With the gradual enhancement of China's political status, activities connected with government affairs and also various domestic construction measures have increased correspondingly, resulting in the accumulation of a steadily increasing amount of political knowledge. In the face of new activities connected with state affairs that are constantly emerging, the mainstream way to obtain ideological and political information is to browse the political news from the current political web portal, which can enable visitors to gain certain information in a short time. However, because the ideological and political news is mostly text-based, each article basically contains more proper nouns. At the same time, China is traversing the road of socialism with Chinese characteristics, which are different from the national conditions of other countries, political activities are numerous and targeted, and ideological and political knowledge is fragmented, so it is difficult for people to establish a clear structure of knowledge in their minds [1,2,3]. At present, this method is time-consuming and cannot provide a clear and effective understanding of the main links that characterise ideological and political information, and moreover lacks a structured browsing platform.

Mapping of knowledge domain is a semantic relation network that connects nodes with relation lines. It uses the structure of “map” to express various relations in the colourful world, and is intuitive, natural and efficient [4, 5]. Using knowledge mapping to represent the knowledge prevailing in the ideological and political field can effectively incorporate these complicated and numerous aspects of knowledge into a system and display them in a custom-structured presentation format, and thus serve as an improvement over the original mode of showing the inquiry on web pages. In addition, because of the structural characteristics of knowledge mapping itself, it can also make ideological and political knowledge inquiry simple and fast, which improves the efficiency and quality of ideological and political learning.

For specialised courses in colleges and universities, in addition to professional knowledge, the ideological elements implied by professional knowledge are equally important. As a kind of ideological element, ideological and political elements play an important role in subject education [6]. Moreover, the ideological and political construction of curriculum is the focus of the current task involving mainstream curriculum construction, and the ideological and political knowledge elements of specialised curriculum have become an important part of specialised curriculum knowledge system, where the effective extraction of ideological and political elements is of vital importance. Therefore, the mining of knowledge element in the ideological and political field can aggregate scattered knowledge in a scientific and effective way, and can greatly improve the accuracy and efficiency of ideological and political knowledge retrieval. At the same time, if we can further study the knowledge mapping integrated with ideological and political elements and expand ideological and political knowledge from the depth level, it can be used as a reference for the ideological and political construction of Chinese colleges and universities.

The data sources of ideological and political knowledge can be divided according to different characteristics. Some data in the acquisition process are in a structured state and generally have a fixed format, and these data are known as structured data [7]. Others are scattered or having no structure, which can be referred to as the semi-structured and unstructured states, respectively. This kind of data needs to be processed separately. First, the noise and inconsistency in the initial data are eliminated, data from various sources are integrated, and relevant data are extracted and analysed from the preliminary data. Then, according to the data mining form that needs to be adopted, the demand data is transformed, such as segmentation of ideological and political words. After data acquisition, pre-processing is needed to effectively extract knowledge from it. Data pre-processing [8, 9] mainly includes data cleaning, data filtering, data deduplication and integration, etc. Data cleaning is to remove unnecessary information from the extracted data, such as redundant characters and random codes, which, if present, would have a direct adverse impact on the accuracy of knowledge acquisition in the next step. The samples of ideological and political knowledge used in this paper are all structured data, which are relatively simple to adopt. Generally, they can be directly used only by converting or calling into the map according to the corresponding rules.

Ontology is the explicit formal specification of shared conceptualisation [10]. Therefore, ontology can be considered as a model specification for the concept of specific domain entities, and their relationship, characteristics and laws. By summarising the entity concepts, the hierarchical representation of conceptual abstraction knowledge can be obtained, which has advantages in the representation and management of knowledge concepts [11]. Based on the difference of automation degree, methods of ontology construction can be divided into manual construction, semi-automatic construction and automatic construction. The manual construction method is to determine the content of knowledge and the relationship between knowledge by experts where the process can be controlled and the quality can be guaranteed. Semi-automation completes the construction by combining manual operation with machine works; on the other hand, the automation mode is that the content and relationship are completely acquired by the machine. In this paper, the artificial construction method is adopted, and its construction process is shown in Figure 1.

Keywords extraction of knowledge elements is an important direction and trend of research on knowledge mapping [12]. The extraction can be constructed from top-down or bottom-up according to different objects [13, 14]. The top-down method is to define the data schema for the knowledge mapping, that is, to define the ontology, and then start with the top-level conceptual ontology and refine it layer by layer, so as to form a better hierarchical structure of taxonomy. Finally, entities are filled in the defined data schema. Compared with the top-down method, the bottom-up method construction process is exactly opposite to it. First, it starts with entity processing, where the entity is induced and organised, and the class hierarchy and relationships between classes are automatically extracted from the knowledge mapping, so as to form the bottom ontology class, and then gradually abstract upwards to form the top ontology class. Since the accuracy of the ideological and political knowledge selected in this paper is related to the learners’ knowledge reserve and application, which is deterministic or easy-control, it often needs high precision. Therefore, the top-down method is selected for keyword construction, and the process is shown in Figure 2.

LDA model is an unsupervised machine learning technology [15, 16] that can be used to identify potential subject information in a large number of document sets or corpora. When LDA model is used in keyword extraction, it is difficult for common words to become keywords, and the obtained keywords cannot completely and accurately cover the subject information of documents that contributes to the improvement of accuracy in keyword extraction [17].

LDA model is a three-level Bayesian probability model, and its basic assumption is that [18]: Each document is a polynomial distribution about subjects, and each subject is a polynomial distribution about vocabulary. Since LDA contains a Bayesian framework, the subject distribution and word distribution of LDA need to be given by prior knowledge, and this process is random. The overall task of LDA model is to infer the subject distribution of each document and the word distribution in each subject according to M documents and a priori parameters

The number of documents to be generated in a given corpus _{1}, _{2}, … _{m}_{1}, _{2}, … _{k}

Based on experience, we give a priori parameters

We assume that the subject prior distribution corresponding to each document is the Dirichlet distribution, and so its subject distribution _{i}

We assume that the prior distribution of words corresponding to each subject is the Dirichlet distribution, and so its word distribution _{k}

The sample subject distribution of the _{i}_{i}_{i}_{1}, _{i}_{2}, … _{ik}

For the _{i}_{i}_{ij}_{i}_{i}

According to step (6), the subject _{ij}_{k}_{k}_{1}, _{k}_{2} … _{kv}_{ij}

The sample from the previous step _{k}_{ij}

We repeat steps (5) to (8), and finally get all words in all ideological and political documents.

In which Beta is distributed in Dirichlet distribution. According to Beta distribution, Eq. (3) can be derived as shown below:

The specific expression of the Dirichlet distribution is shown in Eq. (4):

From the above steps, learning estimation can be made on the variables: _{ij}_{i}_{k}

The main idea underlying Gibbs sampling is Bayesian estimation, and unknown parameters can be solved through the posterior distribution results of subject distribution and word distribution. For the required target distribution, the conditional probability distribution of each feature dimension of subject distribution and word distribution needs to be obtained [21]. The specific steps are as follows:

According to the above analysis of LDA, the joint distribution of all variables can be given as shown in Eq. (5):
_{mn}_{ij}_{mn}_{ij}_{k}

According to the generation process of LDA subject document, prior parameter

According to the above step, the probability distribution of subject feature _{i}_{i}_{¬i}

The definition of association rule is [22]: hypothesis _{1},_{2} …, _{m}

The support degree (Sup) of association rules in D is the probability that transactions in D contain XY at the same time, as shown in Eq. (8):

If the probability of simultaneous occurrence of X, Y is small, there is little relationship between them; but if probability is high, it means that X, Y are correlated. Confidence (Con) is that the transaction in D has contained

If the confidence is 100%, it means that when Y appears, X must also appear; then X, Y can be deduced together, and otherwise, X, Y is irrelevant. When the above indicators are used to measure association rules, if the thresholds of minimum support and minimum confidence are satisfied, a strong association rule can be inferred. Among them, the two thresholds are artificially set according to specific applications.

Common methods of knowledge element extraction include the co-occurrence-based and semantic-based methods [23]. The former means that the potential relationship between entities is obtained by analysing the co-occurrence relationship between entities, which is simple and easy to calculate. Semantic-based method solves the disadvantage of ignoring semantics based on the co-occurrence method, where the relationship between entities is determined by semantic predicates. But it needs more human participation. On the one hand, both of these two methods focus on finding the hidden relationship between various elements of knowledge, without acquiring new hidden knowledge entities. On the other hand, the knowledge discovered exclusively by the co-occurrence method is too simple, and it doesn’t pay attention to the co-occurrence between different types of words.

Therefore, a method of combining LDA model with Apriori association rules is proposed to extract knowledge elements. Since LDA subject model is a method of text clustering, the same type of subject words are clustered under the same subject by Gibbs sampling iteration, so as to obtain different types of subject words, the purpose of this exercise being to find candidate hidden knowledge entities. In order to further screen out accurate tacit knowledge entities from candidate tacit knowledge entities, first, a statistical matrix of co-occurrence frequency is constructed for subject words under different subjects, that is, different types of words by the proposed statistical method of co-occurrence frequency. Since there are more than two subjects, a three-dimensional matrix is constructed, which is different from the co-occurrence matrix. The latter is the co-occurrence statistics of words of the same category, and solves the similarity problem between words. Finally, in order to verify the correlation between words, Apriori algorithm is used to analyse the correlation of knowledge elements.

By setting keywords such as ‘data structure’ and ‘ideological and political education’, 200 related documents integrating data structure and ideological and political education were crawled from Baidu Academic Knowledge Network and other academic platforms as the main source of data. In addition, the ideological attributes hidden in the knowledge points of professional courses were discovered, and the method of associating knowledge that was employed in this paper was adopted to realise the knowledge mining of professional courses in colleges with the attribute of connecting thoughts.

Aiming at the ideological and political education of professional courses in colleges, this paper mainly studies the ideological and political knowledge elements of courses in a major. Adopting the subject model is equivalent to clustering the contents of the documents, and through subject clustering, we can obtain different subjects such as the curriculum subject and the ideological and political subject of each curriculum document, where various elements of useful knowledge can be better separated from the text data. However, in LDA model, all words in corpus are regarded as word bags without context, and only the probability distribution of words–documents–subjects is obtained, which ignores the semantic information of the words themselves and that between words in documents [24]. Therefore, after mining the subject words, in order to find the related subject words under different subjects more accurately, analysis of association rule is needed, and in the calculation of support and confidence, the frequency of common occurrence of subject words under different subjects is needed. However, because the subject words obtained under different subjects are different after subject classification, the algorithm of association rule cannot be directly used to count the frequency of co-occurrence of subject words.

According to the above model and its extraction rules, the specific algorithm flow is as follows:

According to LDA model, the pre-processed literature data are clustered into

Define a two-dimensional array (subject_word) for subject words [

Establish (

The values of the first row and the first column of the matrix are, respectively, two different subjects, that are

Obtain (

Set the distance between two subject words in the document, that is, the window size,

Traverse (subject_word)[i] and (subject_word)[

Obtain the frequency of the co-occurrence of pairwise subject words under different subjects through the matrix.

Substitute the above results into the formulas of support and confidence, which are shown in Eqs (10) and (11):

Among them, _{ij}, w_{pq}_{ij}_{pq}_{ij}_{pq}_{ij}_{pq}_{ij}_{pq}

First, set the window size, which determines the number of related keywords. The window sizes

In the three-dimensional matrix _{ij}_{i}_{i}_{drc}_{ij}_{pq}_{drc}

Three-dimensional matrix of Keywords

X | Y | ||||||
---|---|---|---|---|---|---|---|

Queue | Sort | Recursion | Traverse | Binary tree | Tree | Linear table | |

Seeking truth | 0 | 0 | 0 | 10 | 0 | 0 | 3 |

Innovate | 0 | 0 | 7 | 0 | 0 | 0 | 0 |

Teaching | 2 | 0 | 0 | 0 | 0 | 8 | 5 |

Diligent | 0 | 0 | 0 | 0 | 0 | 13 | 26 |

Course | 17 | 0 | 1 | 0 | 20 | 0 | 20 |

Craftsman | 14 | 32 | 9 | 28 | 2 | 11 | 1 |

Order | 42 | 0 | 16 | 16 | 0 | 0 | 0 |

From Table 1, it can be seen that if the co-occurrence frequency of ‘queue’ and ‘order’ is higher, then ‘queue’ and the thought attribute ‘order’ are closely related. Next, the association is further confirmed by association rules, and the co-occurrence frequency among subject words obtained by statistics is used as the input of association rule analysis.

Set the minimum support to 0.03 and the minimum confidence to 0.27. The association rule obtained by the algorithm represents the association between two subject words under different subjects. Calculate the support and confidence of the co-occurrence frequency matrix obtained in the previous step to screen the rules, and judge according to the threshold value to obtain association rules, as shown in Table 2.

Association analysis of keyword

Association rule | Support degree | Confidence level |
---|---|---|

Queue-Diligence | 0.2180 | 0.1992 |

Queue-Craftsman | 0.3556 | 0.2300 |

Queue-Ordered | 0.1212 | 0.8273 |

From Table 2, it can be seen that the confidences of the ‘Queue-Diligence’ and ‘Queue-Artisan’ rules do not satisfy the threshold setting, but are greater than the support threshold, and so these are related but not strong association rules. Finally, through the threshold screening of support and confidence, 31 association rules are obtained, that is, 31 thought attributes can be obtained.

Since the discovery of ideological and political knowledge elements is unknown and uncertain, it is not possible to make an evaluation and come to a confirmatory conclusion as to whether the obtained knowledge is correct or wrong; also, the knowledge elements expressed visually and explicitly have not yet been certified, and it is thus difficult to verify the validity and correctness of the results of knowledge element mining. Reproduction of known classic examples is a common verification method for knowledge element; however, ideological and political knowledge elements, as new knowledge that has not been acquired by curriculum, cannot be verified by appropriate examples [25]. Therefore, the methods of literature verification and expert evaluation of ideological and political work are used to verify the excavated knowledge elements.

Based on the method of literature verification, the results were compared for 200 literature elements, where 67 out of the 72 pairs of knowledge elements related to the data structure course and humanistic literacy obtained in the final experiment are correct; that is, the accuracy of the verification can reach 93.1%. Ideological and political experts have been involved as researchers in this field for many years, or have been employed as front-line teachers in colleges and universities. The results of literature verification are fed back to 10 professional teachers, and the results are generally good. However, owing to the diversity of ideological attributes, each teacher has a different understanding of the ideological attributes of knowledge elements.

Ideological and political knowledge, as an important part of college students’ study in school, is applied to the construction of professional curriculum knowledge in colleges. By mining and extracting the elements of ideological and political knowledge, the inquiry of ideological and political knowledge can become simple and fast. In this paper, 200 cases of ideological and political knowledge obtained from website crawling and literature research are taken as sample data. Aiming at the deficiency of deep knowledge extraction in ideological and political teaching, a mining method of ideological and political knowledge elements is constructed based on LDA model and Apriori algorithm. First, different subjects are obtained by clustering data by LDA model, then the co-occurrence frequency of keywords under different subjects is counted to build a three-dimensional matrix, and finally the three-dimensional matrix is taken as the input of Apriori algorithm, where the ideological and political knowledge elements can be obtained by setting a threshold to judge the validity of association rules. The results show that the ideological and political knowledge elements extracted by this method can achieve an accuracy rate of 93.1%.

#### Three-dimensional matrix of Keywords

X | Y | ||||||
---|---|---|---|---|---|---|---|

Queue | Sort | Recursion | Traverse | Binary tree | Tree | Linear table | |

Seeking truth | 0 | 0 | 0 | 10 | 0 | 0 | 3 |

Innovate | 0 | 0 | 7 | 0 | 0 | 0 | 0 |

Teaching | 2 | 0 | 0 | 0 | 0 | 8 | 5 |

Diligent | 0 | 0 | 0 | 0 | 0 | 13 | 26 |

Course | 17 | 0 | 1 | 0 | 20 | 0 | 20 |

Craftsman | 14 | 32 | 9 | 28 | 2 | 11 | 1 |

Order | 42 | 0 | 16 | 16 | 0 | 0 | 0 |

#### Association analysis of keyword

Association rule | Support degree | Confidence level |
---|---|---|

Queue-Diligence | 0.2180 | 0.1992 |

Queue-Craftsman | 0.3556 | 0.2300 |

Queue-Ordered | 0.1212 | 0.8273 |

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Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability 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Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model