Hao Shu

Hao Shu, Jicheng Li, Yu Jin et al.

In recent years, the prediction of multidimensional time series data has become increasingly important due to its wide-ranging applications. Tensor-based prediction methods have gained attention for their ability to preserve the inherent structure of such data. However, existing approaches, such as tensor autoregression and tensor decomposition, often have consistently failed to provide clear assertions regarding the number of samples that can be exactly predicted. While matrix-based methods using nuclear norms address this limitation, their reliance on matrices limits accuracy and increases computational costs when handling multidimensional data. To overcome these challenges, we reformulate multidimensional time series prediction as a deterministic tensor completion problem and propose a novel theoretical framework. Specifically, we develop a deterministic tensor completion theory and introduce the Temporal Convolutional Tensor Nuclear Norm (TCTNN) model. By convolving the multidimensional time series along the temporal dimension and applying the tensor nuclear norm, our approach identifies the maximum forecast horizon for exact predictions. Additionally, TCTNN achieves superior performance in prediction accuracy and computational efficiency compared to existing methods across diverse real-world datasets, including climate temperature, network flow, and traffic ride data. Our implementation is publicly available at https://github.com/HaoShu2000/TCTNN.

Hao Shu

Density-based clustering is the most popular clustering algorithm since it can identify clusters of arbitrary shape as long as they are separated by low-density regions. However, a high-density region that is not separated by low-density ones might also have different structures belonging to multiple clusters. As far as we know, all previous density-based clustering algorithms fail to detect such structures. In this paper, we provide a novel density-based clustering scheme to address this problem. It is the rst clustering algorithm that can detect meticulous structures in a high-density region that is not separated by low-density ones and thus extends the range of applications of clustering. The algorithm employs secondary directed differential, hierarchy, normalized density, as well as the self-adaption coefficient, called Structure Detecting Cluster by Hierarchical Secondary Directed Differential with Normalized Density and Self-Adaption, dubbed SDC-HSDD-NDSA. Experiments on synthetic and real datasets are implemented to verify the effectiveness, robustness, and granularity independence of the algorithm, and the scheme is compared to unsupervised schemes in the Python package Scikit-learn. Results demonstrate that our algorithm outperforms previous ones in many situations, especially significantly when clusters have regular internal structures. For example, averaging over the eight noiseless synthetic datasets with structures employing ARI and NMI criteria, previous algorithms obtain scores below 0.6 and 0.7, while the presented algorithm obtains scores higher than 0.9 and 0.95, respectively.

Hao Shu

Image edge detection (ED) faces a fundamental mismatch between training and inference: models are trained using continuous-valued outputs but evaluated using binary predictions. This misalignment, caused by the non-differentiability of binarization, weakens the link between learning objectives and actual task performance. In this paper, we propose a theoretical method to design a Binarization-Aware Adjuster (BAA), which explicitly incorporates binarization behavior into gradient-based optimization. At the core of BAA is a novel loss adjustment mechanism based on a Distance Weight Function (DWF), which reweights pixel-wise contributions according to their correctness and proximity to the decision boundary. This emphasizes decision-critical regions while down-weighting less influential ones. We also introduce a self-adaptive procedure to estimate the optimal binarization threshold for BAA, further aligning training dynamics with inference behavior. Extensive experiments across various architectures and datasets demonstrate the effectiveness of our approach. Beyond ED, BAA offers a generalizable strategy for bridging the gap between continuous optimization and discrete evaluation in structured prediction tasks.