Study on the influence of adolescent smoking on physical training vital capacity in 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, k-means algorithm analyses the similarity of data objects, and artificially places the data with good similarity close to the data in one class [15]. The algorithm belongs to segmentation algorithm, which is simple to implement and has high efficiency. Generally, the object is selected from the cluster data as the initial point, the distance is calculated, and then it is assigned to the corresponding class; and the cluster centre is repeatedly selected until it has ceased to change [16]. Assuming that there are n data objects, all of which are non-data sets, in the calculation, we artificially divide the k value, determine the initial clustering centre, select the corresponding data from the data set and then calculate the distance. According to the shortest distance principle, the data are divided into corresponding classes, and then the cluster centre is modified. Assuming that the given sample set is described by D = {x₁,x₂,…, x_m}, after k-mean clustering, the class is represented by C = {c₁,c₂,…,c_m}. The measurement index is European distance, and the formula is: (1) disted(xi, xj)=[∑u=1n|xi−xj|2]12 dis{t_{ed}}({x_i},{\kern 1pt} {x_j}) = {\left[ {\sum\limits_{u = 1}^n {{\left| {{x_i} - {x_j}} \right|}^2}} \right]^{{1 \over 2}}}

We use this formula to calculate the error. The formula is: (2) E=∑i=1k∑x∈ci‖x−ηi‖2 E = \sum\limits_{i = 1}^k \sum\limits_{x \in {c_i}} {\left\| {x - {\eta _i}} \right\|^2} (3) ηi=1|Ci|∑x∈Cix {\eta _i} = {1 \over {\left| {{C_i}} \right|}}\sum\limits_{x \in {C_i}} x where η_i refers to the mean vector, which can also be called the centroid. The smaller the E value, the higher the similarity in the class, and thus this value needs to be taken as the minimum value. The derivative of x can get the minimum E only in x = η_i. After one iteration, the E value will decrease.

k-mean algorithm is one of the most commonly used clustering algorithms at present. This algorithm is relatively simple, easy to use, easy to combine with other algorithms and has fast convergence speed. At the same time, this kind of algorithm also has many defects, and the question of whether defects arise or not depends on the initial value and may have no solution. Using the gradient method to calculate the objective function, if the initialisation centre itself is close to the local minimum, it might easily fall into the local optimum. This algorithm is sensitive to outliers, and it will take a long time to process massive data.

K-mean algorithm is mainly to calculate and analyze the value range of k after improvement. According to the cluster analysis, there are two statistics. The total SSE value is the sum of squares of deviations of all cluster variables. The formula is expressed as: (4) SSE=∑i=1k∑x∈Cdist(ci, x)2 SSE = \sum\limits_{i = 1}^k \sum\limits_{x \in C} dist{({c_i},{\kern 1pt} x)^2} where c_i represents the cluster and x represents the points in the cluster. The total SSB is only the sum of the squares of the deviations between different categories. The calculation formula is: (5) SSB=∑i=1kmdist(ci, c)2 SSB = \sum\limits_{i = 1}^k mdist{({c_i},{\kern 1pt} c)^2} where m is the cluster size, c is the mean value and dist is the distance. Based on the k value determined, it is generally considered that the smaller the SSE value is, the better, and the larger the SSB value is, the better. Considering the influence of the number of clusters and sample size on the calculation results, it needs to be corrected, and the correction is completed by using the following formula: (6) SSBSSE=n−kk−1 {{SSB} \over {SSE}} = {{n - k} \over {k - 1}}

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

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 D, and the samples in this set are represented by d, which contains m class attributes, the amount of classification information can be expressed as: (7) lnfo(D)=∑i=1mpilog2pi \ln fo(D) = \sum\limits_{i = 1}^m {p_i}\mathop {\log }\nolimits_2 {p_i} where p_i represents the proportion of attributes. Assuming that A is one of the attributes and there are v values, the data set is divided into n subsets. Assuming that the total number of samples of category C is represented by c, the information entropy of attribute A can be calculated by the following formula: (8) lnfo(D)=∑i=1mc1j+c2j+⋯+cmjdlnfo(c1j,c2j,…,cmj) \ln fo(D) = \sum\limits_{i = 1}^m {{{c_{1j}} + {c_{2j}} + \cdots + {c_{mj}}} \over d}\ln fo({c_{1j}},{c_{2j}}, \ldots ,{c_{mj}})

The other information calculation formula of D_j is: (9) lnfo(d1j,d2j,⋯,dmj)=∑i=1mpijlog2pij \ln fo({d_{1j}},{d_{2j}}, \cdots ,{d_{mj}}) = \sum\limits_{i = 1}^m {p_{ij}}\mathop {\log }\nolimits_2 {p_{ij}} where p_ij represents the proportion of samples. The information gain of attribute A can be expressed as: (10) Gain(A)=lnfo(D)−lnfoA(D) Gain(A) = \ln fo(D) - \ln f{o_A}(D) where Gain(A) represents the information gain. We calculate the entropy of A with the formula: (11) SplitlnfoA(D)=∑j=1vpilog2pi Split\ln f{o_A}(D) = \sum\limits_{j = 1}^v {p_i}\mathop {\log }\nolimits_2 {p_i} where p represents the proportion of A in the data set. The information gain rate formula of A can be expressed as: (12) GainRatio(A)=lnfo(D)−lnfoA(D)SplitlnfoA(D) GainRatio(A) = {{\ln fo(D) - \ln f{o_A}(D)} \over {Split\ln f{o_A}(D)}}

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: (13) E{[X−E(X)][Y−E(y)]} E\{ [X - E(X)][Y - E(y)]\}

This expectation is the covariance. The formula is: (14) Cov(x, y)=E{[X−E(X)][Y−E(y)]} Cov(x,{\kern 1pt} y) = E\{ [X - E(X)][Y - E(y)]\}

If this random variable is discrete, the probability distribution is: (15) P{X=xi, Y=yi}=pij P\{ X = {x_i},{\kern 1pt} Y = {y_i}\} = {p_{ij}} where i, j is a natural number. The variance of two random variables can be expressed as: (16) Cov(x, y)=∑i,jE{[xi−E(X)][yi−E(Y)]} Cov(x,{\kern 1pt} y) = \sum\limits_{i,j} E\{ [{x_i} - E(X)][{y_i} - E(Y)]\} where X,Y represents two random variables. If both random variables are discrete, the covariance can be expressed as: (17) Cov(x,y)=∫−∞+∞∫∞+∞E{[xi−E(X)][yi−E(Y)]}f(x, y)dxdy Cov(x,y) = \int_{ - \infty }^{ + \infty } \int_\infty ^{ + \infty } E\{ [{x_i} - E(X)][{y_i} - E(Y)]\} f(x,{\kern 1pt} y)dxdy

The relationship between variance and covariance of random variables can be described as follows: (18) D(X+Y)=D(X)+D(Y)+2cov(x, y) D(X + Y) = D(X) + D(Y) + 2{\mathop{cov}} (x,{\kern 1pt} y)

Assuming that there are random variables that can promote the establishment of D(X) > 0, D(Y) > 0, there are: (19) ρX, Y=Cov(X, Y)D(X)D(Y) {\rho _{X,{\kern 1pt} Y}} = {{Cov(X,{\kern 1pt} Y)} \over {\sqrt {D(X)D(Y)} }}

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: (20) ρ=∑f∈FCov(A, f)D(A)D(f) \rho = \sum\limits_{f \in F} {{Cov(A,{\kern 1pt} f)} \over {\sqrt {D(A)D(f)} }} where ρ represents the sum of correlation coefficients of test attributes and other attributes, that is, redundancy, F represents all test attributes and f is an element of F; ρ represents the correlation degree between attributes and other test attributes, and the average correlation coefficient between test attributes and other attributes can be expressed as: (21) ρ¯=∑f∈FCov(A, f)D(A)D(f)n \bar \rho = {{\sum\limits_{f \in F} {{Cov(A,{\kern 1pt} f)} \over {\sqrt {D(A)D(f)} }}} \over n}

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: (22) GainRatio=Gain(A)ρSplitl(A) GainRatio = {{Gain(A)} \over {\rho Splitl(A)}}

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: (23) f(x)=f(x0)+f′(x0)(x−x0)+f″(x0)2(x−x0)2+⋯+f(n)(x0)n(x−x0)n+Rn(x) f(x) = f({x_0}) + {f^\prime}({x_0})(x - {x_0}) + {{{f^{''}}({x_0})} \over 2}{(x - {x_0})^2} + \cdots + {{{f^{(n)}}({x_0})} \over n}{(x - {x_0})^n} + {R_n}(x) where x represents the value of the function. Assuming that x takes 0, the formula is further simplified as: (24) f(x)=f(0)+f′(0)x+f″(n)2x2+⋯+f(n)(0)nxn f(x) = f(0) + {f^\prime}(0)x + {{{f^{''}}(n)} \over 2}{x^2} + \cdots + {{{f^{(n)}}(0)} \over n}{x^n}

Then we use McLaughlin formula to convert and eliminate logarithmic calculation. The formula can be rewritten as: (25) f(p)=ln(1+p)=p−p22+p33−⋯+(−1)n−1pnn f(p) = \ln (1 + p) = p - {{{p^2}} \over 2} + {{{p^3}} \over 3} - \cdots + {( - 1)^{n - 1}}{{{p^n}} \over n}

When p is at 0~1, according to the limit theorem, with the increase of n, this term becomes smaller, and thus the formula is approximated as follows: (26) lnp=p−1 \ln p = p - 1

The calculation formula of information entropy can be described as: (27) lnfo(D)=∑i=1mpilog2(pi) \ln fo(D) = \sum\limits_{i = 1}^m {p_i}\mathop {\log }\nolimits_2 ({p_i})

We calculate the information entropy according to the above formula: (28) lnfo(D)=∑i=1mcidlog2cid \ln fo(D) = \sum\limits_{i = 1}^m {{{c_i}} \over d}\mathop {\log }\nolimits_2 {{{c_i}} \over d}

The previous formula can be simplified and expressed as: (29) lnfo(D)=1d2ln2∑i=1mci(ci−d) \ln fo(D) = {1 \over {{d^2}\ln 2}}\sum\nolimits_{i = 1}^m {c_i}({c_i} - d)

Finally, the simplified calculation formula of information gain rate is obtained: (30) GainRatio(A)=1ρ∑i=1mci(ci−d)−d∑j=1v∑i=1mcij(cij−dj)dj∑j=1vdj(dj−d) GainRatio(A) = {1 \over \rho }{{\sum\nolimits_{i = 1}^m {c_i}({c_i} - d) - d\sum\nolimits_{j = 1}^v \sum\nolimits_{i = 1}^m {{{c_{ij}}({c_{ij}} - {d_j})} \over {{d_j}}}} \over {\sum\nolimits_{j = 1}^v {d_j}({d_j} - d)}}

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 k-means algorithm to cluster analysis, the selection of initial point will directly affect the convergence speed and stability of the algorithm, and there is no fixed starting point. Therefore, in the simulation test, k value is randomly selected as the initial point. Using the method of selecting the value as far away as possible, we first select one randomly, and then select the point with the largest distance from the carton as the second starting point, and so on until k starting points are found. The clustering analysis algorithm is simulated and analysed, and the parameter indices are shown in Figure 1. Dunn coefficient reflects the shortest distance between different classes. It is generally believed that the larger this value, the better the clustering effect. The contour coefficient reflects the average distance between the object and other objects. The smaller the value, the more compact the cluster. It can be seen from the data in Table 1 that the contour coefficient and Harabasz index of the improved k-means algorithm have been improved, and the Dunn coefficient has decreased, indicating that the improved algorithm has a better effect in the end of clustering and simpler grouping.

Fig. 1

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.

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 k-means improved algorithm divides the data set into six categories, and the corresponding centroid vectors are 63.54, 60.76, 70.54, 76.84, 82.54 and 87.52, respectively.

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%.