BP Neural Network Model-based Physical Exercises and Dietary Habits Relationships Exploration

Abstract

With the continuous progress of society, increment of social pressure, people have paid little and little attentions to physical exercises and dietary necessity. Take Beijing, Shanghai, Guangzhou, Shenzhen, Shijiazhuang and Baotou university students as research objects, targeted at physical exercises time and dietary habits, it starts investigation. Make principal component analysis of investigation results, results indicates that cereal intake is principal component in dietary habits; strenuous exercise time and general physical exercise time are the principal components in physical exercise. Utilize BP neural network model, analyze these seven cities’ physical exercises and dietary habits conditions, the result indicates that except for Shenzhen, all the other six cities haven’t reached the standard.

1. INTRODUCTION

Good dietary habits and necessary physical exercises are important principles to ensure human health. As far as office worker is concerned, as social pressure increases, pace of life speeds up, more and more people have neglected physical exercises and dietary necessity. As far as student is concerned, learning and video game have occupied whole time of life. People possesses with toned body is the important factor to the prosperity of the country; therefore, physical exercises and dietary are especially important [1].

In 2012, Gao Min implemented lifestyle and physical health research on Shandong Medicine and Food Career College’s students, and took freshman as research objects, research results indicated that students’ physical conditions were good, but excellent comprehensive evaluation people amount was fewer, most of students were in the level of pass line [2,3]. Students bad dietary habits was one of reasons that led to health level declining, most of students replaced sleep and physical exercise time with the time of watching TV and surfing online. The writer pointed out that students’ lifestyle and physical health had obvious correlation. Students of good physical exercise habits had higher mental health level and physical test performances [4].

In 2003, Gao Gen-Di and others researched on Shanghai teenagers’ dangerous behaviours, from which it included daily dietary and physical exercises status research, conducted questionnaire survey on 105 schools partial students, investigation contents were weekly dietary contents and physical exercises conditions, the investigation result indicates that nearly half students’ dairy product intake was lower, above quarter students excessively took in sweets, and even fewer students took in deep-fry and pickled food every day. Half the students strenuous exercise amount was not enough, above half students didn’t participate in extracurricular exercises, and as students’ ages increased, phenomenon of not participating in physical exercise became even more serious [5]. At the same time, it indicated that schoolgirls physical exercise level was even lower than that of schoolboys. The writer pointed out that it was very necessary to develop dietary education and physical exercise ideological education targeted at teenagers.

In 2013，Xu Ya-Nan researched on elementary and secondary school students’ food safety education problem. Firstly it explained food safety current status, and then applied multiple research methods to carry out questionnaire survey on Nanjing city elementary and secondary school students, finally, targeted at present problems, it presented solution. Investigation result indicated that local primary and secondary school students’ emphasis on food safety was high, but in students’ contiguous education, school food safety education ranked the last. Most of students suggested integrating food safety education into physical health education course [6-8].

The paper will adopt questionnaire survey, research on physical exercises and dietary necessity, and pointed out current existing issues and presented corresponding countermeasures.

2. QUESTIONNAIRE SURVEY AND RESULTS

Take Beijing, Shanghai, Guangzhou, Shenzhen, Shijiazhuang, Tianjin and Baotou these seven cities as investigation sites, regard university students as investigation objects, questionnaire contents include daily dietary behaviors and physical exercises behaviors.

2.1. Investigation Contents

Use year 2001 American disease control center’s teenagers’ dangerous behaviors questionnaire survey as evidence, combine with Chinese current status, and designs questionnaire survey contents. Among them, daily dietary habits investigation contents include cereal intake amount less than 250 gram, fruit and vegetable intake amount less than 350 gram, protein intake amount less than 70 gram, sugared beverage intake amount above 50 gram, fried and other junk food intake amount above 50 gram. Physical exercises investigation contents include strenuous exercises less than 20 minutes, general exercises less than 40 minutes, physical exercises less than 50 minutes, watching TV and surfing online such entertainment time above 100 minutes [7].

2.2. Investigation Results

Respectively random sample 100 university students in each investigation site, and fill out questionnaire anonymously. Subject in questionnaire independently completes questionnaire to ensure questionnaire survey results validity. Sort out and make statistics of investigation results, it can get investigation result as Table 1, Table 2 shows.

Table 1.

Dietary habits investigation result table.

City	Cereal<250g	Fruit and vegetable<350g	Protein<70g	Fried food>50g	Sugared beverage>50g
Beijing	35%	21%	15%	26%	29%
Shanghai	28%	19%	13%	21%	27%
Guangzhou	46%	15%	10%	19%	31%
Shenzhen	39%	20%	12%	16%	35%
Shijiazhuang	26%	25%	25%	29%	29%
Tianjin	29%	29%	23%	32%	23%
Baotou	35%	35%	19%	23%	28%

Table 2.

Physical exercises behaviors investigation result table.

City	Strenuous exercises<20min	General exercises<40min	Physical exercises<50min	Electronic entertainment>100min
Beijing	80%	65%	69%	86%
Shanghai	76%	68%	72%	79%
Guangzhou	83%	59%	79%	83%
Shenzhen	79%	52%	68%	76%
Shijiazhuang	89%	74%	83%	89%
Tianjin	82%	69%	76%	84%
Baotou	91%	64%	80%	81%

From Table 1, it is clear that all regions university students’ dietary structure has certain differences. Guangzhou students lack of cereal intake, Baotou students lack of fruit and vegetable intake, Shijiazhuang students lack of protein intake, Tianjin students fried food intake amount is larger, and Shenzhen students’ sugared beverage intake amount is larger.

From Table 2, it finds out that Baotou students lack of strenuous exercises, Shijiazhuang students lack of general exercises and physical exercises as well as take too long time in electronic entertainment.

3. PRINCIPAL COMPONENT ANALYSIS

Main thought of principal component analysis is variable’s dimension reduction. It is a statistical analysis method that transforms multiple variables into fewer main variables. It generally is used to data compression, system evaluation, regression analysis and weighted analysis so on.

3.1. Definition of Principal Component Analysis Approach

May way of principal component analysis is reducing dimension of variables, which is recombining original many variables with correlation into a group of uncorrelated variables to replace original variables. Therefore, we can pay attention to every time observation’s variables that have maximum variation, to every time observation’s small changed variables that can be used as constant to process and get rid of them, so that it reduces variables number in question that needs to be considered.

Assume that there is m pieces of original indicators to do principal component analysis, which are recorded as $x_1,x_2,\cdots ,x_m$, now it has pieces of samples, corresponding observation value is $x_{ik}\left(i=1,2,\cdots ,n\right)\mathit{and}k=1,2,\cdots ,m$ takes standardization transformation, and then transform $x_k\mathit{into}{x}_k^{\ast }$ that:

$$x_k^{\ast }=\frac{x_k-\overline{x_k}}{s_k},k=1,2,\cdots ,m$$ (1)

Among them, $\overline{x_k}\mathit{and}{s}_k$ are respectively $x_k$ average number and standard deviation, $x_k^{\ast }$ average number is 0, standard deviation is 1.

According to each sample original indicator observation value $x_{ik}^{\ast }$ or after standardization observation value $x_{ik}$, it solves coefficient $b_{kj}$, establish indicator $x_k^{\ast }$ that is transformed through standardization to express comprehensive indicator $z_j$ equation

$z_j={\displaystyle \sum _k{b}_{kj}{x}_k^{\ast }}$

which can also establish equation that uses original indicator $x_k$ to express comprehensive indicator $z_j$

$$z_j={\displaystyle \sum _k{\tilde{b}}_{\mathit{kj}}{x}_k^{\ast }+a_j}$$ (2)

There are two requirements on defining ：

(1) Comprehensive indicators are mutual independent from each other or uncorrelated.

(2) Every comprehensive indicator reflected each sample gross information content is equal to corresponding feature vector (comprehensive indicator coefficient) feature values. In general, it is required that selected comprehensive indicator feature vales contribution ratios sum to be above.

3.2. Principal Component Analysis General Steps

(1) According to observed data, calculate $\overline{x_k}$ and $s_k\left(k,j=1,2,\cdots ,m\right).$

(2) By correlation coefficient matrix, it can get feature value $R\mathit{and}\left(j=1,2,\cdots ,m\right)$ each principal component variance contribution, contribution ratio and accumulative contribution ratio, p and define principal component reserved number with accumulative contribution ratio as evidence.

(3) m pieces of basic equations are as following：

$$\left\{\begin{array}{c}{r}_{11}{x}_1^{\left(j\right)}+r_{12}{x}_2^{\left(j\right)}+...+r_{1m}{x}_m^{\left(j\right)}={\mathrm{\lambda }}_j{x}_1^{\left(j\right)}\\ r_{21}{x}_1^{\left(j\right)}+r_{22}{x}_2^{\left(j\right)}+...+r_{\mathit{2m}}{x}_m^{\left(j\right)}={\mathrm{\lambda }}_j{x}_2^{\left(j\right)}\\ ...\\ r_{m1}{x}_1^{\left(j\right)}+r_{m2}{x}_2^{\left(j\right)}+...+r_{\mathit{mm}}{x}_m^{\left(j\right)}={\mathrm{\lambda }}_j{x}_m^{\left(j\right)}\end{array}\right.$$ (3)

Among them $j=1,2,...,m.$

Proceed with Schmidt orthogonalization, for every ${\mathrm{\lambda }}_i$, solve its basic equations solution

$x_1^{(j)},x_2^{(j)},...,x_m^{(j)}\left(j=1,2,...,m.\right)$

and then let

$$b_{\mathit{kj}}=\frac{x_k^{\left(j\right)}}{\sqrt{\sum _k{\left(x_k^{\left(j\right)}\right)}^2}}$$ (4)

It can get expressed by $x_1^{\ast },x_2^{\ast },...,x_m^{\ast }$ principal component

$z_j={\displaystyle \sum _k{b}_{kj}{x}_k^{\ast }}\mathit{or}\mathit{input}{x}_k^{\ast }=\frac{x_k-\overline{x_k}}{s_k}$

and then get $x_1,x_2,...,x_m$ expressed principal component .

(4) Input $x_1,x_2,...,x_m$ observed values into principal component expressions, calculate each component value.

(5) Calculate original indicator and principal component correlation coefficient that is also factor loading so that explain principal component significances.

3.3. Principal Component Analysis Result

For dietary habits investigation result, it makes principal component analysis; result is as Fig. (1) shows.

Fig. (1).

Scree plot.

In Fig. (1)，“1” represents cereal intake amount，“2” represents fruit and vegetable intake amount，“3” represents protein intake amount，“4” represents fried food intake amount，“5” represents sugared beverage intake amount. From the figure, it is clear that cereal intake amount is principal component in dietary habits, therefore regard cereal intake as analysis factor.

Targeted at physical exercises, it makes principal component analysis, and can get Fig. (2).

Fig. (2).

Scree plot.

In Fig. (2)，“1” represents strenuous exercises，“2” represents general exercises，“3” represents physical exercises，“4” represents electronic entertainment. From Fig. (2), it is clear that strenuous exercise and general exercise are main factors that affect physical exercises.

In the following, utilize neural network model, establish evaluation model targeted at dietary habits and physical exercises.

4. NEURAL NETWORK MODEL

4.1. Neural Network Model Concept

Neural network model is originated from neurobiology. Its computation process is similar to biology nerve cell reaction process. In neural network, lots of different nerve cells contained axon ends could enter into the same nerve cell Dendron and form into lots of synapses. All synapses of different origins liberative neurotransmitter can exert effects on same nerve cell membrane potential. Therefore, it is clear that nerve cell space integrated information capacity that nerve cell can make integration on input information of different origins in Dendron. Base on the capacity, people imitate nerve cell reaction process and create artificial nerve cell model as Fig. (3) shows. Symbols description in Figure is as Table 3.

Fig. (3).

The schematic of mathematical models of neurons.

Table 3.

Mathematical model’s symbol definition.

Symbol	Definition
$x_1,x_2,\cdots ,x_n$	Nerve cell input part that is information released by previous level
${\mathrm{\theta }}_i$	Nerve cell threshold value
$y_i$	Nerve cell output
$f\left[u_1\right]$	Excitation function

$f\left[u_1\right]$ decides that output form that arrives at threshold value θ_i under common effects of inputting $x_1,x_2,\cdots ,x_n$. Fig. (4) shows two kinds of excitation functions images. The paper adopted models use the second kind excitation function.

Fig. (4).

Typical excitation functions.

Among them，

$$u_i=\sum _j{w}_{\mathit{ij}}{x}_i-\mathrm{\theta }$$ (5)

Therefore

$$y_i=f\left[u_i\right]=f\left(\sum _j{w}_{\mathit{ij}}-{\mathrm{\theta }}_i\right)$$ (6)

Formula (2) is individual nerve cell full mathematical model expression.

4.2. BP Neural Network Model Computational Steps

BP Neural network is a kind of multiple layer forward network, adopts minimum mean square error computational way. When apply counter propagation algorithm into feed forward multiple network, utilize Sigmoid as excitation function, use following steps to make recursion solving on $w_{ij}$ that is network weight coefficient. In case every layer has n pieces of nerve cells, for the k layer the i nerve cell, then it has n pieces of weight coefficients $w_{i1},w_{i2},\cdots ,w_{jn}$. In addition, select one more $w_{jn+1}$ to express ${\mathrm{\theta }}_i$. When input sample x, take $x=\left(x_1,x_2,\cdots ,x_n,1\right)$.

① Align value to $w_{ij}$. To every layer $w_{ij}$, align a very little nonzero random number, and meanwhile $w_{jn+1}=-{\mathrm{\theta }}_i$^o Due to the model utilizes Matlab to operate, the alignment process is computer’s random process, and just because of that, same programming codes in different running processes, the results may appear differences.

② Input sample value $x=\left(x_1,x_2,\cdots ,x_n,1\right)$ and corresponding expected output $y=\left(y_1,y_2,\cdots ,y_n,1\right)$.

③ Calculate each layer output, for the k layer the i nerve cell output $x_{ik}$, it has:

$$y_i^k=f\left[u_i^k\right]$$ (7)

Among them

$$u_i^k=\sum _j{w}_{\mathit{ij}}{x}_j^{k-1}-{\mathrm{\theta }}_i^k$$ (8)

In formula, $x_{n+1}^{k-1}=1,w_{i\left(n+1\right)}=-\mathrm{\theta }$

④Solve each layer computation error $d_i^k$, for output layer, it has k = m, then it has:

$$d_i^m=x_{\mathrm{i}}^m\left(1-x_i^m\right)\left(x_i^m-y_i^m\right)$$ (9)

For other layers, it has

$$d_i^k=x_i^k\left(1-x_i^k\right)\left(\sum _j{w}_{\mathit{ij}}{x}_j^{k-1}-{\mathrm{\theta }}_i^k\right)$$ (10)

⑤ Correct $w_{\mathit{ij}}\mathit{and}{\mathrm{\theta }}_i$, it has

$$w_{\mathit{ij}}\left(t+1\right)=w_{\mathit{ij}}\left(t\right)-\mathrm{\eta }{d}_i^k{x}_j^{k-1}$$ (11)

⑥After solving each layer each weight coefficient, it can judge whether it conforms to requirements according to established criterion. If it don’t conform, then return to the step ③, on the contrary, end computing.

4.3. Model Establishment

Regard dietary habits and physical exercises principal components as evaluation objects that dietary habits is vertical coordinate, physical exercises is horizontal coordinate. According to experiences, set up dietary habits and physical exercises feature values, feature values distribution is as Fig. (5).

Fig. (5).

Eigen value distribution.

Input principal component analysis result factor parameters into the model, through Matlab operational calculation, and then can get Fig. (6).

Fig. (6).

Evaluation results diagram.

CONCLUSION

It is clear from Figure 6 that Shenzhen is a city of better physical exercises and dietary habits that lies in the bottom of boundary, but closely links to boundary. Except for Shenzhen, Beijing, Shanghai, Guangzhou, Shijiazhuang, Tianjin and Baotou, all of them don’t reach the standard; thereupon it is clear about necessity of China developing physical exercises and dietary habits. The paper utilizes principal component analysis approach, takes BP neural network as theoretical basis, establishes evaluation model, states theoretically Chinese physical exercises and dietary habits current status. As far as practical life issues are concerned, it still needs to make specific analysis and presents corresponding improvement measures.

CONFLICT OF INTEREST

The authors confirm that this article content has no conflict of interest.