The measurement of pulmonary function index is one of the important means to study the harm caused by smoking. At present, the research on the impact of smoking on pulmonary ventilation is not completely consistent. Many different research results have appeared because there are many pulmonary function indices and different research emphases. At present, the proportion of smokers remains high, and there is a trend of younger people being drawn towards smoking. The smoking situation of teenagers in the eastern coastal areas is more obvious. Although there are many studies on smoking and vital capacity at home and abroad at the current stage, few of them take teenagers in the eastern coastal areas as the research object, and most of them take the elderly with pulmonary function impairment as the research object. The research population is not typical, and the research results cannot be applied to the public. Most of the research methods also use the existing statistical software for analysis, and there is no in-depth discussion on the relationship and rules between pulmonary function indices. Therefore, in order to better study the harm that smoking causes to lung function, we also need to combine data mining algorithms to mine smoking data and lung function index data, analyse and classify the data, and find the rules between the data.

Based on this background, this paper studies the impact of adolescent smoking on physical training vital capacity in the eastern coastal areas, and is divided into four sections. Section 1 briefly introduces the current research on smoking and vital capacity in the field of medicine, and briefly introduces the section arrangement of this study. The second section focuses on the application of various algorithms in the medical field, introduces the existing data mining algorithms and improved algorithms, and summarises the shortcomings of the existing research. In Section 3, taking the adolescents in the eastern coastal area as an example, the pulmonary function indices are measured, the

The innovation of this paper is to propose a data mining algorithm for adolescent vital capacity. On the one hand, it improves the

In the analysis of public health indicators, data mining has always been a problem that cannot be ignored. If we cannot grasp the data changes in time, it will not only affect the accuracy of test results, but also cause a lot of trouble in the research of diseases. Data mining can not only analyse the relationship between data, but also play a lot of roles in the analysis of public physical quality. At present, there are many research algorithms concerning data mining. For example, in their research and analysis, Tang Y. et al. screened the biochemical test and TCM Constitution questionnaire measurement data from 2014 to 2016 according to the inclusion and exclusion criteria, established the prediction matrix according to the longitudinal data for 3 consecutive years and established the prediction model by using treenet machine learning algorithm to reveal the dependence between physiological indices, TCM Constitution and MS [6]. Scaria et al. [7] proposed a user-friendly rule-based classification model, generated classification rules by using cuckoo search optimisation algorithm, pruned the rules through association rule mining and classified them by using the pruned rules. Janowski et al. [8] identified subjects from the pH registry of the University of Arizona in their study, excluded patients with missing haemodynamic RV function data (

To sum up, it can be seen that at present, most medical data at home and abroad use classification algorithms to realise data analysis, and the types of data studied are also diversified, covering cardiac function, liver function and lung function indicators. However, most of these studies focus on the medical field, and there is little in-depth analysis on the use of algorithms. Although there are many data mining algorithms and related improvement strategies, such as decision tree algorithm, cluster analysis algorithm, ant colony algorithm and so on, they are relatively one-sided and rarely applied to medical data mining. Based on this, it is of great practical significance to carry out an analysis on the influence of adolescent smoking on physical training vital capacity in the eastern coastal areas.

Adolescents in the eastern coastal area were selected as the research object and divided into two groups according to the smoking situation. The non-smoking teenagers were the control group and the smoking teenagers were the observation group. The vital capacity indices of the two groups were measured. The measurement indices included gender, age, maximum vital capacity and forced inspiratory vital capacity in the first second.

The research data were analysed by clustering algorithm. The present situation is that clustering algorithm has been studied in the literature for many years, and it is widely used in medicine. Among various algorithms, _{1},_{2},…, _{m}_{1},_{2},…,_{m}

We use this formula to calculate the error. The formula is:
_{i}_{i}

_{i}

The formula has the advantages of simple calculation and shorter running time and has great advantages in improving

To achieve the classification of vital capacity, we also need to use the decision tree algorithm to classify the data. The decision tree algorithm is based on the development probability of things, calculates the expected value and judges the possibility of things. Decision tree is a kind of machine learning and belongs to prediction model [17]. In the process of generating the decision tree, it is necessary to divide the attribute values of the data set, but the results are different: some are simple and some are very bloated. Therefore, the decision tree algorithm has strong applicability, but it often needs the optimal method. This kind of algorithm takes the root node as the starting point, selects the optimal attribute and generates branches, with the same number of branch nodes [18]. The decision tree algorithm itself is a continuous iterative algorithm, and the calculation will end only when the following conditions are met: the stage attributes belong to the same category; the empty set is marked with the most common attribute value in the parent node; and node to node are marked with the most common attribute values.

ID3 algorithm calculates the information gain on the decision tree node, selects the largest node as the node and detects all attributes. ID3 algorithm belongs to the classic algorithm of decision tree algorithm. The generation rules are easy to understand. In the construction process, from top to bottom, it reduces the number of tests and can process discrete data. However, the disadvantage of this algorithm is also obvious. It can only maintain one solution, and there may be multiple attribute values in the information gain. This algorithm can deal with non-incremental data and cannot deal with other data. C4.5 algorithm is an improved algorithm of ID3 algorithm. It is realised by using information gain rate when selecting attributes. It can deal with continuous value attributes and missing cases. It is easy to understand and has high accuracy. There are two steps in the calculation. The first step is to establish a reasonable model, taking the data to be analysed as the training set and other data as the sample set. The second step is data analysis. At present, there are many algorithms used, and these are needed to calculate the accuracy [19]. In the algorithm, the information gain rate needs to be calculated. Assuming that the data set is represented by _{i}

The other information calculation formula of _{j}_{ij}

C4.5 algorithm is to test the information gain rate from the alternative data set; we take it as the partition attribute, and construct the decision tree through iteration, which is a widely used tactic. However, this algorithm also has its own defects. Although the improvement rate ID3 algorithm has the problem of information gain bias, it also reduces the interpretability of information theory. In the construction process, analyzing the number according to the classification attributes will lead to many empty branches and increase the number of branches of the decision tree [20]. Therefore, this algorithm needs to be improved. Assuming that there is expectation for two-dimensional random variables, it is expressed as:

This expectation is the covariance. The formula is:

If this random variable is discrete, the probability distribution is:

The relationship between variance and covariance of random variables can be described as follows:

Assuming that there are random variables that can promote the establishment of

If this value is 0, the two random variables are considered irrelevant. There are many improved algorithms based on ID3 algorithm, including C4.5, and these are also based on the amount of information [21]. The algorithm considers the correlation of attributes and calculates the sum of correlation coefficients between test attributes and other attributes, which is expressed as:

Due to C4.5 in the calculation of the algorithm, an information gain rate is used as the test standard. To balance other attributes, the average correlation coefficient needs to be added. The improved information gain rate formula is expressed as:

According to this formula, if the correlation between the test attribute and other attributes is very low, the smaller the redundancy and the greater the gain rate.

For C4.5, in terms of algorithm, the information gain rate is the core of the calculation. Each time a node is selected, it needs to be calculated; and every time a calculation is made, the need to calculate the logarithm is involved. If the scale is relatively small, the amount of calculation will not be large. However, in many cases, there is a large amount of data, and logarithmic calculation wastes time [22]. To shorten the running time, it is also necessary to simplify the formula by using Taylor's theorem. Assuming that the function has a derivative in an interval, there is:

Then we use McLaughlin formula to convert and eliminate logarithmic calculation. The formula can be rewritten as:

When

The calculation formula of information entropy can be described as:

We calculate the information entropy according to the above formula:

The previous formula can be simplified and expressed as:

Finally, the simplified calculation formula of information gain rate is obtained:

It can be seen that after improvement, the algorithm no longer needs to calculate a logarithm, but rather the calculation involved is rendered simple, and thus the efficiency stands improved. This improved method considers the problems of information gain and redundancy at the same time, and the attribute result is more reasonable.

In the application of

Comparative analysis of running time (ms).

cleanl | 51.3 | 45.9 | 11.2 |

diabetes | 494.5 | 64.2 | 10.4 |

glass | 31.4 | 29.6 | 7.6 |

wine | 20.5 | 17.4 | 6.4 |

sonar | 45.8 | 30.5 | 8.6 |

iris | 16.5 | 19.3 | 5.3 |

Taking the clean data set, diabetes data set, glass data set, wine data set, sonar data set and iris data set as sample data sets, this paper compares and analyses the traditional C4.5. The running times of the algorithm and the improved algorithm are shown in Table 1. From the data in the table, it can be seen that under different data sets, the running time of the improved algorithm is shorter than that of the traditional algorithm.

The results of comparative analysis of algorithm classification are shown in Table 2. From the data in the table, it can be seen that under different data sets, the error rate of the improved algorithm proposed in this paper is lower than that of the other two algorithms, indicating that the algorithm can also reduce the classification error rate based on shortening the running time.

Analysis of error rate results (%).

cleanl | 7.12 | 6.49 | 0.98 |

diabetes | 8.14 | 4.39 | 0.87 |

glass | 19.74 | 9.34 | 0.92 |

wine | 7.34 | 1.85 | 0.94 |

sonar | 4.74 | 1.29 | 0.87 |

iris | 9.78 | 2.94 | 0.64 |

The processing of medical indicators is more troublesome, and the stored information contains a lot of non-numerical data, which involve personal privacy. Therefore, a combination of multiple methods needs to be adopted in data processing. Moreover, in the system, many data are stored in different databases, and thus the relationship between data cannot be ignored. Firstly, the improved clustering analysis algorithm is used to divide the sample data into different categories. The

When extracting data, it is necessary to establish files, record the original data, make the original office conversion table, and list the training data set and detection data set. We take the vital capacity data of adolescents in the eastern coastal area as the training set and copy it into the actual worksheet. The information gain degree is used to select the attributes that can be distinguished. Generally, indicators with high probability have stronger prediction ability. Using the automatic screening function of the table, the vital capacity indices of non-smoking adolescents were divided into different grades. Taking the test results as the test set, the test results show that the classification accuracy is 96.2% and the qualified rate of vital capacity is 64.6%.

In recent years, for the analysis of medical data, the existing software has been generally used for research and analysis, and there has been no change in the parameters used. Therefore, the analysis speed is slow, the data processing is troublesome and the results are relatively one-sided; thus, the information contained in the data cannot be obtained in depth. Based on this, this paper studies the influence of adolescent smoking on physical training vital capacity in the eastern coastal area. A data mining algorithm is established to mine inactive data. Different algorithms are adopted according to different data information, and the shortcomings of the existing algorithms are improved. The average value of entropy is used as the optimal threshold, and the correlation coefficient is introduced into the calculation of information gain rate. The simulation results show that the improved algorithm proposed in this paper shows its advantages in different data sets. The algorithm is applied to the mining of vital capacity. The

#### Analysis of error rate results (%).

cleanl | 7.12 | 6.49 | 0.98 |

diabetes | 8.14 | 4.39 | 0.87 |

glass | 19.74 | 9.34 | 0.92 |

wine | 7.34 | 1.85 | 0.94 |

sonar | 4.74 | 1.29 | 0.87 |

iris | 9.78 | 2.94 | 0.64 |

#### Comparative analysis of running time (ms).

cleanl | 51.3 | 45.9 | 11.2 |

diabetes | 494.5 | 64.2 | 10.4 |

glass | 31.4 | 29.6 | 7.6 |

wine | 20.5 | 17.4 | 6.4 |

sonar | 45.8 | 30.5 | 8.6 |

iris | 16.5 | 19.3 | 5.3 |

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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 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