Table of Content

  

20 April 2022
Volume 57 Issue 4

Multilabel feature selection algorithm based on improved ReliefF

SUN Lin, CHEN Yu-sheng, XU Jiu-cheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(4):  1-11.  doi:10.6040/j.issn.1671-9352.7.2021.167

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Aiming at the problems that the traditional ReliefF algorithm can only process single-label data, and its improved algorithms do not make full use of the correlation between samples, a multilabel feature selection algorithm based on improved ReliefF is proposed. First, the cosine similarity function is used to measure the similarity between features of samples, the Jaccard distance is employed to measure the correlation of labels among labels of samples, and then the similarity function among samples is defined to measure the similarity relationship between samples in the entire sample space. Second, the discrimination formula of the homogeneous or heterogeneous samples is defined to judge the nearest homogeneous or heterogeneous samples for the random samples. Finally, a new iterative formula of feature weights is proposed to improve the ReliefF algorithm, and then a multi-label feature selection algorithm is designed. The five different evaluation metrics including Average Precision, Coverage, One-error,Ranking Loss and Hamming Loss are employed to analyze and test the classification performance of the proposed algorithm on seven public multilabel datasets. The experimental results show that the proposed algorithm is effective.

Multi-metric learning algorithm based on constraint hierarchical weighting

HAN Lu, GUO Xin-yao, WEI Wei, LIANG Ji-ye

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(4):  12-20.  doi:10.6040/j.issn.1671-9352.7.2021.149

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In order to solve the problem of insufficient local metric fitting ability caused by inaccurate sample partitioning when the classic multi-metric learning algorithm learns metrics from sample partitions obtained in advance, based on the idea of constraint stratification weighting, this paper proposes to assign metrics to constraints layer by layer and makes the measurement as far as possible to meet the optimization model of all constraints, while adding regular terms to make the constraints corresponding to different metrics should be as different as possible. Since different constraints formed by a single sample may correspond to different local metrics, compared with traditional multi-metric learning methods, the proposed algorithm can obtain finer local metrics and is more flexible, making the metric's fitting ability stronger. Experimental results show that the proposed algorithm has obvious advantages compared with representative single-metric learning algorithms and multi-metric learning algorithms on real data sets.

Multi-label classification for medical text based on ALBERT-TextCNN model

ZHENG Cheng-yu, WANG Xin, WANG Ting, DENG Ya-ping, YIN Tian-tian

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(4):  21-29.  doi:10.6040/j.issn.1671-9352.7.2021.083

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Aiming at the problem of existing static word vector representation methods such as Word2Vec and Glove cannot solve the problem of complete text semantics, combined with the ALBERT pre-trained language model and the TextCNN convolutional neural network, a deep neural network model for multi-label medical text classification named ALBERT-TextCNN is proposed. The model use the ALBERT pre-training language model for dynamic word vector representation to obtain a more efficient text vector representation through its internal multi-layer bidirectional Transfomer structure, and introduce the TextCNN convolutional neural network model to construct a multi-label classifier for training to extract semantic information features at different levels of abstraction. The performance of the algorithm is tested on the Chinese health question data set. The experimental results show that the overall F1 value of the model reaches 90.5%, which can effectively improve the multi-label classification effect of the medical text.

Closure elements and closure sets in topological systems and their related properties

GAO Ya, WU Hong-bo

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(4):  30-36.  doi:10.6040/j.issn.1671-9352.0.2021.340

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Because of the lack of closed elements in topological systems, the research on the theory and properties of closed sets in topological systems is restricted to a certain extent. In this paper, the dual topological system, the topological system determined by closed elements, is established by using the coframe and the point set, and its basic properties are discussed. Secondly, the concept of closure element of point set part is given by using closed element, and the properties of closure element are discussed. Thirdly, the definition of condensation point and derived set in topological system is given by using closure element, and the properties of derived set and closure set are discussed. Finally, the relationship between closure element and closure set is discussed.

Intuitionistic similarity based on triangular norms and its application

LI Xing-yu, DUAN Jing-yao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(4):  37-47.  doi:10.6040/j.issn.1671-9352.0.2021.335

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In order to incorporate the similarity analysis of intuitionistic fuzzy sets into the framework of logical reasoning, the two similarities of intuitionistic fuzzy sets based on triangular norm and implication operator are constructed in different ways and proved that they satisfy the four axioms of similarity. As an application, firstly, a medical diagnosis problem about typhoid fever is solved by using the constructed similarity as a measurement, and the result consistent with the intuition by using data analysis. Secondly, the robustness of logical connectives, intuitionistic triangular norm and intuitionistic implication, are analyzed by using the constructed similarity as the disturbance parameter. Furthermore, the robustness of the full implication inference method and the compositional rule of inference method of the intuitionistic fuzzy modus ponens problem are analyzed. The results show that when the input disturbance is very small, the output result changes very little. Both inference methods have good robustness.

Vertex-distinguishing general-total coloring of K4,4,p

MA Jing-jing, CHEN Xiang-en

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(4):  48-54.  doi:10.6040/j.issn.1671-9352.0.2020.029

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The optimal vertex-distinguishing general total coloring of complete tripartite graph K4,4,p is discussed by using of the methods of distributing the color sets in advance, constructing the colorings, contradiction and combinatorial analysis. The vertex-distinguishing general total chromatic number of K4,4,p is determined.

Shadow wave solution for the relativistic Chaplygin Euler equations

JIA Yi-fei, GUO Li-hui, BAI Yin-song

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(4):  55-65.  doi:10.6040/j.issn.1671-9352.0.2021.228

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The main purpose of this article is to construct the shadow wave solution of the relativistic Chaplygin Euler equations. To ensure the weak uniqueness of the shadow wave solution, the over-compressive entropy condition is used as the admissibility criteria. Finally, in the sense of Schwartz generalized function, it is proved that the over-compressive shadow wave solution converges to the delta shock wave solution.

Global attractor of Kirchhoff-type beam equation with memory

ZHANG Ying, LIU Qiang-qiang, MA Qiao-zhen

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(4):  66-75.  doi:10.6040/j.issn.1671-9352.0.2021.248

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By means of energy estimation and contraction function, the long time dynamic behavior of Kirchhoff beam equations with linear memory and nonlinear damping is studied, and the existence of global attractor in weak topological space is obtained, which partially extends the existing results.

Existence of mild solutions for a class of Riemann-Liouville fractional evolution inclusions

REN Qian, YANG He

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(4):  76-84.  doi:10.6040/j.issn.1671-9352.0.2021.414

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By utilizing the multivalued fixed point theorem and the theory of operator semigroup, the existence of mild solutions for the nonlocal problem of a class of Riemann-Liouville fractional semilinear evolution inclusions with noncompact semigroups is investigated. An example is given to illustrate the application of abstract conclusions.

Uniqueness of solutions for initial value problems of implicit fractional order fuzzy differential equations

XI Yan-li, CHEN Peng-yu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(4):  85-90.  doi:10.6040/j.issn.1671-9352.0.2021.325

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By using the principle of power compression mapping, this paper obtains the uniqueness of solution to the initial value problems of implicit fractional fuzzy differential equations{^CD^α,p_a⁺u(t)=f(t,u(t), ^CD^α,p_a⁺u(t)),u(a)=u₀,where 0<a<t≤b, α∈(0,1), p>0 is a fixed real number, and CDα,p_a⁺ is the fuzzy Caputo-Katugampola fractional generalized Hukuhara derivative, f:［a,b］×E×E→E is a fuzzy function. E is the fuzzy space.

Online monitoring of parameter changes in linear regression model with long memory errors

NIANG Mao-cuo, CHEN Zhan-shou, CHENG Shou-yao, WANG Xiao-yang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(4):  91-99.  doi:10.6040/j.issn.1671-9352.0.2021.525

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Based on the modified moving-sum-statistic(mMOSUM)method, this paper studies the online monitoring change points of the regression coefficients of linear regression model with long-memory time series errors. Under the null hypothesis, the limit distribution of the mMOSUM monitoring statistics is obtained by modifying the boundary function, and the consistency of the method is proved under the alternative hypothesis. The results of numerical simulation show that when linear regression model has long memory errors, the mMOSUM method is still effective except for the case where the long memory parameter value is larger. And the location of change point moves further back, the effect of modified method on the increase of the power and the reduction of the run length is more obvious. Finally, the feasibility of this method is demonstrated by an empirical analysis of a set of macroeconomic data for the United States.

Pricing and simulation of lookback options under the mixed sub-fractional jump-diffusion model

AN Xiang, GUO Jing-jun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(4):  100-110.  doi:10.6040/j.issn.1671-9352.0.2021.622

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The pricing model of European lookback options with transaction costs is established based on the mixed sub-fractional Brownian motion and Poisson process. Firstly, the nonlinear partial differential equation satisfied by the price of the option is obtained using the Delta hedging principle, and its numerical solution is obtained by constructing a Crank-Nicolson format. Secondly, the validity of the numerical method is verified, and the effects of transaction costs, volatility and risk-free interest rate on the value of the option are respectively discussed. Finally, the daily closing price of Shanghai Pudong Development Bank is selected for the simulation, and the results show that the simulated price based on the mixed sub-fractional jump-diffusion model is closer to the real value of the stock, and can better reflect the overall stock trend.