ABSTRACT Accurate classification and segmentation of intracranial aneurysms from 3D point cloud data are critical for computer‐aided diagnosis and surgical planning. However, existing point‐based deep learning methods suffer from limited feature representation and poor segmentation performance on medical data due to insufficient training samples and complex geometric variations. M‐PointNet introduces a novel multi‐layer embedded deep learning architecture that significantly enhances the classification and segmentation of intracranial aneurysms through three key innovations: (1) an enhanced PointNet++ with an expanded hierarchical structure for better geometric feature extraction; (2) a multi‐layer embedding mechanism that integrates preprocessed and resampled point cloud data at multiple hierarchical levels to enrich feature representation; and (3) a deep supervision strategy with auxiliary output layers to accelerate convergence and improve performance. Experiments on the IntrA dataset demonstrate that M‐PointNet achieves 91.96% accuracy and a 0.923 F1‐score in classification, surpassing baseline by 5.27% and 3.0%, respectively. For segmentation, it attains 83.85% IoU and 90.25% DSC for aneurysm regions and 95.81% IoU and 97.82% DSC for vessel regions. Additionally, its generalization capability is validated by a 92.8% accuracy on the ModelNet40 dataset. M‐PointNet effectively addresses the challenges of medical point cloud analysis, achieving state‐of‐the‐art performance in intracranial aneurysms classification and segmentation while maintaining robust cross‐domain generalization.

Intracranial aneurysms (IAs) are clinically categorized as ruptured or unruptured. Size variability complicates precise segmentation and rupture assessment. This study integrates deep learning, machine learning, clinical characteristics, and computed tomography angiography (CTA) radiomics to determine IA rupture status. A dataset of 443 aneurysms (101 unruptured and 342 ruptured) was curated from affiliated hospitals. IAs were segmented via Swin UNETR, with radiomic features extracted via PyRadiomics. Following dimensionality reduction, five classifiers, support vector machine (SVM), logistic regression (LR), random forest (RF), multilayer perceptron (MLP), and voting classifier, were evaluated via the area under the receiver operating characteristic curve (AUC‐ROC). Among the 1074 radiomic features, 25 were significantly correlated with rupture status. The RF, voting, MLP, LR, and SVM classifiers achieved AUCs of 0.94, 0.93, 0.88, 0.88, and 0.84, respectively. These results demonstrate the discriminative power of the combined t‐test, LASSO, and PCA feature selection methods.

Weighted low rank approximation is a fundamental problem in numerical linear algebra, and it has many applications in machine learning. Given a matrix $M \in \mathbb{R}^{n \times n}$, a non-negative weight matrix $W \in \mathbb{R}_{\geq 0}^{n \times n}$, a parameter $k$, the goal is to output two matrices $X,Y\in \mathbb{R}^{n \times k}$ such that $\\| W \circ (M - X Y^\top) \\|_F$ is minimized, where $\circ$ denotes the Hadamard product. It naturally generalizes the well-studied low rank matrix completion problem. Such a problem is known to be NP-hard and even hard to approximate assuming the Exponential Time Hypothesis. Meanwhile, alternating minimization is a good heuristic solution for weighted low rank approximation. In particular, [Li, Liang and Risteski, ICML'16] shows that, under mild assumptions, alternating minimization does provide provable guarantees. In this work, we develop an efficient and robust framework for alternating minimization that allows the alternating updates to be computed approximately. For weighted low rank approximation, this improves the runtime of [Li, Liang and Risteski, ICML'16] from $\\|W\\|_0k^2$ to $\\|W\\|_0 k$ where $\\|W\\|_0$ denotes the number of nonzero entries of the weight matrix. At the heart of our framework is a high-accuracy multiple response regression solver together with a robust analysis of alternating minimization.

ABSTRACT Intracranial aneurysm is a common cerebrovascular condition, due to the small size and complex anatomical location of intracranial aneurysms, it remains a challenging task to accurately segmenting the intracranial aneurysms in computed tomography angiography (CTA) images. To address these challenges, we propose SCUX‐Net, a novel lightweight convolutional neural network designed to facilitate the segmentation of intracranial aneurysms. SCUX‐Net builds upon the 3D UX‐Net by introducing two key innovations: (1) a spatial adaptive feature module, integrated before each 3D UX‐Net block, enabling multi‐scale feature fusion for long‐range information interaction; (2) a convolutional block attention module, applied after each downsampling block to emphasize important features across channel and spatial dimensions, suppressing irrelevant information. Experimental results substantiate the effectiveness of SCUX‐Net in segmenting intracranial aneurysms on CTA images, achieving a dice similarity coefficient of 80% on the test set. Notably, SCUX‐Net excels in detecting small aneurysms (3 mm) and multiple aneurysms, showcasing its potential for clinical application.

The multicommodity flow problem is a classic problem in network flow and combinatorial optimization, with applications in transportation, communication, logistics, and supply chain management, etc. Existing algorithms often focus on low-accuracy approximate solutions, while high-accuracy algorithms typically rely on general linear program solvers. In this paper, we present efficient high-accuracy algorithms for a broad family of multicommodity flow problems on undirected graphs, demonstrating improved running times compared to general linear program solvers. Our main result shows that we can solve the 𝓁_{q, p}-norm multicommodity flow problem to a (1 + ε) approximation in time O_{q, p}(m^{1+o(1)} k² log(1/ε)), where k is the number of commodities, and O_{q, p}(⋅) hides constants depending only on q or p. As q and p approach to 1 and ∞ respectively, 𝓁_{q, p}-norm flow tends to maximum concurrent flow. We introduce the first iterative refinement framework for 𝓁_{q, p}-norm minimization problems, which reduces the problem to solving a series of decomposable residual problems. In the case of k-commodity flow, each residual problem can be decomposed into k single commodity convex flow problems, each of which can be solved in almost-linear time. As many classical variants of multicommodity flows were shown to be complete for linear programs in the high-accuracy regime [Ding-Kyng-Zhang, ICALP'22], our result provides new directions for studying more efficient high-accuracy multicommodity flow algorithms.

We provide universally-optimal distributed graph algorithms for (1+∊)-approximate shortest path problems including shortest-path-tree and transshipment. The universal optimality of our algorithms guarantees that, on any n-node network G, our algorithm completes in T · no(1) rounds whenever a T-round algorithm exists for G. This includes D · no(1)-round algorithms for any planar or excluded-minor network. Our algorithms never require more than rounds, resulting in the first sub-linear-round distributed algorithm for transshipment. The key technical contribution leading to these results is the first efficient no(1)-competitive linear ℓ1-oblivious routing operator that does not require the use of ℓ1-embeddings. Our construction is simple, solely based on low-diameter decompositions, and—in contrast to all known constructions—directly produces an oblivious flow instead of just an approximation of the optimal flow cost. This also has the benefit of simplifying the interaction with Sherman's multiplicative weight framework [SODA'17] in the distributed setting and its subsequent rounding procedures.

We study distributed algorithms built around minor-based vertex sparsifiers, and give the first algorithm in the CONGEST model for solving linear systems in graph Laplacian matrices to high accuracy. Our Laplacian solver has a round complexity of$O(n^{o(1)}(\sqrt{n}+D))$, and thus almost matches the lower bound of$\widetilde{\Omega}(\sqrt{n}+D)$, where$n$is the number of nodes in the network and$D$is its diameter. We show that our distributed solver yields new sublinear round algorithms for several cornerstone problems in combinatorial optimization. This is achieved by leveraging the powerful algorithmic framework of Interior Point Methods (IPMs) and the Laplacian paradigm in the context of distributed graph algorithms, which entails numerically solving optimization problems on graphs via a series of Laplacian systems. Problems that benefit from our distributed algorithmic paradigm include exact mincost flow, negative weight shortest paths, maxflow, and bipartite matching on sparse directed graphs. For the maxflow problem, this is the first exact distributed algorithm that applies to directed graphs, while the previous work by [Ghaffari et al. SICOMP'18] considered the approximate setting and works only for undirected graphs. For the mincost flow and the negative weight shortest path problems, our results constitute the first exact distributed algorithms running in a sublinear number of rounds. Given that the hybrid between IPMs and the Laplacian paradigm has proven useful for tackling numerous optimization problems in the centralized setting, we believe that our distributed solver will find future applications. At the heart of our distributed Laplacian solver is the notion of spectral subspace sparsifiers of [Li, Schild FOCS'18]. We present a nontrivial distributed implementation of their construction by (i) giving a parallel variant of their algorithm that avoids the sampling of random spanning trees and uses approximate leverage scores instead, and (ii) showing that the algorithm still produces a high-quality subspace spectral sparsifier by carefully setting up and analyzing matrix martingales. Combining this vertex reduction recursively with both tree and elimination-based preconditioners leads to our algorithm for solving Laplacian systems. The construction of the elimination-based preconditioners is based on computing short random walks, and we introduce a new technique for reducing the congestion incurred by the simulation of these walks on weighted graphs.

(a) (b) Figure 1: Illustration of constructing the coupled dictionaries. The red rectangles in (a) and (b) represent the target bounding boxes. The green squares in (a), which are generated by sliding windows outside the target bounding box, correspond to basis patches involved in the background dictionary N. The blue squares in (a) are generated inside the target bounding box in a similar way, which constitute the noisy target dictionary P.