Tong Mao
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Tong Mao has a total of 15 co-authors. Here are the top co-authors by number of shared publications:
- Houjun Sun
Beijing Institute of Technology
3 shared publications - Kaiqiang Zhu
School of Integrated Circuits and Electronics, Beijing Institute of Technology, Beijing, China
3 shared publications - Yi Zhang
School of Physics, Beijing Institute of Technology, Beijing, China
3 shared publications Houjun Sun
School of Integrated Circuits and Electronics Beijing Institute of Technology Beijing China
2 shared publications- Hrushikesh N. Mhaskar
Institute of Mathematical Sciences, Claremont Graduate University, Claremont, USA
2 shared publications - Ding-Xuan Zhou
School of Mathematics and Statistics, University of Sydney, Sydney, Australia
1 shared publication
Latest Publications
- Open Access
Tractability of approximation by general shallow networks
In this paper, we present a sharper version of the results in the paper Dimension independent bounds for general shallow networks; Neural Networks, \textbf{123} (2020), 142-152. Let $\mathbb{X}$ and $\mathbb{Y}$ be compact metric spaces. We consider approximation of functions of the form $ x\mapsto\int_{\mathbb{Y}} G( x, y)dτ( y)$, $ x\in\mathbb{X}$, by $G$-networks of the form $ x\mapsto \sum_{k=1}^n a_kG( x, y_k)$, $ y_1,\cdots, y_n\in\mathbb{Y}$, $a_1,\cdots, a_n\in\mathbb{R}$. Defining the dimensions of $\mathbb{X}$ and $\mathbb{Y}$ in terms of covering numbers, we obtain dimension independent bounds on the degree of approximation in terms of $n$, where also the constants involved are all dependent at most polynomially on the dimensions. Applications include approximation by power rectified linear unit networks, zonal function networks, certain radial basis function networks as well as the important problem of function extension to higher dimensional spaces.Open AccessTractability of approximation by general shallow networks
In this paper, we present a sharper version of the results in the paper Dimension independent bounds for general shallow networks; Neural Networks, \textbf{123} (2020), 142-152. Let $\mathbb{X}$ and $\mathbb{Y}$ be compact metric spaces. We consider approximation of functions of the form $ x\mapsto\int_{\mathbb{Y}} G( x, y)dτ( y)$, $ x\in\mathbb{X}$, by $G$-networks of the form $ x\mapsto \sum_{k=1}^n a_kG( x, y_k)$, $ y_1,\cdots, y_n\in\mathbb{Y}$, $a_1,\cdots, a_n\in\mathbb{R}$. Defining the dimensions of $\mathbb{X}$ and $\mathbb{Y}$ in terms of covering numbers, we obtain dimension independent bounds on the degree of approximation in terms of $n$, where also the constants involved are all dependent at most polynomially on the dimensions. Applications include approximation by power rectified linear unit networks, zonal function networks, certain radial basis function networks as well as the important problem of function extension to higher dimensional spaces. - Open Access
Rates of Approximation by ReLU Shallow Neural Networks
Neural networks activated by the rectified linear unit (ReLU) play a central role in the recent development of deep learning. The topic of approximating functions from Hölder spaces by these networks is crucial for understanding the efficiency of the induced learning algorithms. Although the topic has been well investigated in the setting of deep neural networks with many layers of hidden neurons, it is still open for shallow networks having only one hidden layer. In this paper, we provide rates of uniform approximation by these networks. We show that ReLU shallow neural networks with $m$ hidden neurons can uniformly approximate functions from the Hölder space $W_\infty^r([-1, 1]^d)$ with rates $O((\log m)^{\frac{1}{2} +d}m^{-\frac{r}{d}\frac{d+2}{d+4}})$ when $r<d/2 +2$. Such rates are very close to the optimal one $O(m^{-\frac{r}{d}})$ in the sense that $\frac{d+2}{d+4}$ is close to $1$, when the dimension $d$ is large.Open AccessRates of Approximation by ReLU Shallow Neural Networks
Neural networks activated by the rectified linear unit (ReLU) play a central role in the recent development of deep learning. The topic of approximating functions from Hölder spaces by these networks is crucial for understanding the efficiency of the induced learning algorithms. Although the topic has been well investigated in the setting of deep neural networks with many layers of hidden neurons, it is still open for shallow networks having only one hidden layer. In this paper, we provide rates of uniform approximation by these networks. We show that ReLU shallow neural networks with $m$ hidden neurons can uniformly approximate functions from the Hölder space $W_\infty^r([-1, 1]^d)$ with rates $O((\log m)^{\frac{1}{2} +d}m^{-\frac{r}{d}\frac{d+2}{d+4}})$ when $r<d/2 +2$. Such rates are very close to the optimal one $O(m^{-\frac{r}{d}})$ in the sense that $\frac{d+2}{d+4}$ is close to $1$, when the dimension $d$ is large. - Open Access
Micro-Motion Extraction for Marine Targets by Multi-Pulse Delay Conjugate Multiplication and Layered Tracking
The detection and recognition of marine targets can be improved by utilizing the micro-motion induced by ocean waves. However, distinguishing and tracking overlapping targets is challenging when multiple extended targets overlap in the range dimension of the radar echo. In this paper, we propose a multi-pulse delay conjugate multiplication and layered tracking (MDCM-LT) algorithm for micro-motion trajectory tracking. The MDCM method is first applied to obtain the conjugate phase from the radar echo, which enables high-precision micro-motion extraction and overlapping state identification of extended targets. Then, the LT algorithm is proposed to track the sparse scattering points belonging to different extended targets. In our simulation, the root mean square errors of the distance and velocity trajectories were better than 0.277 and 0.016 , respectively. Our results demonstrate that the proposed method has the potential to improve the precision and reliability of marine target detection through radar.Open AccessMicro-Motion Extraction for Marine Targets by Multi-Pulse Delay Conjugate Multiplication and Layered Tracking
The detection and recognition of marine targets can be improved by utilizing the micro-motion induced by ocean waves. However, distinguishing and tracking overlapping targets is challenging when multiple extended targets overlap in the range dimension of the radar echo. In this paper, we propose a multi-pulse delay conjugate multiplication and layered tracking (MDCM-LT) algorithm for micro-motion trajectory tracking. The MDCM method is first applied to obtain the conjugate phase from the radar echo, which enables high-precision micro-motion extraction and overlapping state identification of extended targets. Then, the LT algorithm is proposed to track the sparse scattering points belonging to different extended targets. In our simulation, the root mean square errors of the distance and velocity trajectories were better than 0.277 and 0.016 , respectively. Our results demonstrate that the proposed method has the potential to improve the precision and reliability of marine target detection through radar. - Open Access
Encoding of data sets and algorithms
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a mathematically rigorous theory to decide which models (algorithms applied on data sets) are close to each other in terms of certain metrics, such as performance and the complexity level of the algorithm. This involves creating a grid on the hypothetical spaces of data sets and algorithms so as to identify a finite set of probability distributions from which the data sets are sampled and a finite set of algorithms. A given threshold metric acting on this grid will express the nearness (or statistical distance) from each algorithm and data set of interest to any given application. A technically difficult part of this project is to estimate the so-called metric entropy of a compact subset of functions of \textbf{infinitely many variables} that arise in the definition of these spaces.
Open AccessEncoding of data sets and algorithms
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a mathematically rigorous theory to decide which models (algorithms applied on data sets) are close to each other in terms of certain metrics, such as performance and the complexity level of the algorithm. This involves creating a grid on the hypothetical spaces of data sets and algorithms so as to identify a finite set of probability distributions from which the data sets are sampled and a finite set of algorithms. A given threshold metric acting on this grid will express the nearness (or statistical distance) from each algorithm and data set of interest to any given application. A technically difficult part of this project is to estimate the so-called metric entropy of a compact subset of functions of \textbf{infinitely many variables} that arise in the definition of these spaces.
- Open Access
- 16 November 2022
- Published by Institution of Engineering and Technology (IET) in IET Radar, Sonar & Navigation
- Vol. 17 (2) , 236-246
Estimation of human gait features by trajectory tracking and recombination using radar range‐Doppler‐time data
Radar enables a convenient, contactless way for gait analysis in daily scenarios, such as in‐home health monitoring. However, the overlapping of human limb components could occur in both range and velocity dimensions of the radar echo, which makes it difficult to distinguish the limbs. In this study, a trajectory tracking and recombination method based on range‐Doppler‐time data is proposed for gait feature estimation under insufficient radar resolution. In the trajectory tracking step, the scattering amplitude is included for Kalman filtering, and the weighted joint nearest neighbour algorithm is proposed for data association. Then, the trajectories are recombined to construct the limb tracks based on the relative range‐Doppler angles. Finally, the limb tracks are used to estimate the spatial‐temporal and kinematic gait features. In our simulation, the trajectory tracking accuracies range from 98.2% to 99.6%. The gait feature estimation accuracies for simulation and measurement are no less than 91.9% and 93.8% respectively.
- 16 November 2022
- Published by Institution of Engineering and Technology (IET) in IET Radar, Sonar & Navigation
- Vol. 17 (2) , 236-246
Open AccessEstimation of human gait features by trajectory tracking and recombination using radar range‐Doppler‐time data
Radar enables a convenient, contactless way for gait analysis in daily scenarios, such as in‐home health monitoring. However, the overlapping of human limb components could occur in both range and velocity dimensions of the radar echo, which makes it difficult to distinguish the limbs. In this study, a trajectory tracking and recombination method based on range‐Doppler‐time data is proposed for gait feature estimation under insufficient radar resolution. In the trajectory tracking step, the scattering amplitude is included for Kalman filtering, and the weighted joint nearest neighbour algorithm is proposed for data association. Then, the trajectories are recombined to construct the limb tracks based on the relative range‐Doppler angles. Finally, the limb tracks are used to estimate the spatial‐temporal and kinematic gait features. In our simulation, the trajectory tracking accuracies range from 98.2% to 99.6%. The gait feature estimation accuracies for simulation and measurement are no less than 91.9% and 93.8% respectively.
- Open Access
- 23 July 2022
- Published by MDPI AG in Electronics
- Vol. 11 (15) , 2305
Experimental Realization of 16-Pixel Terahertz Receiver Front-End Based on Bulk Silicon MEMS Power Divider and AlGaN/GaN HEMT Linear Detector Array
A 16-pixel terahertz (THz) receiver front-end working at room temperature was designed, built, and measured in this paper. The designed receiver front-end is based on the antenna-coupled AlGaN/GaN high-electron-mobility transistor (HEMT) THz linear detector array (TeraLDA) and a 16-way THz power divider. The local oscillator (LO) signal is divided by the power divider into 16 ways and transmits to the TeraLDA. Each detector contains a planar unified antenna printed on a 150 -thick sapphire substrate and a transistor fabricated on AlGaN/GaN heterostructure. There are 16 silicon hemispheric lenses located on the TeraLDA to increase the responsivity of the TeraLDA. The focus of each lens is aligned in the center of the TeraLDA pixels. Depending on different read out circuits, the receiver front-end could work in homodyne and heterodyne modes. The 16-way power divider is a four-stage power divider that consists of fifteen same 2-way dividers, and was fabricated by bulk silicon microelectromechanical systems (MEMS) technology to achieve low insertion loss (IL). This designed receiver front-end could be a key component of a THz coherent focal plane imaging radar system, that may play a crucial role in nondestructive 3D imaging application.- 23 July 2022
- Published by MDPI AG in Electronics
- Vol. 11 (15) , 2305
Open AccessExperimental Realization of 16-Pixel Terahertz Receiver Front-End Based on Bulk Silicon MEMS Power Divider and AlGaN/GaN HEMT Linear Detector Array
A 16-pixel terahertz (THz) receiver front-end working at room temperature was designed, built, and measured in this paper. The designed receiver front-end is based on the antenna-coupled AlGaN/GaN high-electron-mobility transistor (HEMT) THz linear detector array (TeraLDA) and a 16-way THz power divider. The local oscillator (LO) signal is divided by the power divider into 16 ways and transmits to the TeraLDA. Each detector contains a planar unified antenna printed on a 150 -thick sapphire substrate and a transistor fabricated on AlGaN/GaN heterostructure. There are 16 silicon hemispheric lenses located on the TeraLDA to increase the responsivity of the TeraLDA. The focus of each lens is aligned in the center of the TeraLDA pixels. Depending on different read out circuits, the receiver front-end could work in homodyne and heterodyne modes. The 16-way power divider is a four-stage power divider that consists of fifteen same 2-way dividers, and was fabricated by bulk silicon microelectromechanical systems (MEMS) technology to achieve low insertion loss (IL). This designed receiver front-end could be a key component of a THz coherent focal plane imaging radar system, that may play a crucial role in nondestructive 3D imaging application. - Open Access
- 23 September 2021
- Published by Institution of Engineering and Technology (IET) in IET Radar, Sonar & Navigation
- Vol. 16 (1) , 161-169
Radar backscattering modelling and micro‐motion parameter estimation method for quadcopter
Due to the high-speed rotors and overlapped propellers, it is still a challenge to extract the micro-motion parameters of the quadcopter. In this work, the authors establish a radar backscattering model of the quadcopter based on the flight control theory and radar backscattering characteristics. Then, the improved template matching method and peak grouping method are proposed to capture the periodic information for overlapped propellers on a range-time profile and extract the rotation speeds of rotors. By simulating the nine types of quadcopter movements, the relative error of the rotation speeds is estimated to be lower than 1.4% for each rotor with a signal-to-noise ratio of 15 .- 23 September 2021
- Published by Institution of Engineering and Technology (IET) in IET Radar, Sonar & Navigation
- Vol. 16 (1) , 161-169
Open AccessRadar backscattering modelling and micro‐motion parameter estimation method for quadcopter
Due to the high-speed rotors and overlapped propellers, it is still a challenge to extract the micro-motion parameters of the quadcopter. In this work, the authors establish a radar backscattering model of the quadcopter based on the flight control theory and radar backscattering characteristics. Then, the improved template matching method and peak grouping method are proposed to capture the periodic information for overlapped propellers on a range-time profile and extract the rotation speeds of rotors. By simulating the nine types of quadcopter movements, the relative error of the rotation speeds is estimated to be lower than 1.4% for each rotor with a signal-to-noise ratio of 15 . - 1 May 2019
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 1-3
Human Activity Classification Method Using a Generalized Recurrent Neural Network
Millimeter wave radar offers advantages in scene surveillance, traffic monitoring and health monitoring due to its penetrability and privacy. Abnormal human behaviors could be identified through the radar detection and classification process. In this paper, an abnormal human activity classification method based on micro-Doppler effect is proposed. The singular vector decomposition (SVD) and principle component analysis (PCA) are extracted from simulated radar echo and fed into a Generalized Regression Neural Network (GRNN) for classification.
- 1 May 2019
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 1-3
Human Activity Classification Method Using a Generalized Recurrent Neural Network
Millimeter wave radar offers advantages in scene surveillance, traffic monitoring and health monitoring due to its penetrability and privacy. Abnormal human behaviors could be identified through the radar detection and classification process. In this paper, an abnormal human activity classification method based on micro-Doppler effect is proposed. The singular vector decomposition (SVD) and principle component analysis (PCA) are extracted from simulated radar echo and fed into a Generalized Regression Neural Network (GRNN) for classification.