Pattern sampling has emerged as a promising approach for information discovery in large databases, allowing analysts to focus on a manageable subset of patterns. In this approach, patterns are randomly drawn based on an interestingness measure, such as frequency or hyper-volume. This paper presents the first sampling approach designed to handle interval patterns in numerical databases. This approach, named Fips, samples interval patterns proportionally to their frequency. It uses a multi-step sampling procedure and addresses a key challenge in numerical data: accurately determining the number of interval patterns that cover each object. We extend this work with HFips, which samples interval patterns proportionally to both their frequency and hyper-volume. These methods efficiently tackle the well-known long-tail phenomenon in pattern sampling. We formally prove that Fips and HFips sample interval patterns in proportion to their frequency and the product of hyper-volume and frequency, respectively. Through experiments on several databases, we demonstrate the quality of the obtained patterns and their robustness against the long-tail phenomenon.

The increasing availability of data and advancements in computational intelligence have accelerated the adoption of data-driven methods (DDMs) in product development. However, their integration into product development remains fragmented. This fragmentation stems from uncertainty, particularly the lack of clarity on what types of DDMs to use and when to employ them across the product development lifecycle. To address this, a necessary first step is to investigate the usage of DDM in engineering design by identifying which methods are being used, at which development stages, and for what application. This paper presents a PRISMA systematic literature review. The V-model as a product development framework was adopted and simplified into four stages: system design, system implementation, system integration, and validation. A structured search across Scopus, Web of Science, and IEEE Xplore (2014--2024) retrieved 1{,}689 records. After screening, 114 publications underwent full-text analysis. Findings show that machine learning (ML) and statistical methods dominate current practice, whereas deep learning (DL), though still less common, exhibits a clear upward trend in adoption. Additionally, supervised learning, clustering, regression analysis, and surrogate modeling are prevalent in design, implementation, and integration system stages but contributions to validation remain limited. Key challenges in existing applications include limited model interpretability, poor cross-stage traceability, and insufficient validation under real-world conditions. Additionally, it highlights key limitations and opportunities such as the need for interpretable hybrid models. This review is a first step toward design-stage guidelines; a follow-up synthesis should map computer science algorithms to engineering design problems and activities.

Quantifying numerical data involves addressing two key challenges: first, determining whether the data can be naturally quantified, and second, identifying the numerical intervals or ranges of values that correspond to specific value classes, referred to as "quantums," which represent statistically meaningful states. If such quantification is feasible, continuous streams of numerical data can be transformed into sequences of "symbols" that reflect the states of the system described by the measured parameter. People often perform this task intuitively, relying on common sense or practical experience, while information theory and computer science offer computable metrics for this purpose. In this study, we assess the applicability of metrics based on information compression and the Silhouette coefficient for quantifying numerical data. We also investigate the extent to which these metrics correlate with one another and with what is commonly referred to as "human intuition." Our findings suggest that the ability to classify numeric data values into distinct categories is associated with a Silhouette coefficient above 0.65 and a Dip Test below 0.5; otherwise, the data can be treated as following a unimodal normal distribution. Furthermore, when quantification is possible, the Silhouette coefficient appears to align more closely with human intuition than the "normalized centroid distance" method derived from information compression perspective.

Distribution estimation under local differential privacy (LDP) is a fundamental and challenging task. Significant progresses have been made on categorical data. However, due to different evaluation metrics, these methods do not work well when transferred to numerical data. In particular, we need to prevent the probability mass from being misplaced far away. In this paper, we propose a new approach that express the sample distribution using wavelet expansions. The coefficients of wavelet series are estimated under LDP. Our method prioritizes the estimation of low-order coefficients, in order to ensure accurate estimation at macroscopic level. Therefore, the probability mass is prevented from being misplaced too far away from its ground truth. We establish theoretical guarantees for our methods. Experiments show that our wavelet expansion method significantly outperforms existing solutions under Wasserstein and KS distances.

Discovering valid and meaningful mathematical equations from observed data plays a crucial role in scientific discovery. While this task, symbolic regression, remains challenging due to the vast search space and the trade-off between accuracy and complexity. In this paper, we introduce DiffuSR, a pre-training framework for symbolic regression built upon a continuous-state diffusion language model. DiffuSR employs a trainable embedding layer within the diffusion process to map discrete mathematical symbols into a continuous latent space, modeling equation distributions effectively. Through iterative denoising, DiffuSR converts an initial noisy sequence into a symbolic equation, guided by numerical data injected via a cross-attention mechanism. We also design an effective inference strategy to enhance the accuracy of the diffusion-based equation generator, which injects logit priors into genetic programming. Experimental results on standard symbolic regression benchmarks demonstrate that Dif-fuSR achieves competitive performance with state-of-the-art autoregressive methods and generates more interpretable and diverse mathematical expressions.

Heterogeneous data, which encompass both numerical financial variables and textual records, present substantial challenges for credit monitoring. To address this issue, we propose Advanced Spectral Clustering (ASC), a method that integrates financial and textual similarities through an optimized weight parameter and selects eigenvectors using a novel eigenvalue-silhouette optimization approach. Evaluated on a dataset comprising 1,428 small and medium-sized enterprises (SMEs), ASC achieves a Silhouette score that is 18% higher than that of a single-type data baseline method. Furthermore, the resulting clusters offer actionable insights; for instance, 51% of low-risk firms are found to include the term 'social recruitment' in their textual records. The robustness of ASC is confirmed across multiple clustering algorithms, including k-means, k-medians, and k-medoids, with ΔIntra/Inter < 0.13 and ΔSilhouette Coefficient < 0.02. By bridging spectral clustering theory with heterogeneous data applications, ASC enables the identification of meaningful clusters, such as recruitment-focused SMEs exhibiting a 30% lower default risk, thereby supporting more targeted and effective credit interventions.

The integration of wind energy into power grids necessitates accurate ultra-short-term wind power forecasting to ensure grid stability and optimize resource allocation. This study introduces M2WLLM, an innovative model that leverages the capabilities of Large Language Models (LLMs) for predicting wind power output at granular time intervals. M2WLLM overcomes the limitations of traditional and deep learning methods by seamlessly integrating textual information and temporal numerical data, significantly improving wind power forecasting accuracy through multi-modal data. Its architecture features a Prompt Embedder and a Data Embedder, enabling an effective fusion of textual prompts and numerical inputs within the LLMs framework. The Semantic Augmenter within the Data Embedder translates temporal data into a format that the LLMs can comprehend, enabling it to extract latent features and improve prediction accuracy. The empirical evaluations conducted on wind farm data from three Chinese provinces demonstrate that M2WLLM consistently outperforms existing methods, such as GPT4TS, across various datasets and prediction horizons. The results highlight LLMs' ability to enhance accuracy and robustness in ultra-short-term forecasting and showcase their strong few-shot learning capabilities.

We developed a deep learning algorithm for human activity recognition using sensor signals as input. In this study, we built a pretrained language model based on the Transformer architecture, which is widely used in natural language processing. By leveraging this pretrained model, we aimed to improve performance on the downstream task of human activity recognition. While this task can be addressed using a vanilla Transformer, we propose an enhanced n-dimensional numerical processing Transformer that incorporates three key features: embedding n-dimensional numerical data through a linear layer, binning-based pre-processing, and a linear transformation in the output layer. We evaluated the effectiveness of our proposed model across five different datasets. Compared to the vanilla Transformer, our model demonstrated 10%-15% improvements in accuracy.