Graph Connectivity in Noisy Sparse Subspace Clustering

Subspace clustering is the problem of clustering data points into a union of low-dimensional linear/affine subspaces. It is the mathematical abstraction of many important problems in computer vision, image processing and machine learning. A line of recent work (4, 19, 24, 20) provided strong theoretical guarantee for sparse subspace clustering (4), the state-of-the-art algorithm for subspace clustering, on both noiseless and noisy data sets. It was shown that under mild conditions, with high probability no two points from different subspaces are clustered together. Such guarantee, however, is not sufficient for the clustering to be correct, due to the notorious "graph connectivity problem" (15). In this paper, we investigate the graph connectivity problem for noisy sparse subspace clustering and show that a simple post-processing procedure is capable of delivering consistent clustering under certain "general position" or "restricted eigenvalue" assumptions. We also show that our condition is almost tight with adversarial noise perturbation by constructing a counter-example. These results provide the first exact clustering guarantee of noisy SSC for subspaces of dimension greater then 3.Comment: 14 pages. To appear in The 19th International Conference on Artificial Intelligence and Statistics, held at Cadiz, Spain in 201

A modified airfoil-based piezoaeroelastic energy harvester with double plunge degrees of freedom

In this letter, a piezoaeroelastic energy harvester based on an airfoil with double plunge degrees of freedom is proposed to additionally take advantage of the vibrational energy of the airfoil pitch motion. An analytical model of the proposed energy harvesting system is built and compared with an equivalent model using the well-explored pitch-plunge configuration. The dynamic response and average power output of the harvester are numerically studied as the flow velocity exceeds the cut-in speed (flutter speed). It is found that the harvester with double-plunge configuration generates 4%–10% more power with varying flow velocities while reducing 6% of the cut-in speed than its counterpart

Differentially Private Subspace Clustering

Subspace clustering is an unsupervised learning problem that aims at grouping data points into multiple “clusters ” so that data points in a single cluster lie ap-proximately on a low-dimensional linear subspace. It is originally motivated by 3D motion segmentation in computer vision, but has recently been generically applied to a wide range of statistical machine learning problems, which often in-volves sensitive datasets about human subjects. This raises a dire concern for data privacy. In this work, we build on the framework of differential privacy and present two provably private subspace clustering algorithms. We demonstrate via both theory and experiments that one of the presented methods enjoys formal privacy and utility guarantees; the other one asymptotically preserves differential privacy while having good performance in practice. Along the course of the proof, we also obtain two new provable guarantees for the agnostic subspace clustering and the graph connectivity problem which might be of independent interests.

Differentially Private Subspace Clustering

Subspace clustering is an unsupervised learning problem that aims at grouping data points into multiple "clusters" so that data points in a single cluster lie approximately on a low-dimensional linear subspace. It is originally motivated by 3D motion segmentation in computer vision, but has recently been generically applied to a wide range of statistical machine learning problems, which often involves sensitive datasets about human subjects. This raises a dire concern for data privacy. In this work, we build on the framework of differential privacy and present two provably private subspace clustering algorithms. We demonstrate via both theory and experiments that one of the presented methods enjoys formal privacy and utility guarantees; the other one asymptotically preserves differential privacy while having good performance in practice. Along the course of the proof, we also obtain two new provable guarantees for the agnostic subspace clustering and the graph connectivity problem which might be of independent interests

RLIPv2: Fast Scaling of Relational Language-Image Pre-training

Relational Language-Image Pre-training (RLIP) aims to align vision representations with relational texts, thereby advancing the capability of relational reasoning in computer vision tasks. However, hindered by the slow convergence of RLIPv1 architecture and the limited availability of existing scene graph data, scaling RLIPv1 is challenging. In this paper, we propose RLIPv2, a fast converging model that enables the scaling of relational pre-training to large-scale pseudo-labelled scene graph data. To enable fast scaling, RLIPv2 introduces Asymmetric Language-Image Fusion (ALIF), a mechanism that facilitates earlier and deeper gated cross-modal fusion with sparsified language encoding layers. ALIF leads to comparable or better performance than RLIPv1 in a fraction of the time for pre-training and fine-tuning. To obtain scene graph data at scale, we extend object detection datasets with free-form relation labels by introducing a captioner (e.g., BLIP) and a designed Relation Tagger. The Relation Tagger assigns BLIP-generated relation texts to region pairs, thus enabling larger-scale relational pre-training. Through extensive experiments conducted on Human-Object Interaction Detection and Scene Graph Generation, RLIPv2 shows state-of-the-art performance on three benchmarks under fully-finetuning, few-shot and zero-shot settings. Notably, the largest RLIPv2 achieves 23.29mAP on HICO-DET without any fine-tuning, yields 32.22mAP with just 1% data and yields 45.09mAP with 100% data. Code and models are publicly available at https://github.com/JacobYuan7/RLIPv2.Comment: Accepted to ICCV 2023. Code and models: https://github.com/JacobYuan7/RLIPv

A review of modelling and analysis of morphing wings

Morphing wings have a large potential to improve the overall aircraft performances, in a way like natural flyers do. By adapting or optimising dynamically the shape to various flight conditions, there are yet many unexplored opportunities beyond current proof-of-concept demonstrations. This review discusses the most prominent examples of morphing concepts with applications to two and three-dimensional wing models. Methods and tools commonly deployed for the design and analysis of these concepts are discussed, ranging from structural to aerodynamic analyses, and from control to optimisation aspects. Throughout the review process, it became apparent that the adoption of morphing concepts for routine use on aerial vehicles is still scarce, and some reasons holding back their integration for industrial use are given. Finally, promising concepts for future use are identified