arXiv subjects

Bing Wei

Publications and source records attributed to Bing Wei.

34 records · Page 2Linked to original sources

arXiv2021

Visual Sensation and Perception Computational Models for Deep Learning: State of the art, Challenges and Prospects

Visual sensation and perception refers to the process of sensing, organizing, identifying, and interpreting visual information in environmental awareness and understanding. Computational models inspired by visual perception have the characteristics of complexity and diversity, as they come from many subjects such as cognition science, information science, and artificial intelligence. In this paper, visual perception computational models oriented deep learning are investigated from the biological visual mechanism and computational vision theory systematically. Then, some points of view about the prospects of the visual perception computational models are presented. Finally, this paper also summarizes the current challenges of visual perception and predicts its future development trends. Through this survey, it will provide a comprehensive reference for research in this direction.

cs.AI↗

arXiv2021

Gallai-Ramsey numbers for graphs with chromatic number three

Given a graph $H$ and an integer $k\ge1$, the Gallai-Ramsey number $GR_k(H)$ is defined to be the minimum integer $n$ such that every $k$-edge coloring of the complete graph $K_n$ contains either a rainbow (all different colored) triangle or a monochromatic copy of $H$. In this paper, we study Gallai-Ramsey numbers for graphs with chromatic number three such as $\widehat{K}_m$ for $m\ge2$, where $\widehat{K}_m$ is a kipas with $m+1$ vertices obtained from the join of $K_1$ and $P_m$, and a class of graphs with five vertices, denoted by $\mathscr{H}$. We first study the general lower bound of such graphs and propose a conjecture for the exact value of $GR_k(\widehat{K}_m)$. Then we give a unified proof to determine the Gallai-Ramsey numbers for many graphs in $\mathscr{H}$ and obtain the exact value of $GR_k(\widehat{K}_4)$ for $k\ge1$. Our outcomes not only indicate that the conjecture on $GR_k(\widehat{K}_m)$ is true for $m\le4$, but also imply several results on $GR_k(H)$ for some $H\in \mathscr{H}$ which are proved individually in different papers.

math.CO↗

arXiv2021

Enhanced Gradient for Differentiable Architecture Search

In recent years, neural architecture search (NAS) methods have been proposed for the automatic generation of task-oriented network architecture in image classification. However, the architectures obtained by existing NAS approaches are optimized only for classification performance and do not adapt to devices with limited computational resources. To address this challenge, we propose a neural network architecture search algorithm aiming to simultaneously improve network performance (e.g., classification accuracy) and reduce network complexity. The proposed framework automatically builds the network architecture at two stages: block-level search and network-level search. At the stage of block-level search, a relaxation method based on the gradient is proposed, using an enhanced gradient to design high-performance and low-complexity blocks. At the stage of network-level search, we apply an evolutionary multi-objective algorithm to complete the automatic design from blocks to the target network. The experiment results demonstrate that our method outperforms all evaluated hand-crafted networks in image classification, with an error rate of on CIFAR10 and an error rate of on CIFAR100, both at network parameter size less than one megabit. Moreover, compared with other neural architecture search methods, our method offers a tremendous reduction in designed network architecture parameters.

cs.CV↗

arXiv2021

MLMA-Net: multi-level multi-attentional learning for multi-label object detection in textile defect images

For the sake of recognizing and classifying textile defects, deep learning-based methods have been proposed and achieved remarkable success in single-label textile images. However, detecting multi-label defects in a textile image remains challenging due to the coexistence of multiple defects and small-size defects. To address these challenges, a multi-level, multi-attentional deep learning network (MLMA-Net) is proposed and built to 1) increase the feature representation ability to detect small-size defects; 2) generate a discriminative representation that maximizes the capability of attending the defect status, which leverages higher-resolution feature maps for multiple defects. Moreover, a multi-label object detection dataset (DHU-ML1000) in textile defect images is built to verify the performance of the proposed model. The results demonstrate that the network extracts more distinctive features and has better performance than the state-of-the-art approaches on the real-world industrial dataset.

cs.CV↗

arXiv2020

Optimizing Deep Neural Networks through Neuroevolution with Stochastic Gradient Descent

Deep neural networks (DNNs) have achieved remarkable success in computer vision; however, training DNNs for satisfactory performance remains challenging and suffers from sensitivity to empirical selections of an optimization algorithm for training. Stochastic gradient descent (SGD) is dominant in training a DNN by adjusting neural network weights to minimize the DNNs loss function. As an alternative approach, neuroevolution is more in line with an evolutionary process and provides some key capabilities that are often unavailable in SGD, such as the heuristic black-box search strategy based on individual collaboration in neuroevolution. This paper proposes a novel approach that combines the merits of both neuroevolution and SGD, enabling evolutionary search, parallel exploration, and an effective probe for optimal DNNs. A hierarchical cluster-based suppression algorithm is also developed to overcome similar weight updates among individuals for improving population diversity. We implement the proposed approach in four representative DNNs based on four publicly-available datasets. Experiment results demonstrate that the four DNNs optimized by the proposed approach all outperform corresponding ones optimized by only SGD on all datasets. The performance of DNNs optimized by the proposed approach also outperforms state-of-the-art deep networks. This work also presents a meaningful attempt for pursuing artificial general intelligence.

cs.CV↗

arXiv2020

Gallai-Ramsey numbers for graphs with five vertices of chromatic number four

Given a graph $H$ and an integer $k\ge1$, the Gallai-Ramsey number $GR_k(H)$ is defined to be the minimum integer $n$ such that every $k$-edge coloring of $K_n$ contains either a rainbow (all different colored) triangle or a monochromatic copy of $H$. In this paper, we determine the Gallai-Ramsey numbers for connected graphs with five vertices of chromatic number four.

math.CO↗

arXiv2019

A note on Gallai-Ramsey number of even wheels

A Gallai coloring of a complete graph is an edge-coloring such that no triangle has all its edges colored differently. A Gallai $k$-coloring is a Gallai coloring that uses $k$ colors. Given a graph $H$ and an integer $k\geq 1$, the Gallai-Ramsey number $GR_k(H)$ of $H$ is the least positive integer $N$ such that every Gallai $k$-coloring of the complete graph $K_N$ contains a monochromatic copy of $H$. Let $W_{2n} $ denote an even wheel on $2n+1\ge5$ vertices. In this note, we study Gallai-Ramsey number of $W_{2n}$ and completely determine the exact value of $GR_k(W_4)$ for all $k\ge2$.

math.CO↗

arXiv2018

On the largest $A_α$-spectral radius of cacti

Let $A(G)$ be the adjacent matrix and $D(G)$ the diagonal matrix of the degrees of a graph $G$, respectively. For $0 \leq α\leq 1$, the $A_α$ matrix $A_α(G) = αD(G) +(1-α)A(G)$ is given by Nikiforov. Clearly, $A_{0} (G)$ is the adjacent matrix and $2 A_{\frac{1}{2}}$ is the signless Laplacian matrix. A cactus is a connected graph such that any two of its cycles have at most one common vertex, that is an extension of the tree. The $A_α$-spectral radius of a cactus graph with $n$ vertices and $k$ cycles is explored. The outcomes obtained in this paper can imply previous bounds of Nikiforov et al., and Lovász and Pelikán. In addition, the corresponding extremal graphs are determined. Furthermore, we proposed all eigenvalues of such extremal cacti. Our results extended and enriched previous known results.

math.CO↗

arXiv2017

Generalized Multiplicative Indices of Polycyclic Aromatic Hydrocarbons and Benzeniod Systems

Many types of topological indices such as degree-based topological indices, distance-based topological indices and counting related topological indices are explored during past recent years. Among degree based topological indices, Zagreb indices are the oldest one and studied well. In the paper, we define a generalized multiplicative version of these indices and compute exact formulas for Polycyclic Aromatic Hydrocarbons and Jagged-Rectangle Benzenoid Systems.

math.CO↗

arXiv2016

The ratio of domination and independent domination numbers on trees

Let $γ(G)$ and $i(G)$ be the domination number and the independent domination number of $G$, respectively. In 1977, Hedetniemi and Mitchell began with the comparison of of $i(G)$ and $γ(G)$ and recently Rad and Volkmann posted a conjecture that $i(G)/ γ(G) \leq Δ(G)/2$, where $Δ(G)$ is the maximum degree of $G$. In this work, we prove the conjecture for trees and provide the graph achieved the sharp bound.

math.CO↗

arXiv2016

Multiplicative Zagreb indices of cacti

Let $\prod(G)$ be Multiplicative Zagreb index of a graph G. A connected graph is a cactus graph if and only if any two of its cycles have at most one vertex in common, which has been the interest of researchers in the filed of material chemistry and graph theory. In this paper, we use a new tool to the obtain upper and lower bounds of $\prod(G)$ for all cactus graphs and characterize the corresponding extremal graphs.

math.CO↗

arXiv2016

A note on the independent domination number versus the domination number in bipartite graphs

Let $γ(G)$ and $i(G)$ be the domination number and the independent domination number of $G$, respectively. Rad and Volkmann posted a conjecture that $i(G)/ γ(G) \leq Δ(G)/2$ for any graph $G$, where $Δ(G)$ is its maximum degree (See \cite{5}: N.J. Rad, L. Volkmann, A note on the independent domination number in graphs. Discrete Appl. Math. 161(2013) 3087--3089). In this work, we verify the conjecture for bipartite graphs. Several graph classes attaining the extremal bound and graphs containing odd cycles with the ratio larger than $Δ(G)/2$ are provided as well.

math.CO↗

arXiv2016

Total domination polynomials of graphs

Given a graph $G$, a total dominating set $D_t$ is a vertex set that every vertex of $G$ is adjacent to some vertices of $D_t$ and let $d_t(G,i)$ be the number of all total dominating sets with size $i$. The total domination polynomial, defined as $D_t(G,x)=\sum\limits_{i=1}^{| V(G)|} d_t(G,i)x^i$, recently has been one of the considerable extended research in the field of domination theory. In this paper, we obtain the vertex-reduction and edge-reduction formulas of total domination polynomials. As consequences, we give the total domination polynomials for paths and cycles. Additionally, we determine the sharp upper bounds of total domination polynomials for trees and characterize the corresponding graphs attaining such bounds. Finally, we use the reduction-formulas to investigate the relations between vertex sets and total domination polynomials in $G$.

math.CO↗

arXiv2016

Cacti with Extremal PI Index

The vertex PI index $PI(G) = \sum_{xy \in E(G)} [n_{xy}(x) + n_{xy}(y)]$ is a distance-based molecular structure descriptor, where $n_{xy}(x)$ denotes the number of vertices which are closer to the vertex $x$ than to the vertex $y$ and which has been the considerable research in computational chemistry dating back to Harold Wiener in 1947. A connected graph is a cactus if any two of its cycles have at most one common vertex. In this paper, we completely determine the extremal graphs with the largest and smallest vertex PI indices among all the cacti. As a consequence, we obtain the sharp bounds with corresponding extremal cacti and extend a known result.

math.CO↗

arXiv2016

Multiplicative Zagreb indices of k-trees

Let G be a graph with vertex set V (G) and edge set E(G). The first generalized multiplicative Zagreb index of G is M_1(G) and the second multiplicative Zagreb index is M_2(G). The multiplicative Zagreb indices have been the focus of considerable research in computational chemistry dating back to Narumi and Katayama in 1980s. In this paper, we generalize Narumi-Katayama index and the first multiplicative index, where c = 1, 2, respectively, and extend the results of Gutman to the generalized tree, the k-tree, where the results of Gutman are for k = 1. Additionally, we characterize the extremal graphs and determine the exact bounds of these indices of k-trees, which attain the lower and upper bounds.

math.CO↗

arXiv2013

On the eccentric distance sum of unicyclic graphs with a given matching number

Let $G = (V_G,E_G)$ be a simple connected graph. The eccentric distance sum of $G$ is defined as $ξ^d(G)=\sum_{v \in V_G}\,\varepsilon_G(v)D_G(v),$ where $\varepsilon_G(v)$ is the eccentricity of the vertex $v$ and $D_G(v)=\sum_{u \in V_G}\,d(u,v)$ is the sum of all distances from the vertex $v$. In this paper, we characterize $n$-vertex unicyclic graphs with given matching number having the minimal and second minimal eccentric distance sums, respectively.

math.CO↗