Adaptive regularization parameter selection for high-dimensional inverse problems: A Bayesian approach with Tucker low-rank constraints

This paper introduces a novel variational Bayesian method that integrates Tucker decomposition for efficient high-dimensional inverse problem solving. The method reduces computational complexity by transforming variational inference from a high-dimensional space to a lower-dimensional core tensor space via Tucker decomposition. A key innovation is the introduction of per-mode precision parameters, enabling adaptive regularization for anisotropic structures. For instance, in directional image deblurring, learned parameters align with physical anisotropy, applying stronger regularization to critical directions (e.g., row vs. column axes). The method further estimates noise levels from data, eliminating reliance on prior knowledge of noise parameters (unlike conventional benchmarks such as the discrepancy principle (DP)). Experimental evaluations across 2D deblurring, 3D heat conduction, and Fredholm integral equations demonstrate consistent improvements in quantitative metrics (PSNR, SSIM) and qualitative visualizations (error maps, precision parameter trends) compared to L-curve criterion, generalized cross-validation (GCV), unbiased predictive risk estimator (UPRE), and DP. The approach scales to problems with 110,000 variables and outperforms existing methods by 0.73-2.09 dB in deblurring tasks and 6.75 dB in 3D heat conduction. Limitations include sensitivity to rank selection in Tucker decomposition and the need for theoretical analysis. Future work will explore automated rank selection and theoretical guarantees. This method bridges Bayesian theory and scalable computation, offering practical solutions for large-scale inverse problems in imaging, remote sensing, and scientific computing.

GARCH-FIS: A Hybrid Forecasting Model with Dynamic Volatility-Driven Parameter Adaptation

This paper proposes a novel hybrid model, termed GARCH-FIS, for recursive rolling multi-step forecasting of financial time series. It integrates a Fuzzy Inference System (FIS) with a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to jointly address nonlinear dynamics and time-varying volatility. The core innovation is a dynamic parameter adaptation mechanism for the FIS, specifically activated within the multi-step forecasting cycle. In this process, the conditional volatility estimated by a rolling window GARCH model is continuously translated into a price volatility measure. At each forecasting step, this measure, alongside the updated mean of the sliding window data -- which now incorporates the most recent predicted price -- jointly determines the parameters of the FIS membership functions for the next prediction. Consequently, the granularity of the fuzzy inference adapts as the forecast horizon extends: membership functions are automatically widened during high-volatility market regimes to bolster robustness and narrowed during stable periods to enhance precision. This constitutes a fundamental advancement over a static one-step-ahead prediction setup. Furthermore, the model's fuzzy rule base is automatically constructed from data using the Wang-Mendel method, promoting interpretability and adaptability. Empirical evaluation, focused exclusively on multi-step forecasting performance across ten diverse financial assets, demonstrates that the proposed GARCH-FIS model significantly outperforms benchmark models -- including Support Vector Regression(SVR), Long Short-Term Memory networks(LSTM), and an ARIMA-GARCH econometric model -- in terms of predictive accuracy and stability, while effectively mitigating error accumulation in extended recursive forecasts.

Orthogonal Subspace Clustering: Enhancing High-Dimensional Data Analysis through Adaptive Dimensionality Reduction and Efficient Clustering

This paper presents Orthogonal Subspace Clustering (OSC), an innovative method for high-dimensional data clustering. We first establish a theoretical theorem proving that high-dimensional data can be decomposed into orthogonal subspaces in a statistical sense, whose form exactly matches the paradigm of Q-type factor analysis. This theorem lays a solid mathematical foundation for dimensionality reduction via matrix decomposition and factor analysis. Based on this theorem, we propose the OSC framework to address the "curse of dimensionality" -- a critical challenge that degrades clustering effectiveness due to sample sparsity and ineffective distance metrics. OSC integrates orthogonal subspace construction with classical clustering techniques, introducing a data-driven mechanism to select the subspace dimension based on cumulative variance contribution. This avoids manual selection biases while maximizing the retention of discriminative information. By projecting high-dimensional data into an uncorrelated, low-dimensional orthogonal subspace, OSC significantly improves clustering efficiency, robustness, and accuracy. Extensive experiments on various benchmark datasets demonstrate the effectiveness of OSC, with thorough analysis of evaluation metrics including Cluster Accuracy (ACC), Normalized Mutual Information (NMI), and Adjusted Rand Index (ARI) highlighting its advantages over existing methods.

Edge Detection based on Channel Attention and Inter-region Independence Test

Existing edge detection methods often suffer from noise amplification and excessive retention of non-salient details, limiting their applicability in high-precision industrial scenarios. To address these challenges, we propose CAM-EDIT, a novel framework that integrates Channel Attention Mechanism (CAM) and Edge Detection via Independence Testing (EDIT). The CAM module adaptively enhances discriminative edge features through multi-channel fusion, while the EDIT module employs region-wise statistical independence analysis (using Fisher's exact test and chi-square test) to suppress uncorrelated noise.Extensive experiments on BSDS500 and NYUDv2 datasets demonstrate state-of-the-art performance. Among the nine comparison algorithms, the F-measure scores of CAM-EDIT are 0.635 and 0.460, representing improvements of 19.2\% to 26.5\% over traditional methods (Canny, CannySR), and better than the latest learning based methods (TIP2020, MSCNGP). Noise robustness evaluations further reveal a 2.2\% PSNR improvement under Gaussian noise compared to baseline methods. Qualitative results exhibit cleaner edge maps with reduced artifacts, demonstrating its potential for high-precision industrial applications.

Edge-preserving Image Denoising via Multi-scale Adaptive Statistical Independence Testing

Edge detection is crucial in image processing, but existing methods often produce overly detailed edge maps, affecting clarity. Fixed-window statistical testing faces issues like scale mismatch and computational redundancy. To address these, we propose a novel Multi-scale Adaptive Independence Testing-based Edge Detection and Denoising (EDD-MAIT), a Multi-scale Adaptive Statistical Testing-based edge detection and denoising method that integrates a channel attention mechanism with independence testing. A gradient-driven adaptive window strategy adjusts window sizes dynamically, improving detail preservation and noise suppression. EDD-MAIT achieves better robustness, accuracy, and efficiency, outperforming traditional and learning-based methods on BSDS500 and BIPED datasets, with improvements in F-score, MSE, PSNR, and reduced runtime. It also shows robustness against Gaussian noise, generating accurate and clean edge maps in noisy environments.

Orthogonal Factor-Based Biclustering Algorithm (BCBOF) for High-Dimensional Data and Its Application in Stock Trend Prediction

Biclustering is an effective technique in data mining and pattern recognition. Biclustering algorithms based on traditional clustering face two fundamental limitations when processing high-dimensional data: (1) The distance concentration phenomenon in high-dimensional spaces leads to data sparsity, rendering similarity measures ineffective; (2) Mainstream linear dimensionality reduction methods disrupt critical local structural patterns. To apply biclustering to high-dimensional datasets, we propose an orthogonal factor-based biclustering algorithm (BCBOF). First, we constructed orthogonal factors in the vector space of the high-dimensional dataset. Then, we performed clustering using the coordinates of the original data in the orthogonal subspace as clustering targets. Finally, we obtained biclustering results of the original dataset. Since dimensionality reduction was applied before clustering, the proposed algorithm effectively mitigated the data sparsity problem caused by high dimensionality. Additionally, we applied this biclustering algorithm to stock technical indicator combinations and stock price trend prediction. Biclustering results were transformed into fuzzy rules, and we incorporated profit-preserving and stop-loss rules into the rule set, ultimately forming a fuzzy inference system for stock price trend predictions and trading signals. To evaluate the performance of BCBOF, we compared it with existing biclustering methods using multiple evaluation metrics. The results showed that our algorithm outperformed other biclustering techniques. To validate the effectiveness of the fuzzy inference system, we conducted virtual trading experiments using historical data from 10 A-share stocks. The experimental results showed that the generated trading strategies yielded higher returns for investors.