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Ming-Jun Lai

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3 papers

2 author rows

JMLR Journal 2024 Journal Article

Nonparametric Regression for 3D Point Cloud Learning

Xinyi Li
Shan Yu
Yueying Wang
Guannan Wang
Li Wang
Ming-Jun Lai

In recent years, there has been an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient smoothing tool based on multivariate splines over the triangulation to extract the underlying signal and build up a 3D solid model from the point cloud. The proposed method can denoise or deblur the point cloud effectively, provide a multi-resolution reconstruction of the actual signal, and handle sparse and irregularly distributed point clouds to recover the underlying trajectory. In addition, our method provides a natural way of numerosity data reduction. We establish the theoretical guarantees of the proposed method, including the convergence rate and asymptotic normality of the estimator, and show that the convergence rate achieves optimal nonparametric convergence. We also introduce a bootstrap method to quantify the uncertainty of the estimators. Through extensive simulation studies and a real data example, we demonstrate the superiority of the proposed method over traditional smoothing methods in terms of estimation accuracy and efficiency of data reduction. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2024. ( edit, beta )

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IJCAI Conference 2023 Conference Paper

Graph-based Semi-supervised Local Clustering with Few Labeled Nodes

Zhaiming Shen
Ming-Jun Lai
Sheng Li

Local clustering aims at extracting a local structure inside a graph without the necessity of knowing the entire graph structure. As the local structure is usually small in size compared to the entire graph, one can think of it as a compressive sensing problem where the indices of target cluster can be thought as a sparse solution to a linear system. In this paper, we apply this idea based on two pioneering works under the same framework and propose a new semi-supervised local clustering approach using only few labeled nodes. Our approach improves the existing works by making the initial cut to be the entire graph and hence overcomes a major limitation of the existing works, which is the low quality of initial cut. Extensive experimental results on various datasets demonstrate the effectiveness of our approach.

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ICML Conference 2014 Conference Paper

Rank-One Matrix Pursuit for Matrix Completion

Zheng Wang 0011
Ming-Jun Lai
Zhaosong Lu
Wei Fan 0001
Hasan Davulcu
Jieping Ye

Low rank matrix completion has been applied successfully in a wide range of machine learning applications, such as collaborative filtering, image inpainting and Microarray data imputation. However, many existing algorithms are not scalable to large-scale problems, as they involve computing singular value decomposition. In this paper, we present an efficient and scalable algorithm for matrix completion. The key idea is to extend the well-known orthogonal matching pursuit from the vector case to the matrix case. In each iteration, we pursue a rank-one matrix basis generated by the top singular vector pair of the current approximation residual and update the weights for all rank-one matrices obtained up to the current iteration. We further propose a novel weight updating rule to reduce the time and storage complexity, making the proposed algorithm scalable to large matrices. We establish the linear convergence of the proposed algorithm. The fast convergence is achieved due to the proposed construction of matrix bases and the estimation of the weights. We empirically evaluate the proposed algorithm on many real-world large scale datasets. Results show that our algorithm is much more efficient than state-of-the-art matrix completion algorithms while achieving similar or better prediction performance.

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