Ideological and political (IAP) education is an important method and means for the party and the country to carry out mainstream ideological propaganda, improve people's ideological, political and moral literacy and consciousness and promote people's free, comprehensive and sustainable development. How to improve its educational effect is an important topic that experts and scholars have been devoted to studying. They always combine IAP education with the latest scientific and technological achievements to obtain the latest research ideas. For example, since the birth of computer, there have been some new words [1,2,3] such as network IAP education, “Internet + IAP education”, massive open online course, flipping classroom, etc. Now, in the era of big data, the research upsurge of the new model of “big data + IAP education” will inevitably be formed. In terms of policy, it is also at the forefront to support the combination of IAP education and the latest technology.

As the core function of big data, prediction can analyse the ideological trends and predict the behaviours of the educated objects through quantitative data so as to formulate the corresponding innovation mechanism and education model and serve to better improve the effect of IAP education. The difference between it and the traditional thought prediction lies in the means of data information acquisition, the intelligence of analysis process and the reliability of analysis results [4, 5]. Therefore, the function and effect of the traditional IAP education prediction provides ideas for the application of big data prediction function in IAP education. In addition, IAP education in higher vocational colleges involves a wide range, diverse audience levels, and has not formed a unified standard model. It belongs to a complex system engineering, which must be analysed by systematic methods and learnt using collaborative theory. Building a collaborative platform, perfecting the collaborative mechanism, creating a collaborative culture and establishing a dynamic early warning model are the only way to realise the overall collaborative control of IAP education in higher vocational colleges [6]. IAP education is influenced by many complicated factors, and the lack of timely and accurate prevention of abnormal changes in any one of them may lead to serious deviations from or even contrary to the expected target, triggering various crisis events.

At present, the early warning of IAP education crisis has the characteristics of nonlinear development path, incomplete information collection, irregular data distribution and difficult quantification of index design [7,8,9] As an organisational means to monitor, diagnose and pre-control the changes of influencing factors in the process of IAP education, if the early warning method is not used properly, it will not only achieve the expected effect; on the contrary, it will waste a lot of manpower, material resources and financial resources due to false alarm and even lose the right to speak in IAP education. Therefore, how to take active and effective measures to educate and guide college students to consciously establish a national security concept, build a dynamic early warning mechanism of IAP education for college students and strengthen the IAP defence line in higher vocational colleges is a new challenge to carry out IAP education in higher vocational colleges.

“Social computing” has two meanings [10]: one is to serve social work as a tool of “social software”, which means to apply the latest information computing technology to social activities; the second one is to embed humanities and social sciences into computer or computing technology so as to realise in-depth research in social and humanities fields.

Although the concepts of social computing and big data are contemporary words, in recent years, with the rise of big data, both of them are based on computing technology and gradually blend with each other and complement each other. It can even be redefined as follows: scientific computing theories and technologies such as system theory, cloud computing, artificial intelligence and data analysis are used as methods and means in social science theory, which effectively solves the multifarious problems in the field of humanities and social sciences. Social computing in the era of big data is based on massive data, by continuously recording, mining and analysing personal thought and behaviour data information, it is possible for scientific, quantitative analysis and accurate research and calculation of humanities and social sciences, interpersonal interaction and social complex adaptive system.

The assumption and possibility of applying big data prediction function in the field of IAP education are based on social computing theory. The guidance of social computing ideas provides a new opportunity for big data technicians and researchers of IAP education to explore deeply, that is, using big data prediction technology and cloud computing technology to explore the IAP education in the field of humanities and social sciences.

As shown in Figure 1, at present, there are two explanations of educational informatization in academic circles: “technology theory” and “process theory”.

Technology theory takes information as a scientific and technological means and applies modern information technologies such as computer, Internet, mobile terminal, big data and cloud computing to the process of education, thus promoting the comprehensive reform of education and enhancing its effectiveness. This theory holds that information technology assumes a significant part in the advancement of education, which is an indispensable tool and means to realise educational informatization; so, it implies the attributes of “technology” and “education” [11].

Process theory holds that educational informatization is a process of improving the effectiveness of teaching methods by modern information technology so as to cultivate the information literacy of educational objects and realise the modernisation of education. Specifically, it refers to taking the educational thought as the guidance in all categories; by using information technology, we can effectively develop and make full use of information resources at all levels and train high-tech talents for the society, thus accelerating the process of educational modernisation.

The method of IAP education is accompanied by educational practice, which is attached to the different stages of the process of IAP education and the constant renewal of its activity forms; so, there are various concrete forms, such as indoctrination education method, practice exercise method, example demonstration method, self-education method, psychological guidance method, etc. [12, 13]. The method of IAP education follows the principle of creativity, that is to say, educators should constantly study new situations, creatively use traditional educational methods or summarise and explore new educational methods. The most important innovative way is to innovate IAP education methods by absorbing and applying research results of related disciplines or to use modern scientific and technological achievements to realise the modernisation of educational means.

With the advent of the era of big data, big data thinking and technology not only participate in the whole process of IAP education research and innovate the practical activities of IAP education but also promote its traditional process, that is, the process of making, implementing and evaluating educational programmes can be realised by new ways of thinking. Meanwhile, under the background of big data prediction function, the IAP education modes such as intelligent calculation, precise customisation and immediate prevention have been born, which also provide new educational methods for educators.

It is essentially a user learning behaviour collection system based on the computer system, which is used to collect user learning behaviour [14]. As shown in Figure 2, it has the functions of interactive, analogue and management platform.

With the high-level development of quality-oriented education, educational data mining is gradually becoming a mainstream research trend. In recent years, the rapid development has attracted many educational scholars and research institutions to invest in this research. At present, education data mining mainly includes the following processes and steps:

Pretreatment technology is an important part of data mining. Especially for data with particularly complex data sources, it is necessary to improve the quality of data in data mining. There are often incomplete data information or even inconsistent data, and so, data preprocessing is needed [15]. For this study, because of the diversity of data sources, data preprocessing is essential in this study; the quality of data set through data preprocessing can be improved.

The research topic is clarified. After the data preprocessing is completed, the mining algorithms are filtered according to the research objectives. The preprocessed data are trained by feature extraction, and the effective experimental results [16] are obtained. In this stage, the selection and optimisation of algorithms are extremely important, which will have a far-reaching impact on the quality of data mining. Data mining is also a process of discovering new knowledge, and its technology has powerful computing and processing capabilities, which can further improve the experimental efficiency.

After obtaining the results of data mining, it is necessary to evaluate the results so as to eliminate possible redundant problems or irrelevant patterns and finally determine whether the test results are accurate. If the user's demand cannot be met, it is necessary to return to the previous step, such as re-selecting feature parameters or data preprocessing [17]. To put it simply, the whole mining process needs to be constantly adjusted according to the feedback of the results, and finally, the model that meets the research objectives is obtained and used in new data mining, and the mining results will be used to guide the actual work or serve as the reference basis for decision-making.

The dynamic early warning system of IAP education based on the improved SVM algorithm mainly realises the data collection and potential law mining of the courses, effect evaluation, ideological dynamic control, early warning feedback and other links of IAP education for students in higher vocational colleges with obvious potential ideological dynamic differences [18] so as to realise the complete life cycle information management and control of IAP education in higher vocational colleges. This is shown in Figure 3.

As shown in Figure 4, corresponding to the dynamic early warning model of IAP education based on the improved SVM algorithm, the internal workflow flow order is as follows:

Step 1: Enter the important speech made by General Secretary Xi Jinping under the new situation and relevant national policies and regulations as the general basis for higher vocational colleges to formulate individualised IAP education programmes;

Step 2: Carry out standardised inspection and small-scale experiments on the individualised IAP education plan formulated by higher vocational colleges;

Step 3: Decide whether to popularise according to the experimental results. If the experimental results support popularisation, start the IAP education effect analysis submodule and evaluate the personalised IAP education scheme formulated by higher vocational colleges from multi-dimensional effect evaluation; otherwise, return to the first step;

Step 4: Start the dynamic early warning submodule of IAP education, find out the students with dangerous ideological trends in advance and give early warning tips and take timely and active intervention measures to ensure that the IAP education in higher vocational colleges plays an effective role.

To make comprehensive fuzzy evaluation on the quantitative data of users' invisible early warning, it is integrated into the decision analysis system mechanism, as shown in Figure 5.

Fuzzy neural network is introduced for decision evaluation and adaptive training of fuzzy rules. Structurally, the user's invisible interest input layer, membership function fuzzification layer [19], fuzzy rule adaptive training layer, output variable fuzziness division layer and user's invisible interest decision analysis layer are formed. Functionally, the BP neural network is used as the pattern memory. The self-learning ability is used to continuously update the optimisation weight coefficient, which makes the fuzzy system have generalisation ability, realises the comprehensive evaluation of personalised service and feeds back the results to the improved support vector machine algorithm, thus realising a benign closed loop.

Support vector machine (SVM) algorithm essentially belongs to an efficient, limited and generalised classifier with supervised and extensible classifiers, which can overcome linear and nonlinear obstacles. In order to realise nonlinear multi-core data mining and clustering effect, improve the memory consumption ratio, balance generalisation ability and learning ability, improve the interpretability of data sets and strengthen the adaptability of kernel functions and so on, introducing cold and hot data separation factor and random gradient descent factor to improve the SVM algorithm [20]. The specific steps are as follows.

It can be seen from Figure 3 that the dynamic early warning model of IAP education oriented to multidimensional application is transformed into an unlimited experience loss minimisation problem with penalty factors, and the objective function is defined as Eq. (1).

Using random gradient descent to solve the objective function, in each iteration period, randomly select training samples and map the corresponding objective function gradient and select the gradient step length on the opposite side of the iteration direction to ensure that the running time of the algorithm is satisfied

After the mapping of Eq. (3), the problem of minimising unlimited experience loss with penalty factors under the multidimensional constraint given in Eq. (1) is transformed into the problem of solving extreme value under the single constraint. Further, smooth loss functions are used to replace hinge loss to further transform the problem into a smooth and unconstrained optimisation problem under the hyperplane. The specific solution process is as follows:

A training sample _{t}

Sub-gradients are used to solve Eq. (4), such as Eq. (5).

In Eq. (5), _{it}_{t}, _{ii}

In Eq. (6),

Further, simplify the Eq. (7) and backward deduce the available Eq. (8).

Based on Eq. (8), if the indicator function is true, it is converted to Eq. (9).

Based on Eq. (8), if the indicator function is false, it is converted to Eq. (10).

It can be seen from Eq. (8) that the cold and hot data can be separated by setting the comprehensive bias term. Furthermore, by introducing the online learning mechanism, the predictor with low generalisation error can be obtained, which balances the generalisation ability and learning ability.

The construction of the early warning index system is the basis of whether its evaluation method is effective or not. The basic way is to decompose the target layer by layer according to certain standards to form an index system. Through interviews and investigations with educational scholars and experts from industrial enterprises in higher vocational colleges, the early warning evaluation index system of IAP teaching effectiveness as shown in Table 1 is adopted.

Early warning evaluation index system

Teaching staff of IAP education | Doctoral proportion of teachers | 0–100 |

Teaching level | 0–100 | |

Professional quality | 0–100 (poor–good) | |

Proportion of senior titles | 0–100 | |

Ideological expression | National pride | 0–100 (poor–good) |

Social responsibility | 0–100 (very weak–strong) | |

Career ideal | 0–100 (poor–good) | |

Socialist identity | 0–100 (very low–high) | |

Behaviour expression | Attendance rate of IAP class | 0–100 |

Social practice ratio | 0–100 | |

Failure rate of IAP course | 0–100 | |

employment rate | 0–100 |

The early warning evaluation value of higher vocational education quality is directly related to the determination of early warning limits. In view of its fuzziness and subjectivity, this paper uses the fuzzy comprehensive evaluation method [22], which combines fuzzy mathematics with analytic hierarchy process to calculate.

Assign each index 1, 2, 3, 4 and 5 points, respectively. Namely:

There is a certain degree of membership between the elements in the fuzzy set and the set, that is, the degree of membership, whose value is [0,1]. In this paper, the membership degree is determined by the data of experts' scoring. As shown in Eq. (11),
_{ij}

Use

The calculation of comprehensive early warning value is to combine the early warning value of individual indicators with the weight of indicators for comprehensive consideration. Therefore, the comprehensive early warning evaluation value of warning indicators can be determined by multiplying the early warning evaluation value _{1}, _{2}, . . . , _{n}_{1},_{2}, . . . , _{n}

In early warning, the early warning limit is determined by the range of early warning value, and different early warning signals need to be determined according to the early warning limit so as to send a warning to the manager with an intuitive image. So, the rationality of early warning limit determination is an important factor to determine the accuracy of early warning. This paper uses the theory of statistics 3σ to determine the early warning limit [23]
_{i} is the standard deviation of the i-th index. Then, the comprehensive standard deviation σ of the warning sign early warning evaluation value is calculated using Eq. (15).

According to the principle of normal distribution in statistics, when the early warning evaluation value of each index is within the interval of (

After dividing the warning interval, it is necessary to determine the warning level and output the corresponding warning status by signal light method. In the design of warning signal system, ★ indicates the first-level warning, ★★ indicates the second-level warning, ★★★ indicates the third-level warning and ★★★★ indicates the crisis warning. The more serious the warning situation, the fewer stars, as shown in Table 2.

Classification of alert status

★★★★ | ★★★ | ★★ | ★ |
---|---|---|---|

No police area | Light police area | Middle police area | Heavy police area |

Good | Common | Danger | Crisis |

( |
( |
( |
(−∞, |

In order to better meet the needs of IAP education in higher vocational colleges under the new situation and overcome the problems existing in IAP education in higher vocational colleges, such as lagging information feedback, imperfect early warning intervention mechanism, weak risk management and control ability and so on, an early warning model of IAP teaching effectiveness based on the SVM algorithm logic design and BP neural network decision analysis is proposed. In this paper, the fuzzy comprehensive evaluation method is used to determine the early warning evaluation value of warning indicators. Based on the statistical 3σ theory, the early warning boundary is calculated, the early warning interval is divided and the early warning signal system is designed and the early warning model of education quality is constructed. It effectively enhances the ability to monitor and predict the crisis of IAP education in colleges and universities so as to improve the comprehensive evaluation and dynamic analysis theory of IAP education quality.

#### Classification of alert status

★★★★ | ★★★ | ★★ | ★ |
---|---|---|---|

No police area | Light police area | Middle police area | Heavy police area |

Good | Common | Danger | Crisis |

( |
( |
( |
(−∞, |

#### Early warning evaluation index system

Teaching staff of IAP education | Doctoral proportion of teachers | 0–100 |

Teaching level | 0–100 | |

Professional quality | 0–100 (poor–good) | |

Proportion of senior titles | 0–100 | |

Ideological expression | National pride | 0–100 (poor–good) |

Social responsibility | 0–100 (very weak–strong) | |

Career ideal | 0–100 (poor–good) | |

Socialist identity | 0–100 (very low–high) | |

Behaviour expression | Attendance rate of IAP class | 0–100 |

Social practice ratio | 0–100 | |

Failure rate of IAP course | 0–100 | |

employment rate | 0–100 |

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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 Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in 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 Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas 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 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 Evaluation and prediction of regional human capital based on optimised BP neural network 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 A study of local smoothness-informed convolutional neural network models for image inpainting 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 Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System 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 Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences 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 An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area 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 Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network