms traditional models, achieving a mean squared error of 0.421 and a mean absolute error of 0.410 on the ETTm1 dataset. The results confirm the robustness and prediction accuracy of the proposed model, particularly in capturing sharp short-term fluctuations and handling complex multi-frequency intertwined data.

Spark is a widely-used big data computing framework to process and analyze the explosive-growing data. The cloud can provide on-demand and pay-as-you-go computing resources to satisfy the users’ requirements. Currently, many organizations have deployed big data computing clusters on the cloud. These clusters are required to efficiently handle the Spark job scheduling problem so as to meet the QoS requirements of various users, such as reducing the cost of resource usage and shortening the job response time. However, most of the existing methods don’t consider the requirements of multiple users together, and fail to take into account the characteristics of Spark cluster environmentsand workloads. To address the above-mentioned challenge, a new Spark job scheduler based on DRL technology was designed to adapt to multiple QoS requirements by modeling the job scheduling problem of Spark clusters deployed in the cloud. A DRL cluster simulation environment was built to train the core DRL Agent of job scheduler. In the scheduling environment, training methods based on absolute deep Q-network and a combination of proximal policy optimization and generalized advantage estimation were implemented, enabling DRL agent to adaptively learn the characteristics of different types of jobs as well as the characteristics of dynamic and bursty cluster environments. This enables rational scheduling of Spark jobs to reduce the total usage cost of the cluster and shorten the average response time of jobs. Testing results of DRL Agent on the benchmark suite show that compared with other existing Spark job scheduling solutions, the newly designed DRL Agent job scheduler in this paper has significant advantages in terms of total cluster usage cost, average job response time and QoS achievement rate, which confirming the feasibility and effectiveness of the job scheduler designed in this paper.

The Gaussian mixture model (GMM) is a classical probabilistic representation model widely used in unsupervised learning. GMM performs poorly on high-dimensional data (HDD) due to the requirement of estimating a large number of parameters with relatively few observations. To address this, the paper proposes a novel subspace-based GMM clustering ensemble (SubGMM-CE) algorithm tailored for HDD. The proposed SubGMM-CE algorithm comprises three key components. A series of low-dimensional subspaces are dynamically determined, considering the optimal number of GMM components. The GMM-based clustering algorithm is applied to each subspace to obtain a series of heterogeneous GMM models. These GMM base clustering results are merged using the newly-designed relabeling strategy based on the average shared affiliation probability, generating the final clustering result for high-dimensional unlabeled data. An exhaustive experimental evaluation validates the feasibility, rationality, effectiveness, and robustness to noise of the SubGMM-CE algorithm. Results show that SubGMM-CE achieves higher stability and more accurate clustering results, outperforming nine state-of-the-art clustering algorithms in normalized mutual information, clustering accuracy, and adjusted rand index scores. This demonstrates the viability of the SubGMM-CE algorithm in addressing HDD clustering challenges.

High Dynamic Range (HDR) images present unique challenges for Learned Image Compression (LIC) due to their complex domain distribution compared to Low Dynamic Range (LDR) images. In coding practice, HDR-oriented LIC typically adopts preprocessing steps (e.g., perceptual quantization and tone mapping operation) to align the distributions between LDR and HDR images, which inevitably comes at the expense of perceptual quality. To address this challenge, we rethink the HDR imaging process which involves fusing multiple exposure LDR images to create an HDR image and propose a novel HDR image compression paradigm, Unifying Imaging and Compression (HDR-UIC). The key innovation lies in establishing a seamless pipeline from image capture to delivery and enabling end-to-end training and optimization. Specifically, a Mixture-ATtention (MAT)-based compression backbone merges LDR features while simultaneously generating a compact representation. Meanwhile, the Reference-guided Misalignment-aware feature Enhancement (RME) module mitigates ghosting artifacts caused by misalignment in the LDR branches, maintaining fidelity without introducing additional information. Furthermore, we introduce an Appearance Redundancy Removal (ARR) module to optimize coding resource allocation among LDR features, thereby enhancing the final HDR compression performance. Extensive experimental results demonstrate the efficacy of our approach, showing significant improvements over existing state-of-the-art HDR compression schemes. Our code is available at: https://github.com/plf1999/HDR-UIC.

Clustering high-dimensional data presents a critical technical challenge due to the curse of dimensionality, feature redundancy, and sensitivity to noise-issues that significantly degrade clustering accuracy in applications such as gene expression analysis, image recognition, and anomaly detection. Existing solutions often rely on dimensionality reduction techniques that risk discarding discriminative features, or on deep learning methods that require large-scale training data and suffer from poor interpretability. To address these limitations, this study proposes a novel discriminative subspace clustering algorithm that avoids traditional dimensionality reduction and instead operates directly in the high-dimensional space. Our method partitions the sample space into multiple local affine hulls and introduces a discriminative geometric distance metric that accounts for both relevant and irrelevant subspaces. Specifically, the model measures the ratio between a query sample's proximity to its class-specific affine hull and its distance from unrelated class subspaces. This dual-space modeling improves both intra-class compactness and inter-class separation. To ensure computational efficiency, we reformulate distance calculations as matrix multiplications and leverage SVD for subspace projection, enabling scalable performance across large datasets. Extensive experiments on seven benchmark datasets demonstrate that the proposed method consistently outperforms state-of-the-art clustering algorithms. It achieves up to 92.60% accuracy on MNIST and maintains high robustness on sparse and noisy data, validating its effectiveness for high-dimensional clustering tasks. This work contributes a geometrically interpretable and computationally efficient framework that closes a long-standing gap in unsupervised learning under high-dimensional constraints.