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Hou-biao Li

Publications and source records attributed to Hou-biao Li.

15 recordsLinked to original sources
arXiv2026

Anisotropic View Distance Metric for High-Dimensional Data: Theory, Geometry, and Fast Computation

K-Means clustering algorithm is one of the most commonly used clustering algorithms because of its simplicity and efficiency. K-Means clustering algorithm based on Euclidean distance only pays attention to the linear distance between Euclidean distance is an efficient and interpretable similarity measurement, but its effectiveness may deteriorate in sample spaces with anisotropic structures, redundant features, or complex feature interactions. In this paper, we propose a novel distance metric called View distance. Inspired by orthographic projection, the proposed metric projects the sample space onto $n(n-1)/2$ two-dimensional planes and defines the final distance as the sum of the Euclidean distances across the projected planes. Theoretical derivations verify that the View distance strictly satisfies the metric axioms and norm constraints. Beyond that, the View distance achieves feature coupling through projection and not only enables constant features to indirectly participate in distance calculation, but also suppresses interference from redundant features while exhibiting anisotropic geometric properties. Furthermore, to address the high computational complexity and poor scalability of full-projection View distance, we propose a two-dimensional projection plane selection strategy based on iterative Maximum Weight Matching, which reduces the computational complexity of distance calculation from $\mathcal{O}(n^2)$ to $\mathcal{O}(k)$. Extensive experiments on 12 diverse datasets demonstrate that View distance and the deterministic selection strategy provide competitive or superior performance compared with Euclidean distance and other $L_{p}$ metrics while maintaining strong interpretability and computational efficiency. The View distance provides a new perspective and option for similarity measurements.

cs.LG↗
arXiv2026

Multi-level Self-supervised Pretraining on Compositional Hierarchical Graph for Molecular Property Prediction

Self-supervised pretraining on molecular graphs has emerged as a promising approach for molecular property prediction, yet most existing methods operate at a single structural granularity and treat bond information as auxiliary edge attributes rather than as an independent semantic layer. In this work, we propose MolCHG, a multi-level self-supervised pretraining framework built upon a novel Compositional Hierarchical Graph that organizes molecular structure into four types of nodes across three semantic levels. By introducing a bond graph that operates in parallel with the atom graph, our architecture elevates bond-level information to independently evolving node representations, enabling fragment nodes to aggregate atom-level and bond-level semantics on an equal footing. We design three level-specific pretraining objectives: an atom-bond cross-view contrastive task that aligns the atom-view and bond-view representations within each fragment, a fragment-level functional group prediction task to inject domain-relevant chemical knowledge, and graph-level structure prediction tasks to encode global molecular topology. Experiments on nine MoleculeNet benchmarks demonstrate that MolCHG achieves the best performance on seven datasets across both classification and regression tasks, remaining competitive with the strongest baselines on the rest. Ablation studies further confirm that the multi-level supervision signals are complementary and that each component contributes to the overall performance.

cs.LG↗
arXiv2026

Local-Global Multimodal Contrastive Learning for Molecular Property Prediction

Accurate molecular property prediction requires integrating complementary information from molecular structure and chemical semantics. In this work, we propose LGM-CL, a local-global multimodal contrastive learning framework that jointly models molecular graphs and textual representations derived from SMILES and chemistry-aware augmented texts. Local functional group information and global molecular topology are captured using AttentiveFP and Graph Transformer encoders, respectively, and aligned through self-supervised contrastive learning. In addition, chemically enriched textual descriptions are contrasted with original SMILES to incorporate physicochemical semantics in a task-agnostic manner. During fine-tuning, molecular fingerprints are further integrated via Dual Cross-attention multimodal fusion. Extensive experiments on MoleculeNet benchmarks demonstrate that LGM-CL achieves consistent and competitive performance across both classification and regression tasks, validating the effectiveness of unified local-global and multimodal representation learning.

cs.LG↗
arXiv2025

FlatFormer: A Flat Transformer Knowledge Tracing Model Based on Cognitive Bias Injection

Knowledge Tracing (KT) models face a critical ``Performance-Complexity Trap'': capturing complex cognitive dynamics like learning sessions and memory decay typically requires deep hierarchical architectures, which incur prohibitive computational costs for real-time deployment. To resolve this, we propose FlatFormer, a streamlined architecture based on the novel design paradigm of ``Information Injection over Structural Stacking.'' Unlike parameter-heavy hierarchical models, FlatFormer leverages a standard flat Transformer augmented with two lightweight injection mechanisms: (i) a hybrid input encoding strategy combining learnable session identifiers with fixed sinusoidal step embeddings; and (ii) a pre-computed power-law bias integrated directly into attention logits to explicitly model the forgetting curve. Extensive experiments on four large-scale datasets (e.g., EdNet, Junyi) show that FlatFormer achieves state-of-the-art performance. For example, on the EdNet dataset, compared to the strongest hierarchical baseline (HiTSKT), its absolute AUC increased by 8.3%, while using less than 15% of parameters, and inference speed was about three times faster. These results validate that high cognitive fidelity does not necessitate architectural complexity.

cs.AI↗
arXiv2025

Multi-Level Fusion Graph Neural Network for Molecule Property Prediction

Accurate prediction of molecular properties is essential in drug discovery and related fields. However, existing graph neural networks (GNNs) often struggle to simultaneously capture both local and global molecular structures. In this work, we propose a Multi-Level Fusion Graph Neural Network (MLFGNN) that integrates Graph Attention Networks and a novel Graph Transformer to jointly model local and global dependencies. In addition, we incorporate molecular fingerprints as a complementary modality and introduce a mechanism of interaction between attention to adaptively fuse information across representations. Extensive experiments on multiple benchmark datasets demonstrate that MLFGNN consistently outperforms state-of-the-art methods in both classification and regression tasks. Interpretability analysis further reveals that the model effectively captures task-relevant chemical patterns, supporting the usefulness of multi-level and multi-modal fusion in molecular representation learning.

cs.LG↗
arXiv2025

A note on the growth factor in Gaussian elimination for Higham matrices

The Higham matrix is a complex symmetric matrix A=B+iC, where both B and C are real, symmetric and positive definite and $\mathrm{i}=\sqrt{-1}$ is the imaginary unit. For any Higham matrix A, Ikramov et al. showed that the growth factor in Gaussian elimination is less than 3. In this paper, based on the previous results, a new bound of the growth factor is obtained by using the maximum of the condition numbers of matrixes B and C for the generalized Higham matrix A, which strengthens this bound to 2 and proves the Higham's conjecture.

math.NA↗
arXiv2023

A Matrix Decomposition Model Based on Feature Factors in Movie Recommendation System

Currently, matrix decomposition is one of the most widely used collaborative filtering algorithms by using factor decomposition to effectively deal with large-scale rating matrix. It mainly uses the interaction records between users and items to predict ratings. Based on the characteristic attributes of items and users, this paper proposes a new UISVD++ model that fuses the type attributes of movies and the age attributes of users into SVD++ framework. By projecting the age attribute into the user's implicit space and the type attribute into the item's implicit space, the model enriches the side information of the users and items. At last, we conduct comparative experiments on two public data sets, Movielens-100K and Movielens-1M. Experiment results express that the prediction accuracy of this model is better than other baselines in the task of predicting scores. In addition, these results also show that UISVD++ can effectively alleviate the cold start situation.

cs.IR↗
arXiv2023

A rule-general abductive learning by rough sets

In real-world tasks, there is usually a large amount of unlabeled data and labeled data. The task of combining the two to learn is known as semi-supervised learning. Experts can use logical rules to label unlabeled data, but this operation is costly. The combination of perception and reasoning has a good effect in processing such semi-supervised tasks with domain knowledge. However, acquiring domain knowledge and the correction, reduction and generation of rules remain complex problems to be solved. Rough set theory is an important method for solving knowledge processing in information systems. In this paper, we propose a rule general abductive learning by rough set (RS-ABL). By transforming the target concept and sub-concepts of rules into information tables, rough set theory is used to solve the acquisition of domain knowledge and the correction, reduction and generation of rules at a lower cost. This framework can also generate more extensive negative rules to enhance the breadth of the knowledge base. Compared with the traditional semi-supervised learning method, RS-ABL has higher accuracy in dealing with semi-supervised tasks.

cs.LG↗
arXiv2023

DBGSA: A Novel Data Adaptive Bregman Clustering Algorithm

With the development of Big data technology, data analysis has become increasingly important. Traditional clustering algorithms such as K-means are highly sensitive to the initial centroid selection and perform poorly on non-convex datasets. In this paper, we address these problems by proposing a data-driven Bregman divergence parameter optimization clustering algorithm (DBGSA), which combines the Universal Gravitational Algorithm to bring similar points closer in the dataset. We construct a gravitational coefficient equation with a special property that gradually reduces the influence factor as the iteration progresses. Furthermore, we introduce the Bregman divergence generalized power mean information loss minimization to identify cluster centers and build a hyperparameter identification optimization model, which effectively solves the problems of manual adjustment and uncertainty in the improved dataset. Extensive experiments are conducted on four simulated datasets and six real datasets. The results demonstrate that DBGSA significantly improves the accuracy of various clustering algorithms by an average of 63.8\% compared to other similar approaches like enhanced clustering algorithms and improved datasets. Additionally, a three-dimensional grid search was established to compare the effects of different parameter values within threshold conditions, and it was discovered the parameter set provided by our model is optimal. This finding provides strong evidence of the high accuracy and robustness of the algorithm.

cs.LG↗
arXiv2022

RNNCTPs: A Neural Symbolic Reasoning Method Using Dynamic Knowledge Partitioning Technology

Although traditional symbolic reasoning methods are highly interpretable, their application in knowledge graph link prediction is limited due to their low computational efficiency. In this paper, we propose a new neural symbolic reasoning method: RNNCTPs, which improves computational efficiency by re-filtering the knowledge selection of Conditional Theorem Provers (CTPs), and is less sensitive to the embedding size parameter. RNNCTPs are divided into relation selectors and predictors. The relation selectors are trained efficiently and interpretably, so that the whole model can dynamically generate knowledge for the inference of the predictor. In all four datasets, the method shows competitive performance against traditional methods on the link prediction task, and can have higher applicability to the selection of datasets relative to CTPs.

cs.AI↗
arXiv2022

Neural Theorem Provers Delineating Search Area Using RNN

Although traditional symbolic reasoning methods are highly interpretable, their application in knowledge graphs link prediction has been limited due to their computational inefficiency. A new RNNNTP method is proposed in this paper, using a generalized EM-based approach to continuously improve the computational efficiency of Neural Theorem Provers(NTPs). The RNNNTP is divided into relation generator and predictor. The relation generator is trained effectively and interpretably, so that the whole model can be carried out according to the development of the training, and the computational efficiency is also greatly improved. In all four data-sets, this method shows competitive performance on the link prediction task relative to traditional methods as well as one of the current strong competitive methods.

cs.LG↗
arXiv2019

A note on Dodgson's determinant condensation algorithm

Recently, the Dodgson's determinant condensation algorithm was revisited in many papers [College Math. Journal 42(1)(2011): 43--54, College Math. Journal 38(2)(2007): 85--95, Math Horizons 14(2)(2006): 12--15},etc.]. This method is attractive, but there also exist some shortcomings. In this paper, a symbolic algorithm and the corresponding problems are discussed to overcome these shortcomings. Numerical experiments show that this symbolic modified algorithm has highly sensitivity on initial configuration of the matrix in condensation process.

math.NA↗
arXiv2018

Techniques for Accelerating the Convergence of Restarted GMRES Based on the Projection

In this paper, we study the restarted Krylov subspace method, which is typically represented by the GMRES(m) method. Our work mainly focused on the amount of change in the iterative solution of GMRES(m) at each restart. We propose an extension of the GMRES(m) method based on the idea of projection. The algorithm is named as LGMRES. In addition, LLBGMRE method is also obtained by adding backtracking restart technology to LGMRES. Theoretical analysis and numerical experiments show that LGMRES and LLBGMRES have better convergence than traditional restart GMRES(m) method.

math.NA↗
arXiv2014

From Sylvester's determinant identity to Cramer's rule

The object of this paper is to introduce a new and fascinating method of solving large linear equations, based on Cramer's rule or Gaussian elimination but employing Sylvester's determinant identity in its computation process. In addition, a scheme suitable for parallel computing is presented for this kind of generalized Chiò's determinant condensation processes, which makes this new method have a property of natural parallelism. Finally, some numerical experiments also confirm our theoretical analysis.

math.NA↗