Bingjie Li

Tianhao Ni, Bingjie Li, Zhigang Yao

To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME) algorithm. By introducing ordinal distance to replace traditional Euclidean distances, we theoretically demonstrate that ordinal distance overcomes the constraints of the curse of dimensionality in high-dimensional spaces, effectively distinguishing heterogeneous samples. We design an adaptive neighborhood adjustment method to construct similarity graphs that simultaneously balance intra-cluster compactness and inter-cluster separability. Furthermore, we develop a two-stage embedding framework: the first stage achieves preliminary cluster separation while preserving connectivity between structurally similar clusters via the similarity graph, and the second stage enhances inter-cluster separation through a label-driven distance reweighting. Experimental results demonstrate that AMSME significantly preserves intra-cluster topological structures and improves inter-cluster separation on real-world datasets. Additionally, leveraging its multi-resolution analysis capability, AMSME discovers novel neuronal subtypes in the mouse lumbar dorsal root ganglion scRNA-seq dataset, with marker gene analysis revealing their distinct biological roles.

Ruizhi Wang, Kai Liu, Bingjie Li et al.

In online advertising, the demand-side platform (a.k.a. DSP) enables advertisers to create different ad creatives for real-time bidding. Intuitively, advertisers tend to create more ad creatives for a single photo to increase the probability of participating in bidding, further enhancing their ad cost. From the perspective of DSP, the following are two overlooked issues. On the one hand, the number of ad creatives cannot grow indefinitely. On the other hand, the marginal effects of ad cost diminish as the number of ad creatives increases. To this end, this paper proposes a two-stage framework named Automated Creatives Quota (ACQ) to achieve the automatic creation and deactivation of ad creatives. ACQ dynamically allocates the creative quota across multiple advertisers to maximize the revenue of the ad platform. ACQ comprises two components: a prediction module to estimate the cost of a photo under different numbers of ad creatives, and an allocation module to decide the quota for photos considering their estimated costs in the prediction module. Specifically, in the prediction module, we develop a multi-task learning model based on an unbalanced binary tree to effectively mitigate the target variable imbalance problem. In the allocation module, we formulate the quota allocation problem as a multiple-choice knapsack problem (MCKP) and develop an efficient solver to solve such large-scale problems involving tens of millions of ads. We performed extensive offline and online experiments to validate the superiority of our proposed framework, which increased cost by 9.34%.

Bingjie Li, Guohua Wu, Yongming He et al.

Vehicle routing problem (VRP) is a typical discrete combinatorial optimization problem, and many models and algorithms have been proposed to solve the VRP and its variants. Although existing approaches have contributed a lot to the development of this field, these approaches either are limited in problem size or need manual intervening in choosing parameters. To solve these difficulties, many studies have considered the learning-based optimization (LBO) algorithms to solve the VRP. This paper reviews recent advances in this field and divides relevant approaches into end-to-end approaches and step-by-step approaches. We performed a statistical analysis of the reviewed articles from various aspects and designed three experiments to evaluate the performance of four representative LBO algorithms. Finally, we conclude the applicable types of problems for different LBO algorithms and suggest directions in which researchers can improve LBO algorithms.

Zhigang Yao, Bingjie Li, Wee Chin Tan

Modern sample points in many applications no longer comprise real vectors in a real vector space but sample points of much more complex structures, which may be represented as points in a space with a certain underlying geometric structure, namely a manifold. Manifold learning is an emerging field for learning the underlying structure. The study of manifold learning can be split into two main branches: dimension reduction and manifold fitting. With the aim of combining statistics and geometry, we address the problem of manifold fitting in the ambient space. Inspired by the relation between the eigenvalues of the Laplace-Beltrami operator and the geometry of a manifold, we aim to find a small set of points that preserve the geometry of the underlying manifold. From this relationship, we extend the idea of subsampling to sample points in high-dimensional space and employ the Moving Least Squares (MLS) approach to approximate the underlying manifold. We analyze the two core steps in our proposed method theoretically and also provide the bounds for the MLS approach. Our simulation results and theoretical analysis demonstrate the superiority of our method in estimating the underlying manifold.