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Xiaobo Liu

Publications and source records attributed to Xiaobo Liu.

At least 55 records · Page 3Linked to original sources
arXiv2022

Schur Q-Polynomials and Kontsevich-Witten Tau Function

Using matrix model, Mironov and Morozov recently gave a formula which represents Kontsevich-Witten tau-function as a linear expansion of Schur Q-polynomials. In this paper, we will show directly that the Q-polynomial expansion in this formula satisfies the Virasoro constraints, and consequently obtain a proof of this formula without using matrix model. We also give a proof for Alexandrov's conjecture that Kontsevich-Witten tau-function is a hypergeometric tau-function of the BKP hierarchy after re-scaling.

math.AG↗
arXiv2022

Dynamic Cooperative Vehicle Platoon Control Considering Longitudinal and Lane-changing Dynamics

This paper presents a distributed cascade Proportional Integral Derivate (DCPID) control algorithm for the connected and automated vehicle (CAV) platoon considering the heterogeneity of CAVs in terms of the inertial lag. Furthermore, a real-time dynamic cooperative lane-changing model for CAVs, which can seamlessly combine the DCPID algorithm and the improved sine function is developed. The DCPID algorithm determines the appropriate longitudinal acceleration and speed of the lane-changing vehicle considering the speed fluctuations of the front vehicle on the target lane (TFV). In the meantime, the sine function plans a reference trajectory which is further updated in real time using the model predictive control (MPC) to avoid potential collisions until lane-changing is completed. Both the local and the asymptotic stability conditions of the DCPID algorithm are mathematically derived, and the sensitivity of the DCPID control parameters under different states is analyzed. Simulation experiments are conducted to assess the performance of the proposed model and the results indicate that the DCPID algorithm can provide robust control for tracking and adjusting the desired spacing and velocity for all 400 scenarios, even in the relatively extreme initial state. Besides, the proposed dynamic cooperative lane-changing model can guarantee an effective and safe lane-changing with different speeds and even in emergency situations (such as the sudden deceleration of the TFV).

math.OC↗
arXiv2021

Fully Linear Graph Convolutional Networks for Semi-Supervised Learning and Clustering

This paper presents FLGC, a simple yet effective fully linear graph convolutional network for semi-supervised and unsupervised learning. Instead of using gradient descent, we train FLGC based on computing a global optimal closed-form solution with a decoupled procedure, resulting in a generalized linear framework and making it easier to implement, train, and apply. We show that (1) FLGC is powerful to deal with both graph-structured data and regular data, (2) training graph convolutional models with closed-form solutions improve computational efficiency without degrading performance, and (3) FLGC acts as a natural generalization of classic linear models in the non-Euclidean domain, e.g., ridge regression and subspace clustering. Furthermore, we implement a semi-supervised FLGC and an unsupervised FLGC by introducing an initial residual strategy, enabling FLGC to aggregate long-range neighborhoods and alleviate over-smoothing. We compare our semi-supervised and unsupervised FLGCs against many state-of-the-art methods on a variety of classification and clustering benchmarks, demonstrating that the proposed FLGC models consistently outperform previous methods in terms of accuracy, robustness, and learning efficiency. The core code of our FLGC is released at https://github.com/AngryCai/FLGC.

cs.LG↗
arXiv2021

Large-Scale Hyperspectral Image Clustering Using Contrastive Learning

Clustering of hyperspectral images is a fundamental but challenging task. The recent development of hyperspectral image clustering has evolved from shallow models to deep and achieved promising results in many benchmark datasets. However, their poor scalability, robustness, and generalization ability, mainly resulting from their offline clustering scenarios, greatly limit their application to large-scale hyperspectral data. To circumvent these problems, we present a scalable deep online clustering model, named Spectral-Spatial Contrastive Clustering (SSCC), based on self-supervised learning. Specifically, we exploit a symmetric twin neural network comprised of a projection head with a dimensionality of the cluster number to conduct dual contrastive learning from a spectral-spatial augmentation pool. We define the objective function by implicitly encouraging within-cluster similarity and reducing between-cluster redundancy. The resulting approach is trained in an end-to-end fashion by batch-wise optimization, making it robust in large-scale data and resulting in good generalization ability for unseen data. Extensive experiments on three hyperspectral image benchmarks demonstrate the effectiveness of our approach and show that we advance the state-of-the-art approaches by large margins.

cs.CV↗
arXiv2021

Polar foliations on symmetric spaces and the mean curvature flow

In this paper, we study polar foliations on simply connected symmetric spaces with non-negative curvature. We will prove that all such foliations are isoparametric as defined by Heintze, Liu and Olmos. We will also prove a splitting theorem which reduces the study of such foliations to polar foliations in compact simply connected symmetric spaces. Moreover, we will show that solutions to mean curvature flow of regular leaves in such foliations are always ancient solutions. This generalizes part of the results of Liu and Terng for the mean curvature flow of isoparametric submanifolds in spheres.

math.DG↗
arXiv2021

Weighted Ensemble-model and Network Analysis: A method to predict fluid intelligence via naturalistic functional connectivity

Objectives: Functional connectivity triggered by naturalistic stimulus (e.g., movies) and machine learning techniques provide a great insight in exploring the brain functions such as fluid intelligence. However, functional connectivity are considered to be multi-layered, while traditional machine learning based on individual models not only are limited in performance, but also fail to extract multi-dimensional and multi-layered information from brain network. Methods: In this study, inspired by multi-layer brain network structure, we propose a new method namely Weighted Ensemble-model and Network Analysis, which combines the machine learning and graph theory for improved fluid intelligence prediction. Firstly, functional connectivity analysis and graphical theory were jointly employed. The functional connectivity and graphical indices computed using the preprocessed fMRI data were then all fed into auto-encoder parallelly for feature extraction to predict the fluid intelligence. In order to improve the performance, tree regression and ridge regression model were automatically stacked and fused with weighted values. Finally, layers of auto-encoder were visualized to better illustrate the connectome patterns, followed by the evaluation of the performance to justify the mechanism of brain functions. Results: Our proposed methods achieved best performance with 3.85 mean absolute deviation, 0.66 correlation coefficient and 0.42 R-squared coefficient, outperformed other state-of-the-art methods. It is also worth noting that, the optimization of the biological pattern extraction was automated though the auto-encoder algorithm. Conclusion: The proposed method not only outperforming the state-of-the-art reports, but also able to effectively capturing the biological patterns from functional connectivity during naturalistic movies state for potential clinical explorations.

cs.AI↗
arXiv2020

DeepClaw: A Robotic Hardware Benchmarking Platform for Learning Object Manipulation

We present DeepClaw as a reconfigurable benchmark of robotic hardware and task hierarchy for robot learning. The DeepClaw benchmark aims at a mechatronics perspective of the robot learning problem, which features a minimum design of robot cell that can be easily reconfigured to host robot hardware from various vendors, including manipulators, grippers, cameras, desks, and objects, aiming at a streamlined collection of physical manipulation data and evaluation of the learned skills for hardware benchmarking. We provide a detailed design of the robot cell with readily available parts to build the experiment environment that can host a wide range of robotic hardware commonly adopted for robot learning. We also propose a hierarchical pipeline of software integration, including localization, recognition, grasp planning, and motion planning, to streamline learning-based robot control, data collection, and experiment validation towards shareability and reproducibility. We present benchmarking results of the DeepClaw system for a baseline Tic-Tac-Toe task, a bin-clearing task, and a jigsaw puzzle task using three sets of standard robotic hardware. Our results show that tasks defined in DeepClaw can be easily reproduced on three robot cells. Under the same task setup, the differences in robotic hardware used will present a non-negligible impact on the performance metrics of robot learning. All design layouts and codes are hosted on Github for open access.

cs.RO↗
arXiv2020

Graph Convolutional Subspace Clustering: A Robust Subspace Clustering Framework for Hyperspectral Image

Hyperspectral image (HSI) clustering is a challenging task due to the high complexity of HSI data. Subspace clustering has been proven to be powerful for exploiting the intrinsic relationship between data points. Despite the impressive performance in the HSI clustering, traditional subspace clustering methods often ignore the inherent structural information among data. In this paper, we revisit the subspace clustering with graph convolution and present a novel subspace clustering framework called Graph Convolutional Subspace Clustering (GCSC) for robust HSI clustering. Specifically, the framework recasts the self-expressiveness property of the data into the non-Euclidean domain, which results in a more robust graph embedding dictionary. We show that traditional subspace clustering models are the special forms of our framework with the Euclidean data. Basing on the framework, we further propose two novel subspace clustering models by using the Frobenius norm, namely Efficient GCSC (EGCSC) and Efficient Kernel GCSC (EKGCSC). Both models have a globally optimal closed-form solution, which makes them easier to implement, train, and apply in practice. Extensive experiments on three popular HSI datasets demonstrate that EGCSC and EKGCSC can achieve state-of-the-art clustering performance and dramatically outperforms many existing methods with significant margins.

cs.CV↗
arXiv2020

Rigid-Soft Interactive Learning for Robust Grasping

Inspired by widely used soft fingers on grasping, we propose a method of rigid-soft interactive learning, aiming at reducing the time of data collection. In this paper, we classify the interaction categories into Rigid-Rigid, Rigid-Soft, Soft-Rigid according to the interaction surface between grippers and target objects. We find experimental evidence that the interaction types between grippers and target objects play an essential role in the learning methods. We use soft, stuffed toys for training, instead of everyday objects, to reduce the integration complexity and computational burden and exploit such rigid-soft interaction by changing the gripper fingers to the soft ones when dealing with rigid, daily-life items such as the Yale-CMU-Berkeley (YCB) objects. With a small data collection of 5K picking attempts in total, our results suggest that such Rigid-Soft and Soft-Rigid interactions are transferable. Moreover, the combination of different grasp types shows better performance on the grasping test. We achieve the best grasping performance at 97.5\% for easy YCB objects and 81.3\% for difficult YCB objects while using a precise grasp with a two-soft-finger gripper to collect training data and power grasp with a four-soft-finger gripper to test.

cs.RO↗
arXiv2019

Ancient solutions to mean curvature flow for isoparametric submanifolds

Mean curvature flow for isoparametric submanifolds in Euclidean spaces and spheres was studied by the authors in [LT]. In this paper, we will show that all these solutions are ancient solutions. We also discuss rigidity of ancient mean curvature flows for hypersurfaces in spheres and its relation to the Chern's conjecture on the norm of the second fundamental forms of minimal hypersurfaces in spheres.

math.DG↗
arXiv2019

The mean curvature flow for isoparametric submanifolds

A submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant. We study the mean curvature flow with initial data an isoparametric submanifold in Euclidean space and sphere. We show that the mean curvature flow preserves the isoparametric condition, develops singularities in finite time, and converges in finite time to a smooth submanifold of lower dimension. We also give a precise description of the collapsing.

math.DG↗
arXiv2019

Multi-PCA based Fault Detection Model Combined with Prior knowledge of HVAC

The traditional PCA fault detection methods completely depend on the training data. The prior knowledge such as the physical principle of the system has not been taken into account. In this paper, we propose a new multi-PCA fault detection model combined with prior knowledge. This new model can adapt to the variable operating conditions of the central air conditioning system, and it can detect small deviation faults of sensors and significantly shorten the time delay of detecting drift faults. We also conducted enough ablation experiments to demonstrate that our model is more robust and efficient.

cs.LG↗
arXiv2019

BS-Nets: An End-to-End Framework For Band Selection of Hyperspectral Image

Hyperspectral image (HSI) consists of hundreds of continuous narrow bands with high spectral correlation, which would lead to the so-called Hughes phenomenon and the high computational cost in processing. Band selection has been proven effective in avoiding such problems by removing the redundant bands. However, many of existing band selection methods separately estimate the significance for every single band and cannot fully consider the nonlinear and global interaction between spectral bands. In this paper, by assuming that a complete HSI can be reconstructed from its few informative bands, we propose a general band selection framework, Band Selection Network (termed as BS-Net). The framework consists of a band attention module (BAM), which aims to explicitly model the nonlinear inter-dependencies between spectral bands, and a reconstruction network (RecNet), which is used to restore the original HSI cube from the learned informative bands, resulting in a flexible architecture. The resulting framework is end-to-end trainable, making it easier to train from scratch and to combine with existing networks. We implement two BS-Nets respectively using fully connected networks (BS-Net-FC) and convolutional neural networks (BS-Net-Conv), and compare the results with many existing band selection approaches for three real hyperspectral images, demonstrating that the proposed BS-Nets can accurately select informative band subset with less redundancy and achieve significantly better classification performance with an acceptable time cost.

cs.CV↗
arXiv2017

Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators

In this paper, we show that the generating function for linear Hodge integrals over moduli spaces of stable maps to a nonsingular projective variety $X$ can be connected to the generating function for Gromov-Witten invariants of $X$ by a series of differential operators $\{ L_m \mid m \geq 1 \}$ after a suitable change of variables. These operators satisfy the Virasoro bracket relation and can be seen as a generalization of the Virasoro operators appeared in the Virasoro constraints for Kontsevich-Witten tau-function in the point case. This result is an extension of the work in \cite{LW} for the point case which solved a conjecture of Alexandrov.

math.AG↗
arXiv2015

Topological Recursion Relations on $\bar{\cal M}_{3,2}$

In this paper, we give some new genus-3 universal equations for Gromov-Witten invariants of compact symplectic manifolds. These equations were obtained by studying new relations in the tautological ring of the moduli space of 2-pointed genus-3 stable curves. A byproduct of our search for genus-3 equations is a new genus-2 universal equation for Gromov-Witten invariants.

math.DG↗
arXiv2014

Conditions for the vanishing of the genus-2 G-function

In this paper we give some sufficient conditions for the vanishing of the genus-2 G-function, which was introduced by B. Dubrovin, S. Liu and Y. Zhang in [DLZ]. As a corollary we prove their conjecture for the vanishing of the genus-2 G-function for ADE singularities.

math.DG↗