arXiv subjects

Can Chen

Publications and source records attributed to Can Chen.

83 records · Page 5Linked to original sources

arXiv2021

Hypergraph Dissimilarity Measures

In this paper, we propose two novel approaches for hypergraph comparison. The first approach transforms the hypergraph into a graph representation for use of standard graph dissimilarity measures. The second approach exploits the mathematics of tensors to intrinsically capture multi-way relations. For each approach, we present measures that assess hypergraph dissimilarity at a specific scale or provide a more holistic multi-scale comparison. We test these measures on synthetic hypergraphs and apply them to biological datasets.

cs.LG↗

arXiv2021

Controllability of Hypergraphs

In this paper, we develop a notion of controllability for hypergraphs via tensor algebra and polynomial control theory. Inspired by uniform hypergraphs, we propose a new tensor-based multilinear dynamical system representation, and derive a Kalman-rank-like condition to determine the minimum number of control nodes (MCN) needed to achieve controllability of even uniform hypergraphs. We present an efficient heuristic to obtain the MCN. MCN can be used as a measure of robustness, and we show that it is related to the hypergraph degree distribution in simulated examples. Finally, we use MCN to examine robustness in real biological networks.

math.OC↗

arXiv2020

Multilinear Control Systems Theory

In this paper, we provide a system theoretic treatment of a new class of multilinear time-invariant (MLTI) systems in which the states, inputs and outputs are tensors, and the system evolution is governed by multilinear operators. The MLTI system representation is based on the Einstein product and even-order paired tensors. There is a particular tensor unfolding which gives rise to an isomorphism from this tensor space to the general linear group, i.e. the group of invertible matrices. By leveraging this unfolding operation, one can extend classical linear time-invariant (LTI) system notions including stability, reachability and observability to MLTI systems. While the unfolding based formulation is a powerful theoretical construct, the computational advantages of MLTI systems can only be fully realized while working with the tensor form, where hidden patterns/structures can be exploited for efficient representations and computations. Along these lines, we establish new results which enable one to express tensor unfolding based stability, reachability and observability criteria in terms of more standard notions of tensor ranks/decompositions. In addition, we develop a generalized CANDECOMP/PARAFAC decomposition and tensor train decomposition based model reduction framework, which can significantly reduce the number of MLTI system parameters. We demonstrate our framework with numerical examples.

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arXiv2020

Relation3DMOT: Exploiting Deep Affinity for 3D Multi-Object Tracking from View Aggregation

Autonomous systems need to localize and track surrounding objects in 3D space for safe motion planning. As a result, 3D multi-object tracking (MOT) plays a vital role in autonomous navigation. Most MOT methods use a tracking-by-detection pipeline, which includes object detection and data association processing. However, many approaches detect objects in 2D RGB sequences for tracking, which is lack of reliability when localizing objects in 3D space. Furthermore, it is still challenging to learn discriminative features for temporally-consistent detection in different frames, and the affinity matrix is normally learned from independent object features without considering the feature interaction between detected objects in the different frames. To settle these problems, We firstly employ a joint feature extractor to fuse the 2D and 3D appearance features captured from both 2D RGB images and 3D point clouds respectively, and then propose a novel convolutional operation, named RelationConv, to better exploit the correlation between each pair of objects in the adjacent frames, and learn a deep affinity matrix for further data association. We finally provide extensive evaluation to reveal that our proposed model achieves state-of-the-art performance on KITTI tracking benchmark.

cs.CV↗

arXiv2020

RoIFusion: 3D Object Detection from LiDAR and Vision

When localizing and detecting 3D objects for autonomous driving scenes, obtaining information from multiple sensor (e.g. camera, LIDAR) typically increases the robustness of 3D detectors. However, the efficient and effective fusion of different features captured from LIDAR and camera is still challenging, especially due to the sparsity and irregularity of point cloud distributions. This notwithstanding, point clouds offer useful complementary information. In this paper, we would like to leverage the advantages of LIDAR and camera sensors by proposing a deep neural network architecture for the fusion and the efficient detection of 3D objects by identifying their corresponding 3D bounding boxes with orientation. In order to achieve this task, instead of densely combining the point-wise feature of the point cloud and the related pixel features, we propose a novel fusion algorithm by projecting a set of 3D Region of Interests (RoIs) from the point clouds to the 2D RoIs of the corresponding the images. Finally, we demonstrate that our deep fusion approach achieves state-of-the-art performance on the KITTI 3D object detection challenging benchmark.

cs.CV↗

arXiv2020

Tensor Entropy for Uniform Hypergraphs

In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory. We employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the Laplacian tensors, to fit into the Shannon entropy formula. We show that this tensor entropy is an extension of von Neumann entropy for graphs. In addition, we establish results on the lower and upper bounds of the entropy and demonstrate that it is a measure of regularity for uniform hypergraphs in simulated and experimental data. We exploit the tensor train decomposition in computing the proposed tensor entropy efficiently. Finally, we introduce the notion of robustness for uniform hypergraphs.

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arXiv2020

Data-Driven Model Reduction for Multilinear Control Systems via Tensor Trains

In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD), which provides a good compromise between numerical stability and level of compression, and has an associated algebra that facilitates computations. Using TTD, we propose a new BT approach which we refer to as higher-order balanced truncation, and consider different data-driven variations including higher-order empirical gramians, higher-order balanced proper orthogonal decomposition and a higher-order eigensystem realization algorithm. We perform computational and memory complexity analysis for these different flavors of TTD based BT methods, and compare with the corresponding standard BT methods in order to develop insights into where the proposed framework may be beneficial. We provide numerical results on simulated and experimental datasets showing the efficacy of the proposed framework.

eess.SY↗

arXiv2019

Go Wider: An Efficient Neural Network for Point Cloud Analysis via Group Convolutions

In order to achieve better performance for point cloud analysis, many researchers apply deeper neural networks using stacked Multi-Layer-Perceptron (MLP) convolutions over irregular point cloud. However, applying dense MLP convolutions over large amount of points (e.g. autonomous driving application) leads to inefficiency in memory and computation. To achieve high performance but less complexity, we propose a deep-wide neural network, called ShufflePointNet, to exploit fine-grained local features and reduce redundancy in parallel using group convolution and channel shuffle operation. Unlike conventional operation that directly applies MLPs on high-dimensional features of point cloud, our model goes wider by splitting features into groups in advance, and each group with certain smaller depth is only responsible for respective MLP operation, which can reduce complexity and allows to encode more useful information. Meanwhile, we connect communication between groups by shuffling groups in feature channel to capture fine-grained features. We claim that, multi-branch method for wider neural networks is also beneficial to feature extraction for point cloud. We present extensive experiments for shape classification task on ModelNet40 dataset and semantic segmentation task on large scale datasets ShapeNet part, S3DIS and KITTI. We further perform ablation study and compare our model to other state-of-the-art algorithms in terms of complexity and accuracy.

cs.CV↗

arXiv2019

Fast Hierarchical Neural Network for Feature Learning on Point Cloud

The analyses relying on 3D point clouds are an utterly complex task, often involving million of points, but also requiring computationally efficient algorithms because of many real-time applications; e.g. autonomous vehicle. However, point clouds are intrinsically irregular and the points are sparsely distributed in a non-Euclidean space, which normally requires point-wise processing to achieve high performances. Although shared filter matrices and pooling layers in convolutional neural networks (CNNs) are capable of reducing the dimensionality of the problem and extracting high-level information simultaneously, grids and highly regular data format are required as input. In order to balance model performance and complexity, we introduce a novel neural network architecture exploiting local features from a manually subsampled point set. In our network, a recursive farthest point sampling method is firstly applied to efficiently cover the entire point set. Successively, we employ the k-nearest neighbours (knn) algorithm to gather local neighbourhood for each group of the subsampled points. Finally, a multiple layer perceptron (MLP) is applied on the subsampled points and edges that connect corresponding point and neighbours to extract local features. The architecture has been tested for both shape classification and segmentation using the ModelNet40 and ShapeNet part datasets, in order to show that the network achieves the best trade-off in terms of competitive performance when compared to other state-of-the-art algorithms.

cs.CV↗

arXiv2019

GAPNet: Graph Attention based Point Neural Network for Exploiting Local Feature of Point Cloud

Exploiting fine-grained semantic features on point cloud is still challenging due to its irregular and sparse structure in a non-Euclidean space. Among existing studies, PointNet provides an efficient and promising approach to learn shape features directly on unordered 3D point cloud and has achieved competitive performance. However, local feature that is helpful towards better contextual learning is not considered. Meanwhile, attention mechanism shows efficiency in capturing node representation on graph-based data by attending over neighboring nodes. In this paper, we propose a novel neural network for point cloud, dubbed GAPNet, to learn local geometric representations by embedding graph attention mechanism within stacked Multi-Layer-Perceptron (MLP) layers. Firstly, we introduce a GAPLayer to learn attention features for each point by highlighting different attention weights on neighborhood. Secondly, in order to exploit sufficient features, a multi-head mechanism is employed to allow GAPLayer to aggregate different features from independent heads. Thirdly, we propose an attention pooling layer over neighbors to capture local signature aimed at enhancing network robustness. Finally, GAPNet applies stacked MLP layers to attention features and local signature to fully extract local geometric structures. The proposed GAPNet architecture is tested on the ModelNet40 and ShapeNet part datasets, and achieves state-of-the-art performance in both shape classification and part segmentation tasks.

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arXiv2019

Multilinear Time Invariant System Theory

In biological and engineering systems, structure, function and dynamics are highly coupled. Such interactions can be naturally and compactly captured via tensor based state space dynamic representations. However, such representations are not amenable to the standard system and controls framework which requires the state to be in the form of a vector. In order to address this limitation, recently a new class of multiway dynamical systems has been introduced in which the states, inputs and outputs are tensors. We propose a new form of multilinear time invariant (MLTI) systems based on the Einstein product and even-order paired tensors. We extend classical linear time invariant (LTI) system notions including stability, reachability and observability for the new MLTI system representation by leveraging recent advances in tensor algebra.

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