#### Table of Content

25 December 2021, Volume 41 Issue 12
Superpixel Merging-Based Hyperspectral Image Classification
XIE Fuding, LI Xu, HUAGN Dan, JIN Cui
2021, 41(12):  3268-3279.  DOI: 10.12341/jssms21388
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Superpixel-level hyperspectral image classification is a representative spec-tral-spatial classification method. Compared with the pixel-wise classification method, it has obvious advantages in classification accuracy and efficiency. However, the main disadvantage of superpixel-level classification algorithms is that the classification results depend heavily on the segmentation scale of superpixels. Existing literature shows that the optimal segmentation scale of superpixels is usually an experimental result, and it is difficult to be specified in advance. To weaken this dependency, a superpixel-level hyperspectral image classification algorithm based on superpixel merging is proposed in this work. Local modularity function is first used to merge the sparse weighted superpixel graph constructed. By the newly defined mapping, each superpixel is represented as a sample. Then popular KNN method is adopted to classify the merged image at the superpixel level. The superpixel merging enhances the role of spatial information in classification, effectively weakens the dependence of classification results on the segmentation scale of superpixels, and improves the classification accuracy. To evaluate the effectiveness of the method, the proposed algorithm is compared with some competitive hyperspectral image classification methods on four publicly real hyperspectral datasets. The experimental and comparative results show that the proposed method not only effectively reduces the influence of superpixel segmentation scale on the classification results, but also has obvious advantages both in classification accuracy and computational efficiency.
Analysis of Zero-Hopf Bifurcation in High Dimensional Polynomial Differential Systems with Algorithm Derivation
HUANG Bo, HAN Deren
2021, 41(12):  3280-3298.  DOI: 10.12341/jssms21399
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This paper deals with the Zero-Hopf bifurcation in high dimensional polynomial differential systems. First, we reduce the problem of bifurcation analysis to an algebraic problem, and we give a method for determining the bifurcation set of the Zero-Hopf bifurcation points of differential systems by using symbolic algorithm for solving semi-algebraic systems. Then, based on the second order averaging method, the algorithmic framework of the Zero-Hopf bifurcation analysis of differential systems is derived, and the limit cycle bifurcation problem is studied through specific examples by using the methods of symbolic computation, and some new results are obtained. Finally, we propose several related research problems.
Further Results on the Equivalence of Multivariate Polynomial Matrices
LI Dongmei, GUI Yingying
2021, 41(12):  3299-3310.  DOI: 10.12341/jssms21407
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Multidimensional systems are often described by polynomial matrices, and problems on the equivalence of multidimensional systems in system theory are often transformed into problems on the equivalence of polynomial matrices. In this paper, we mainly study the equivalence of two kinds of multivariate polynomial matrices, and obtain the discriminant conditions for the equivalence of these matrices and their Smith forms, respectively. The conditions are easily verified, and an example is also used to illustrate these in the paper.
A Mechanical Proof of Ramsey's Theorem via Symbolic Computation
LU Jian, ZENG Zhenbing
2021, 41(12):  3311-3323.  DOI: 10.12341/jssms21441
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This paper presented a method of algebraic representation of the Ramsey Theorem and gave an implementation for the mechanical proofs to the theorem for two classic cases, i.e., $R(3,3)=6$ and $R(3,4)=9$ using symbolic computation. A divide-and-conquer method was also suggested for tackling with complicated cases including $R(3,5)=14$ and $R(3,3,3)=17$. Different from the existed computer aided algorithms, the proposed method can generate mechanical proof of Ramsey theorem through polynomial computation.
Sparse Polynomial Interpolation Based on Diversification with High Probability
QI Niuniu, TANG Min, DENG Guoqiang
2021, 41(12):  3324-3341.  DOI: 10.12341/jssms21400
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Interpolation strategies have shown to be very effective in the reconstruction black-box functions, in particular in polynomial algebra, for sparse multivariate polynomials. In addition, sparse multivariate interpolation algorithms with polynomial time complexity have been widely studied and applied. Recently, Huang(2021) presented a sparse polynomial interpolation algorithm based on diversification. The algorithm costs $O(nT \log^2 q + nT\sqrt D\log q)$ bit operations and it is the first one to achieve the complexity of fractional power about $D$, while keeping linear in $n$, $T$ over finite fields $\mathbb{F}_q$. Since Huang's algorithm is probabilistic with correct interpolates $f$ with probability at lest $\frac{3}{4}$, in order to improve the success probabilistic of interpolation, three failure cases of Huang's algorithm are analyzed, and the corresponding modification schemes are given. Based on revised strategies, a high probability sparse interpolation algorithm based on diversified polynomial is designed. Extensive numerical experiments show the effectiveness of the algorithm.
Symbolic Computation of Partial Orders on the Finite Set
ZHANG Shengrong, LI Yongbin, ZI Junwei, Luo Mengyu
2021, 41(12):  3342-3350.  DOI: 10.12341/jssms21437
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Different from the known methods of order theory and topology theory on partial order and $T_0$ topology, this paper presents a method to find all partial orders as well as $T_0$ topologies on the finite set $[n]=\{1,2,\cdots,n\}$ through solving a polynomial set over the finite field $\mathbb{F}_2$, and illustrates the correspondence between zeros of the polynomial set and partial orders as well as $T_0$ topologies by examples. Based on Gr$\ddot{\text{o}}$bner bases theory, a symbolic computation method for computing the number of partial orders and the number of $T_0$ topologies on $[n]$ is obtained. Some examples are given to illustrate our method using Maple.
A Criterion for the Reducibility of a Class of Integer Polynomials over the Field of Rational Numbers
ZHAO Shizhong, FU Hongguang, QIN XiaoLin, LIU Jing, LIU YunHao
2021, 41(12):  3351-3362.  DOI: 10.12341/jssms21438
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For the integer polynomials $\sum_{i=0}^m a_i\,x^i$ of degree $m$, where $a_m=1$, this paper presents a fixed-point iterative algorithm: %and the corresponding fixed point iterative algorithm $$\left\{ \begin{array}{ll} u_1=\tilde{u}_1, & \\ u_2=\tilde{u}_2, & \\ \quad\,\,\,\vdots& \\ u_{m-1}=\tilde{u}_{m-1}, & \\ \displaystyle{u_n=-\Big{(}a_{m-1}+\frac{a_{m-2}}{u_{n-1}}+\frac{a_{m-3}}{u_{n-1}u_{n-2}}+\cdots+\frac{a_{0}}{u_{n-1}u_{n-2}\cdots u_{n-(m-1)}}\Big{)}\,\,(n\geq m).} & %\displaystyle{u_n=-\frac{a_{m-1}}{a_m}-\frac{a_{m-2}}{a_mu_{n-1}}-\frac{a_{m-3}}{a_mu_{n-1}u_{n-2}}-\cdots-\frac{a_{0}}{a_mu_{n-1}u_{n-2}\cdots u_{n-(m-1)}}\,\,(n\geq m).} & \end{array} \right.$$ 1) Obviously, if the iteration has a rational limit value, then the value is a zero of the polynomial, so that the polynomial is reducible over $\mathbb{Q}$. 2) This iteration does not need to choose the initial values: If the polynomial has $m$ rational zeros with different absolute values, then for any $m-1$ non-zero rational initial values $u_i\,(1\leq i\leq m-1)$, the iteration approaches to one of the zeros. Therefore, the polynomial is reducible. 3) Assuming that $\{\zeta_i\,\big{|}\, |\zeta_1|\geq|\zeta_{2}|\geq\cdots\geq|\zeta_m|,\,\zeta_i\in\mathcal{C},\,1\leq i\leq m\}$ are the distinct zeros of the above polynomial, there exist $m$ complex numbers $\{\beta_i\,|\, \beta_i\in\mathcal{C},\,1\leq i\leq m\}$ such that $u_n$ can be expressed in the following form \begin{equation*}u_n=\frac{\beta_1\zeta_1^{n+1}+\beta_2\zeta_2^{n+1}+\cdots+\beta_m\zeta_m^{n+1}}{\beta_1\zeta_1^n+\beta_2\zeta_2^n+\cdots+\beta_m\zeta_m^n}%\,\,(\beta_i\in\mathcal{R}) .\end{equation*} Among the $m$ elements of the vector $\beta$, let $\beta_l$ be the first non-zero element and $\beta_k$ the first non-zero element after it, that is, $\{\beta_i\,|\, \beta_i\in\mathcal{C},\,1\leq i\leq m\}= \{\!\!\underbrace{0,0,\cdots,0}_{\mbox{All are zero.}},\beta_l(\neq0), \underbrace{0,0,\cdots,0}_{\mbox{ All are zero.}},\beta_k(\neq0),\cdots,\beta_m\}.$ In this case, if $|\zeta_l|>|\zeta_k|$, then the iteration converges to $\zeta_l$. Therefore, if $\zeta_l\in\mathcal{Q}$, then the polynomial is reducible.
The Model and Algorithm of Generalized Weighted Robust Principal Component Analysis (GWRPCA)
WANG Xingqu, JIA Shihui, CHI Xiaoni
2021, 41(12):  3363-3373.  DOI: 10.12341/jssms20472
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Based on the weighted robust principal component analysis (WRPCA) model and the generalized robust principal component analysis (GRPCA) model, so as to build the generalized weighted robust principal component analysis (GWRPCA) model, increase the robustness of the model, and apply the alternating direction algorithm of random sorting to solve the new model. The results of numerical experiments show that when the new model GWRPCA processes images with mixed noise pollution, it can not only effectively separate the low-rank part, the sparse large noise part and the dense small noise part, but also has better image denoising effect. PSNR and ERR values of GWRPCA are also better than those of the WRPCA and GRPCA model in objective standards.
Neutral Passivity Filtering for Uncertain Markovian Jump Systems with Neutral-Retarded Mixed Time-Varying Delays
ZHAO Guowei, ZHUANG Guangming, XIA Jianwei, SUN Wei, CHEN Guoliang
2021, 41(12):  3374-3394.  DOI: 10.12341/jssms20223
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This paper deals with the problems of passivity analysis and passivity-based neutral-retarded mixed delays filter design for neutral Markovian jump systems (NMJSs) with time-varying delays and norm-bounded parametric uncertainties. Firstly, new delay-dependent conditions for the NMJSs are obtained by constructing a mode-dependent Lyapunov functional and introducing some free weight matrices (FWMs). Secondly, new mode-dependent neutral passivity filter is designed to ensure the passivity of the augmented neutral Markovian jump filtering error system via linear matrix inequalities (LMIs). A numerical example and a partial element equivalent circuit (PEEC) are utilized to show the effectiveness of the method.
Interval Solutions of Interval Linear Systems
LI Haohao, XIA Mengxue, JIN Jianghong
2021, 41(12):  3395-3404.  DOI: 10.12341/jssms20542
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The mathematical models of various uncertain systems in engineering and scientific practice can be described by interval systems and interval optimization models. In this paper, we discuss the problem of interval solutions for interval systems. We define several new interval solutions for mixed interval linear systems, including weak interval solutions, strong interval solutions, tolerance interval solution and control interval solution and study their related properties. In particular, the characterizations of weak interval solution, strong interval solution, tolerance interval solution and control interval solution of the interval equations ${\bm A}{\bm x}={\bm b}$ and the interval inequalities ${\bm A}{\bm x}\leq{\bm b}$ are established. These characterizations are similar to the classical Oettli-Prager inequality and Gerlach inequality. At the same time, we give some examples to illustrate the application background and calculation method of interval solutions.
Leverage Quality News to Analyze Quality Risk of Industry Products
LENG Jie, TANG Xijin, YAN Zhihua, PENG Qin
2021, 41(12):  3405-3421.  DOI: 10.12341/jssms20497
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This paper firstly analyzes the main methods of quality risk analysis and product injury analysis in the field of market quality supervision, and then focuses on several industrial goods as the research object and creates risk word set, through the text data of people's livelihood news from China Quality News Net, discusses a method of quality risk analysis of key industrial products based on several word embedding models. By calculating the cosine similarity between specific product and each risk word vectors, the quality risk level of each product and manufacturer under different risk types is approximately obtained. The unqualified items in product quality inspection reports, which are from the State Administration for Market Regulation and the same department in each province or municipality directly under the central government over the years, are taken to validate and supplementary with the results of the experiment. Finally, according to the extent of possible injury, we further carry out quality risk assessment to provide suggestions for consumption tips and quality credit assessment.
Research on Reserve and Distribution Problem of Emergency Medical Supplies
LI Zhenping, ZHANG Yuwei, TIAN Xin, FANG Yong
2021, 41(12):  3422-3445.  DOI: 10.12341/jssms21294
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The optimal medical material reserve and distribution strategy can effectively reduce the loss caused by the major public health emergency. Based on the suddenness of major public health events and the stochastic demand for medical supplies after an event occurred, the reserve and distribution strategy of medical supplies for major public health emergencies is investigated. The reserve quantity of medical supplies is determined before major public health emergencies occur; and the optimal distribution plans are determined after the event occurs. A two-stage stochastic programming model is formulated to minimized the sum of reserve costs (including purchasing cost and inventory holding cost) of medical material before the public health emergencies occurred and the expected loss after the occurrence of the event (including transportation expenses and shortage loss). The model is solved by the Gurobi solver. By conducting simulations on different scale examples and comparing with the classical expected value model, the effectiveness of stochastic programming method is verified. By conducting sensitivity analysis on parameters of unit reserve cost and unit shortage cost respectively, the optimal reserve strategies of different type of medical supplies are proposed. The simulation experiment is carried out based on the real data of a city and the medical protective clothing as an example, by comparing the optimal reserve and distribution scheme obtained by two-stage stochastic programming method and its actual reserve quantity determined by the requirements of provincial health emergency basic material reserve list, we find that the sum of reserve cost and the expected total loss of our optimal solution will reduce by 34%. The satisfaction rate for the demand under the serious scenario will increase from 5.26% to 75.43%, and the sum of reserve cost and the actual loss will reduce by 35.8%. The medical supplies reserve and emergency distribution scheme determined by our method can greatly reduce the sum of reserve cost and the expected total loss, improve the expected demand satisfaction rate after major public health emergencies, and improve the emergency rescue ability and rapid response level.
PM2.5 Concentration Prediction Based on Time Series Decomposition and Neural Network—Take Shenyang as an Example
JIANG Hongxun, YAN Chaochao, ZHANG Lifeng
2021, 41(12):  3446-3460.  DOI: 10.12341/jssms20510
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The formation and diffusion of PM2.5 is affected by both human production and seasonal climate conditions. The variation of PM2.5 concentration has the nonlinear characteristics of regular and random interaction, which makes the traditional prediction method difficult. In this paper, a deep learning prediction model WD-LSTM based on wavelet decomposition is proposed firstly, then EMD-LSTM based on EMD-LSTM is proposed for the limitation of wavelet decomposition that is not adaptive. Empirical mode decomposition is carried out on PM2.5 concentration time series data to obtain its subsequences in different time period scales, and then LSTM is used to predict each subsequence calculation. In this paper, 7316 hourly data of 11 air quality monitoring stations in Shenyang, Liaoning Province from January 2017 to November 2017 are collected, and the WD-LSTM, EMD-LSTM proposed in this paper are compared with LSTM, Xgboost, etc. The results show that WD-LSTM and EMD-LSTM have higher prediction accuracy in general, and show stronger generalization ability in the comparison of sub stations and sub time scales, and EMD-LSTM has better prediction accuracy than other models in the case of high pollution.
Forest Fires Emergency Resource Scheduling Considering Rescue Priority Under Resource Constraints
WU Peng, WANG Lubing, CHU Chengbin
2021, 41(12):  3461-3477.  DOI: 10.12341/jssms21225
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Implementing fast and efficient forest firefighting and rescue has become a hot issue. This paper studies how to minimize the loss of resources caused by forest fires under resource constraints. According to the characteristics of forest firefighting, this paper divides the firefighting sequence by the severity of different fire spots and the spreading speed. On this basis, a mixed integer linear programming model for routing optimization of firefighting and rescue vehicles is established with the objective of minimizing the total firefighting time. To solve the scheduling problem of forest firefighting and rescue under resource constraints, an improved artificial bee colony algorithm based on real number encoding is proposed. Specifically, we design a heuristic method for population initialization, propose a uniform decoding method to improve the decoding quality, and design an efficient crossover operator to improve the optimization search ability of the employer bee and the follower bee, so as to avoid the algorithm falling into local optimum. Finally, the algorithm is tested on a benchmark instance and a large number of randomly generated instance to demonstrate its effectiveness and efficiency.
An Alternate Tree Method Based on Binomial and Trinomial Tree for Option Pricing
GONG Wenxiu, XU Zuoliang
2021, 41(12):  3478-3499.  DOI: 10.12341/jssms19395
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This article aims to propose a simple alternate tree discrete-time model for valuing options. Based on the problems and characteristics of traditional binomial tree and trinomial tree pricing models, this article combines the traditional binomial tree and the trinomial tree to construct a new alternate option pricing model, and discusses the convergence of the model. By using this model, the prices of European option and American option are numerically calculated respectively, and the empirical analysis is carried out through SSE 50ETF data. The numerical results show that the proposed tree pricing method is effective for European options, American options pricing and market data, and the convergence speed and computation accuracy are improved compared with the binomial tree and the trinomial tree method.
Technology Accumulation in High-Tech Industries: Mechanism, Performance and Problems
YU Liping
2021, 41(12):  3500-3516.  DOI: 10.12341/jssms20532
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It is of great significance to study the mechanism of technology accumulation in China's high-tech industry from the industrial perspective, and to evaluate its performance and identify potential problems. This paper establishes a research framework on the basis of theoretical analysis, and comprehensively adopts Panel data model, Panel threshold regression model and Bayesian vector autoregressive model to conduct research. The results show:The positive mechanism of technology accumulation for innovation is greater than the negative mechanism, and the performance of technology accumulation is generally good; China's high-tech industry has entered the mature period of technology accumulation, and the elasticity of its contribution to innovation has gradually decreased; As the level of innovation increases, the elasticity of the contribution of technology accumulation to innovation achievements is greater; With the increase of R&D expenditure, the elasticity of the contribution of technology accumulation to innovation achievements is lower; The interaction effect between technology accumulation, R&D expenditure and innovation results is good. Finally, it is proposed that we should pay attention to the accumulation of revolutionary new technologies and encourage enterprises with strong innovation capabilities to carry out technology accumulation.
Neutral Interval Cross-Efficiency Model by Considering the Random Distribution
HUANG Yan, YOU Cuiling, HE Xiao
2021, 41(12):  3517-3529.  DOI: 10.12341/jssms19492
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In this paper, under the uncertain environment, the input and output values are expressed by interval numbers, the neutral interval cross efficiency evaluation model is constructed, the interval cross evaluation efficiency matrix of the decisionmaking unit in the best and worst production state is calculated, and the comprehensive interval cross efficiency matrix is obtained by aggregating the two through the average operator. Furthermore, the random factor in the evaluation process is considered, the SN ratio value is used to express the stability of the evaluation results. Based on the stability, the corresponding weights are assigned to the decision-making units, and the comprehensive interval crossover efficiency matrix is aggregated to calculate the interval cross efficiency of each decision-making unit. Finally, an example is given to illustrate the rationality of the method.
Applying Multi-granularity Probabilistic Linguistic TODIM Method for Evaluating Waste Recycling APP
MA Yanfang, ZHAO Yuanyuan, FENG Cuiying, LI Zongmin
2021, 41(12):  3530-3547.  DOI: 10.12341/jssms20413
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With respect to the evaluation of sorting and recycling APP with the multi-granular probabilistic linguistic environment, in which the loss aversion behaviors of the decision maker are considered, a TODIM method based on prospect theory is proposed. Firstly, to deal with the multi-granularity probabilistic evaluation value of each expert in the group decision-making, the new transfer function of multi-granular probabilistic linguistic variables is constructed to unify the decision matrix. Then, an innovative BWM is put forward to derive the attributes' weights. Furthermore, introducing prospect theory under probabilistic linguistic environment, the TODIM decision model with considering the psychological behavior of decision makers is calculated, which can derive the priority of benefit-loss value of each alternative relative to other alternatives about attributes. And the global priority of alternatives is obtained by integrating these value. Finally, taking the evaluation of waste sorting and recycling APP as example, the validity of the proposed method is illustrated. In addition, the sensitivity analysis of standard granularity is conducted, in which the multi-granular probabilistic linguistic function has strong stability. And a comparative analysis with the TOPSIS method based on prospect theory and traditional TODIM method are carried out to verify the superiority of the proposed method.
Spammer Detection Method of Recommendation Based on Double-Layer Under-Sampling Cost Sensitive Learning
Lü Chengshu
2021, 41(12):  3548-3558.  DOI: 10.12341/jssms21072
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Spammer detection is the key to ensure information security in recommendation. The existing methods ignore the adverse effects of cost sensitive features on detection accuracy. A detection method based on double under-sampling and cost sensitive support vector machine is proposed. First, we use double under-sampling technology to balance data sets. The first under-sampling eliminates the noise samples while preserving the useful boundary samples; The second under-sampling compresses the redundant information based on the distribution characteristics and importance of the large class samples. Then, the dynamic function based on class confidence is introduced into the cost-sensitive optimization, and a cost-sensitive support vector machine with different miscalculation costs is established. Finally, we use the model to train the balanced sample set. Experimental results show that the proposed method effectively solves the cost sensitive problem and improves the detection accuracy.