The paper introduces DelTriC (Delaunay Triangulation Clustering), a clustering algorithm which integrates PCA/UMAP-based projection, Delaunay triangulation, and a novel back-projection mechanism to form clusters in the original high-dimensional space. DelTriC decouples neighborhood construction from decision-making by first triangulating in a low-dimensional proxy to index local adjacency, and then back-projecting to the original space to perform robust edge pruning, merging, and anomaly detection. DelTriC can outperform traditional methods such as k-means, DBSCAN, and HDBSCAN in many scenarios; it is both scalable and accurate, and it also significantly improves outlier detection.

We study the problem of constructing Steiner Minimal Trees (SMTs) in hyperbolic space. Exact SMT computation is NP-hard, and existing hyperbolic heuristics such as HyperSteiner are deterministic and often get trapped in locally suboptimal configurations. We introduce Randomized HyperSteiner (RHS), a stochastic Delaunay triangulation heuristic that incorporates randomness into the expansion process and refines candidate trees via Riemannian gradient descent optimization. Experiments on synthetic data sets and a real-world single-cell transcrip-tomic data show that RHS outperforms Minimum Spanning Tree (MST), Neighbour Joining, and vanilla HyperSteiner (HS). In near-boundary configurations, RHS can achieve a 32% reduction in total length over HS, demonstrating its effectiveness and robustness in diverse data regimes.

Neural Information Processing Systems http://nips.cc/

Due to their inherent ability to process data in a graph-based format, GCNs are especially well-suited for applications where relational context and structural information play a crucial role. This introduction explores recent advancements in image classification using GCNs, with a particular focus on the integration of superpixels and wavelet techniques. Graph Convolutional Networks (GCNs) have become a powerful framework for image classification, largely due to their ability to capture and process the non-Euclidean structure of data. Zhou et al. provided a comprehensive review of GCN applications across various domains, highlighting their effectiveness in image classification tasks [1]. Their study emphasized that, unlike traditional Convolutional Neural Networks (CNNs), GCNs excel at capturing long-range dependencies and complex relational patterns within images. Meanwhile, wavelet techniques [2] have transformed image processing by introducing a multi-resolution analysis framework that is essential for applications such as image compression, feature extraction, and noise reduction. In this context, Wavelet transforms have been utilized in conjunction with GCNs for feature extraction in image classification, denoising, compression and other tasks. Wavelets provide a multi-resolution image analysis, capturing spatial and frequency domain information [3]. This paper presents an innovative framework that integrates Graph Convolutional Networks (GCNs) with Voronoi diagrams for image classification, leveraging their exceptional ability to model relational data.

Bayesian optimization involves "inner optimization" over a new-data acquisition

--We introduce an end-to-end pipeline that leverages a fine-tuned YOLO12l-seg model--trained on over 500 annotated post-blast images--to deliver real-time instance segmentation (Box mAP@0.5 0.769, Mask mAP@0.5 0.800 at 15 FPS). High-fidelity masks are converted into normalized 3D coordinates, from which we extract multi-metric spatial descriptors: principal component directions, kernel density hotspots, size-depth regression, and Delaunay edge statistics. We present four representative examples to illustrate key fragmentation patterns. Experimental results confirm the framework's accuracy, robustness to small-object crowding, and feasibility for rapid, automated blast-effect assessment in field conditions. Accurate assessment of rock fragmentation following blasting is critical for optimizing downstream mining efficiency and safety [1].

Object detection and identification is surely a fundamental topic in the computer vision field; it plays a crucial role in many applications such as object tracking, industrial robots control, image retrieval, etc. We propose a feature-based approach for detecting and identifying distorted occurrences of a given template in a scene image by incremental grouping of feature matches between the image and the template. For this purpose, we consider the Delaunay triangulation of template features as an useful tool through which to be guided in this iterative approach. The triangulation is treated as a graph and, starting from a single triangle, neighboring nodes are considered and the corresponding features are identified; then matches related to them are evaluated to determine if they are worthy to be grouped. This evaluation is based on local consistency criteria derived from geometric and photometric properties of local features. Our solution allows the identification of the object in situations where geometric models (e.g. homography) does not hold, thus enable the detection of objects such that the template is non planar or when it is planar but appears distorted in the image. We show that our approach performs just as well or better than application of homography-based RANSAC in scenarios in which distortion is nearly absent, while when the deformation becomes relevant our method shows better description performance.

Linear representation learning is widely studied due to its conceptual simplicity and empirical utility in tasks such as compression, classification, and feature extraction. Given a set of points $[\mathbf{x}_1, \mathbf{x}_2, \ldots, \mathbf{x}_n] = \mathbf{X} \in \mathbb{R}^{d \times n}$ and a vector $\mathbf{y} \in \mathbb{R}^d$, the goal is to find coefficients $\mathbf{w} \in \mathbb{R}^n$ so that $\mathbf{X} \mathbf{w} \approx \mathbf{y}$, subject to some desired structure on $\mathbf{w}$. In this work we seek $\mathbf{w}$ that forms a local reconstruction of $\mathbf{y}$ by solving a regularized least squares regression problem. We obtain local solutions through a locality function that promotes the use of columns of $\mathbf{X}$ that are close to $\mathbf{y}$ when used as a regularization term. We prove that, for all levels of regularization and under a mild condition that the columns of $\mathbf{X}$ have a unique Delaunay triangulation, the optimal coefficients' number of non-zero entries is upper bounded by $d+1$, thereby providing local sparse solutions when $d \ll n$. Under the same condition we also show that for any $\mathbf{y}$ contained in the convex hull of $\mathbf{X}$ there exists a regime of regularization parameter such that the optimal coefficients are supported on the vertices of the Delaunay simplex containing $\mathbf{y}$. This provides an interpretation of the sparsity as having structure obtained implicitly from the Delaunay triangulation of $\mathbf{X}$. We demonstrate that our locality regularized problem can be solved in comparable time to other methods that identify the containing Delaunay simplex.

Hyperbolic machine learning is an emerging field aimed at representing data with a hierarchical structure. However, there is a lack of tools for evaluation and analysis of the resulting hyperbolic data representations. To this end, we propose Hyperbolic Delaunay Geometric Alignment (HyperDGA) -- a similarity score for comparing datasets in a hyperbolic space. The core idea is counting the edges of the hyperbolic Delaunay graph connecting datapoints across the given sets. We provide an empirical investigation on synthetic and real-life biological data and demonstrate that HyperDGA outperforms the hyperbolic version of classical distances between sets. Furthermore, we showcase the potential of HyperDGA for evaluating latent representations inferred by a Hyperbolic Variational Auto-Encoder.

We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that are discrete tokens corresponding to positions in an input sequence. Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence [1] and Neural Turing Machines [2], because the number of target classes in each step of the output depends on the length of the input, which is variable. Problems such as sorting variable sized sequences, and various combinatorial optimization problems belong to this class. Our model solves the problem of variable size output dictionaries using a recently proposed mechanism of neural attention. It differs from the previous attention attempts in that, instead of using attention to blend hidden units of an encoder to a context vector at each decoder step, it uses attention as a pointer to select a member of the input sequence as the output.