The escalating threat posed by low-altitude swarm targets underscores the critical need for precise tracking and situation awareness to secure key areas. While existing tracking methods based on random matrix theory offer promising opportunities, they face significant challenges. The high similarity among swarm targets, combined with radar resolution limitations, often leads to instabilities in target counts and measurements due to occlusion, environmental factors, and other disturbances, significantly increasing tracking complexity. To address these challenges, we design a digital staring radar system integrated with an adaptive random matrix method for efficient tracking of low-altitude swarm targets. The system achieves full spatiotemporal coverage without beam scanning or complex resource scheduling, enabling simultaneous detection and tracking of multiple targets. Algorithmically, the random matrix model is enhanced by introducing extension parameters to accurately capture the dynamic changes in swarm shape. Leveraging an adaptive Rao-Blackwellized Particle Filter (RBPF), the presented method jointly estimates the motion and extension states of swarm targets. Extensive simulation experiments and real-data validation demonstrate that the proposed method significantly improves the estimation accuracy for swarm extension states under complex shape variations while maintaining high precision in motion state estimation. This work provides a practical and effective solution for countering low-altitude swarm threats, with strong potential for real-world security applications.

Covariance matrices, known as symmetric positive definite (SPD) matrices, are usually regarded as points lying on Riemannian manifolds. We describe a new covariance descriptor, which could improve the discriminative learning ability of region covariance descriptor by taking into account the mean of feature vectors. Due to the specific geometry of Riemannian manifolds, classical learning methods cannot be directly used on it. In this paper, we propose a subspace projection framework for the classification task on Riemannian manifolds and give the mathematical derivation for it. It is different from the common technique used for Riemannian manifolds, which is to explicitly project the points from a Riemannian manifold onto Euclidean space based upon a linear hypothesis. Under the proposed framework, we define a Gaussian Radial Basis Function‐ (RBF‐) based kernel with a Log‐Euclidean Riemannian Metric (LERM) to embed a Riemannian manifold into a high‐dimensional Reproducing Kernel Hilbert Space (RKHS) and then project it onto a subspace of the RKHS. Finally, a variant of Linear Discriminative Analyze (LDA) is recast onto the subspace. Experiments demonstrate the considerable effectiveness of the mixed region covariance descriptor and the proposed method.

In manifold learning, alignment is performed with the objective of deriving the global low‐dimensional coordinates of input data from their local coordinates. In virtually all alignment processes, the relation between the local and global coordinates is designed intuitively, without mathematical deduction and detailed analysis. In this study, the authors propose a local non‐linear alignment manifold learning algorithm (LNA) for non‐linear dimensionality reduction, based on the concept of local pullback and the mathematical characteristics of a manifold. According to mathematical manifold theory, a function defined on a manifold cannot be differentiated directly on the manifold directly. Instead, it has to be pulled back to Euclidean space with the help of local homeomorphism between the manifold and Euclidean space, where it is then differentiated. In the authors’ proposed algorithm, the component functions of global homeomorphism are regarded as the functions defined on the manifold and pulled back to the Euclidean space. Then, Taylor expansion is utilised up to the second order to establish the relation between the global and local coordinates. The objective function in LNA is based on the alignment error and can be solved with an eigenvalue problem. The experimental results conducted on various datasets verify the validity of the authors’ method.

While multimodal large language models (MLLMs) exhibit strong performance on single-video tasks (e.g., video question answering), their capability for spatiotemporal pattern reasoning across multiple videos remains a critical gap in pattern recognition research. However, this capability is essential for real-world applications, including multi-camera surveillance and cross-video procedural learning. To bridge this gap, we present CVBench, the first diagnostic benchmark designed to assess cross-video relational reasoning rigorously. CVBench comprises 1,000 question-answer pairs spanning three hierarchical tiers: cross-video object association (identifying shared entities), cross-video event association (linking temporal or causal event chains), and cross-video complex reasoning (integrating commonsense and domain knowledge). Built from five domain-diverse video clusters (e.g., sports, life records), the benchmark challenges models to analyze and integrate spatiotemporal patterns from dynamic visual streams. Extensive evaluation of 10+ leading MLLMs (including GPT-4o, Gemini-2.0-flash, Qwen2.5-VL) under zero-shot or chain-of-thought prompting paradigms. Key findings reveal stark performance gaps: even top models, such as GPT-4o, achieve only 63.5% accuracy on causal reasoning tasks, compared to the 91.3% accuracy of human performance. Crucially, our analysis reveals fundamental bottlenecks inherent in current MLLMs architectures, notably deficient inter-video context retention and poor disambiguation of overlapping entities. CVBench establishes a rigorous framework for advancing pattern recognition methodologies in multi-video scenarios, providing architectural insights for next-generation models. The data and evaluation code are available at: https://github.com/Hokhim2/CVBench.