arXiv subjects

Minchang Kim

Publications and source records attributed to Minchang Kim.

4 recordsLinked to original sources

arXiv2026

Khintchine's Theorem for Symmetric matrices via Flows on the Space of Symplectic Lattices

We establish Diophantine approximation results for real symmetric matrices by collections of linearly independent integer vectors. For $X \in \mathrm{Sym}_d(\mathbb{R})$, we prove a Dirichlet-type theorem guaranteeing the existence of integral Lagrangian frames $(Q, P) \in \mathrm{Mat}_{d \times 2d}(\mathbb{Z})$ that satisfy $\lVert QX + P \rVert_{\mathrm{op}} \leq c_d/N$ and $\lVert Q \rVert_{\mathrm{op}} \leq N$ for any $N \geq 1$. Furthermore, we establish a Khintchine-type zero-one law, demonstrating that the size of the set of $\psi$-approximable symmetric matrices is determined by the convergence or divergence of the series $\sum_{q \geq 1} q^{\varsigma - 1}\psi(q)^{\varsigma}$, where $\varsigma = d(d+1)/2$. The proofs rely on the reduction theory of the Siegel upper half-space, dynamical formulation over the space of symplectic lattices, and an analysis of the Siegel transform adapted to count Lagrangian frames instead of single lattice points.

math.NT↗

arXiv2023

3DTeethSeg'22: 3D Teeth Scan Segmentation and Labeling Challenge

Teeth localization, segmentation, and labeling from intra-oral 3D scans are essential tasks in modern dentistry to enhance dental diagnostics, treatment planning, and population-based studies on oral health. However, developing automated algorithms for teeth analysis presents significant challenges due to variations in dental anatomy, imaging protocols, and limited availability of publicly accessible data. To address these challenges, the 3DTeethSeg'22 challenge was organized in conjunction with the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI) in 2022, with a call for algorithms tackling teeth localization, segmentation, and labeling from intraoral 3D scans. A dataset comprising a total of 1800 scans from 900 patients was prepared, and each tooth was individually annotated by a human-machine hybrid algorithm. A total of 6 algorithms were evaluated on this dataset. In this study, we present the evaluation results of the 3DTeethSeg'22 challenge. The 3DTeethSeg'22 challenge code can be accessed at: https://github.com/abenhamadou/3DTeethSeg22_challenge

cs.CV↗

arXiv2023

Meta-Learning with Adaptive Weighted Loss for Imbalanced Cold-Start Recommendation

Sequential recommenders have made great strides in capturing a user's preferences. Nevertheless, the cold-start recommendation remains a fundamental challenge as they typically involve limited user-item interactions for personalization. Recently, gradient-based meta-learning approaches have emerged in the sequential recommendation field due to their fast adaptation and easy-to-integrate abilities. The meta-learning algorithms formulate the cold-start recommendation as a few-shot learning problem, where each user is represented as a task to be adapted. While meta-learning algorithms generally assume that task-wise samples are evenly distributed over classes or values, user-item interactions in real-world applications do not conform to such a distribution (e.g., watching favorite videos multiple times, leaving only positive ratings without any negative ones). Consequently, imbalanced user feedback, which accounts for the majority of task training data, may dominate the user adaptation process and prevent meta-learning algorithms from learning meaningful meta-knowledge for personalized recommendations. To alleviate this limitation, we propose a novel sequential recommendation framework based on gradient-based meta-learning that captures the imbalanced rating distribution of each user and computes adaptive loss for user-specific learning. Our work is the first to tackle the impact of imbalanced ratings in cold-start sequential recommendation scenarios. Through extensive experiments conducted on real-world datasets, we demonstrate the effectiveness of our framework.

cs.IR↗

arXiv2022

Accurate Ground-Truth Depth Image Generation via Overfit Training of Point Cloud Registration using Local Frame Sets

Accurate three-dimensional perception is a fundamental task in several computer vision applications. Recently, commercial RGB-depth (RGB-D) cameras have been widely adopted as single-view depth-sensing devices owing to their efficient depth-sensing abilities. However, the depth quality of most RGB-D sensors remains insufficient owing to the inherent noise from a single-view environment. Recently, several studies have focused on the single-view depth enhancement of RGB-D cameras. Recent research has proposed deep-learning-based approaches that typically train networks using high-quality supervised depth datasets, which indicates that the quality of the ground-truth (GT) depth dataset is a top-most important factor for accurate system; however, such high-quality GT datasets are difficult to obtain. In this study, we developed a novel method for high-quality GT depth generation based on an RGB-D stream dataset. First, we defined consecutive depth frames in a local spatial region as a local frame set. Then, the depth frames were aligned to a certain frame in the local frame set using an unsupervised point cloud registration scheme. The registration parameters were trained based on an overfit-training scheme, which was primarily used to construct a single GT depth image for each frame set. The final GT depth dataset was constructed using several local frame sets, and each local frame set was trained independently. The primary advantage of this study is that a high-quality GT depth dataset can be constructed under various scanning environments using only the RGB-D stream dataset. Moreover, our proposed method can be used as a new benchmark GT dataset for accurate performance evaluations. We evaluated our GT dataset on previously benchmarked GT depth datasets and demonstrated that our method is superior to state-of-the-art depth enhancement frameworks.

cs.CV↗