# Compression and Storage Algorithm of Key Information of Communication Data Based on Backpropagation Neural Network

Authors: Dahuan Wei; Gang Feng
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

This paper presents a backpropagation neural network algorithm for data compression and data storage. Data compression or establishing model ten coding is the most basic idea of traditional data compression. The traditionally designed ideas are mainly based on reducing the redundancy in the information and focus on the coding design, and its compression ratio has been hovering around dozens of percent. After the traditional coding compression of information, it is difficult to further compress by similar methods. In order to solve the above problems, the information that takes up less signal space can be used to represent the information that takes up more signal space to realize data compression. This new design idea of data compression breaks through the traditional limitation of relying only on coding to reduce data redundancy and achieves a higher compression ratio. At the same time, the information after such compression can be repeatedly compressed, and it has a very good performance. This is the basic idea of the combination of neural network and data compression introduced in this paper. According to the theory of multiobjective function optimization, this paper puts forward the theoretical model of multiobjective optimization neural network and studies a multiobjective data compression method based on neural network. According to the change of data characteristics, this method automatically adjusts the structural parameters (connection weight and bias value) of neural network to obtain the largest amount of data compression at the cost of small information loss. This method has the characteristics of strong adaptability, parallel processing, knowledge distributed storage, and anti-interference. Experimental results show that, compared with other methods, the proposed method has significant advantages in performance index, compression time and compression effect, high efficiency. and high-quality robustness.


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## Body

## 1. Introduction

In large-scale database, the storage and analysis of its internal information and complex data usually take a lot of space and time, which cannot meet the practical application. How to compress the data efficiently becomes particularly important. In computer network data communication [1–3], the amount of information transmission is increasing, and the bottleneck of communication transmission is becoming more and more obvious. While improving the efficiency of transmitting effective information, people attach great importance to the rational use of existing communication conditions and equipment to compress a large amount of data and improve its accuracy and performance.Abenstein and Tompkins [4] proposed a lossless and lossy compression coding based on grid data. Firstly, the bidirectional correspondence between Gosper curve and regular hexagonal grid data is established to provide guidance support for data encoding and decoding. Then, the Gosper coding value of each grid unit is determined, and the coding set of the target area unit is run length coded to realize the lossless compression of the data. According to the curve trend, the attribution of some grid cells is changed to reduce the number of coding objects, and run length coding is carried out again to simplify and compress the coding amount. Experimental results show that the proposed method has good compression performance.Hudson et al.[5] proposed a data transmission and compression method based on spatiotemporal compression network coding. It makes full use of the temporal and spatial correlation of data, adopts the compressed network coding method containing the selection of intermediate nodes, avoids the redundant transmission of data to a certain extent, and uses the idea of K-SVD to obtain the best time observation matrix by training the time sparse dictionary, so as to promote the better compression of data information. Experimental results show that the proposed method can significantly reduce the data information and improve the accuracy of data compression.Although the above two methods have high compression accuracy, they spend too much time in operation, do not have high requirements for processing time, and do not have scalability [6]. The method proposed in this paper compresses mobile communication data efficiently based on big data technology and further implements reconstruction processing through wavelet transform, so as to obtain high compression accuracy, reliability, and scalability.


### 1.1. Traditional Data Compression Ideas

Redundant information in a message takes up additional bits to encode, and if additional information is to be removed, the size of the message will be reduced. In order to compress the data better, a model with high probability of predicting symbols is needed [7]. Symbols with high probability have low information content and only need less bits to encode. This is the basic idea of traditional data compression, that is, data compression = model building + coding. The traditional design idea is mainly based on reducing redundancy in information, focusing on coding design, and has made considerable achievements, which will not be described in detail here. However, with the traditional design idea, the compression ratio has been hovering around dozens of percent, so it is difficult to make further progress. In addition, the information compressed by traditional coding is difficult to be further compressed by similar methods. These two problems cannot be solved by traditional design ideas.


### 1.2. New Data Compression Ideas

Since the redundancy of information representation can be reduced through appropriate coding to achieve the purpose of data compression, can we also find a suitable method to use other information that occupies less signal space to represent information that occupies more signal space to achieve data compression? The answer is yes. The key is to establish the mapping relationship between the information occupying less signal space and the information occupying more signal space. This is the new design idea of data compression. In this way, it breaks through the traditional limitation of reducing data redundancy only by coding and achieves a higher compression ratio. At the same time, the compressed information can be compressed repeatedly and has good performance [8]. Theoretically, such a compression method can repeat the compression until a satisfactory compression ratio is obtained.The proposed idea of data compression breaks through the traditional obstacles and enables people to further compress information. But its meaning is not only that; there are many excellent compression algorithms, which have their own advantages and disadvantages. It is difficult to find the best and most common algorithm in all aspects. Moreover, the environment and purpose of using the algorithm change from time to time and the requirements for compression are also different. Each algorithm has its own application occasions. It is necessary to study and improve the information processing methods and methods in a specific field. Based on the compression results of existing algorithms, less information is used to represent the information that has reduced the redundancy to the minimum according to new ideas, so as to compress the signal space to the greatest extent, and the existing compression results in various fields can be used. It can also save much more signal space than the other competing methods.


### 1.3. Efficient Compression Method of Mobile Communication Data under Big Data Technology

Big data technology has been widely used, and the collection is very fast. From it, accurate and important data information can be extracted, used, and analyzed [9].Firstly, distributed processing is implemented for big data, which can complete data processing according to its effectiveness and scalability. Big data technology can store and process massive data information with high reliability. It can also be used on the computer to reasonably divide the data between nodes and complete the operation, which has high scalability. It can dynamically move data between nodes to keep it peaceful and improve the processing speed, which is efficient. Finally, it can automatically store many copies of data, can reassign failed tasks, and has high fault tolerance.Efficient compression of mobile communication data describes the compression processing of a large number of communication data, which needs to remove unnecessary redundancy, save a large amount of internal storage space, reduce running time, and improve its performance to a great extent. The flow chart of data compression is shown in Figure1.Figure 1
Data compression flow chart.It can be seen from Figure1 that the original data is preprocessed, and the compression is completed using this procedure, and finally the efficient compression data is obtained. This compression technology is widely used by people and is applicable.


## 1.1. Traditional Data Compression Ideas

Redundant information in a message takes up additional bits to encode, and if additional information is to be removed, the size of the message will be reduced. In order to compress the data better, a model with high probability of predicting symbols is needed [7]. Symbols with high probability have low information content and only need less bits to encode. This is the basic idea of traditional data compression, that is, data compression = model building + coding. The traditional design idea is mainly based on reducing redundancy in information, focusing on coding design, and has made considerable achievements, which will not be described in detail here. However, with the traditional design idea, the compression ratio has been hovering around dozens of percent, so it is difficult to make further progress. In addition, the information compressed by traditional coding is difficult to be further compressed by similar methods. These two problems cannot be solved by traditional design ideas.


## 1.2. New Data Compression Ideas

Since the redundancy of information representation can be reduced through appropriate coding to achieve the purpose of data compression, can we also find a suitable method to use other information that occupies less signal space to represent information that occupies more signal space to achieve data compression? The answer is yes. The key is to establish the mapping relationship between the information occupying less signal space and the information occupying more signal space. This is the new design idea of data compression. In this way, it breaks through the traditional limitation of reducing data redundancy only by coding and achieves a higher compression ratio. At the same time, the compressed information can be compressed repeatedly and has good performance [8]. Theoretically, such a compression method can repeat the compression until a satisfactory compression ratio is obtained.The proposed idea of data compression breaks through the traditional obstacles and enables people to further compress information. But its meaning is not only that; there are many excellent compression algorithms, which have their own advantages and disadvantages. It is difficult to find the best and most common algorithm in all aspects. Moreover, the environment and purpose of using the algorithm change from time to time and the requirements for compression are also different. Each algorithm has its own application occasions. It is necessary to study and improve the information processing methods and methods in a specific field. Based on the compression results of existing algorithms, less information is used to represent the information that has reduced the redundancy to the minimum according to new ideas, so as to compress the signal space to the greatest extent, and the existing compression results in various fields can be used. It can also save much more signal space than the other competing methods.


## 1.3. Efficient Compression Method of Mobile Communication Data under Big Data Technology

Big data technology has been widely used, and the collection is very fast. From it, accurate and important data information can be extracted, used, and analyzed [9].Firstly, distributed processing is implemented for big data, which can complete data processing according to its effectiveness and scalability. Big data technology can store and process massive data information with high reliability. It can also be used on the computer to reasonably divide the data between nodes and complete the operation, which has high scalability. It can dynamically move data between nodes to keep it peaceful and improve the processing speed, which is efficient. Finally, it can automatically store many copies of data, can reassign failed tasks, and has high fault tolerance.Efficient compression of mobile communication data describes the compression processing of a large number of communication data, which needs to remove unnecessary redundancy, save a large amount of internal storage space, reduce running time, and improve its performance to a great extent. The flow chart of data compression is shown in Figure1.Figure 1
Data compression flow chart.It can be seen from Figure1 that the original data is preprocessed, and the compression is completed using this procedure, and finally the efficient compression data is obtained. This compression technology is widely used by people and is applicable.


## 2. Data Compression Based on Neural Networks

At present, due to its autonomous learning function, deep learning has become a research hotspot in the fields of natural language understanding, speech recognition, computer vision, and image processing. Among them, convolutional neural network, cyclic neural network, and multilayer sparse automatic encoder have been applied to image compression coding, smart meter data compression, and high-throughput genome data lossless compression. As a neural network model with the ability to learn arbitrary complex mappings and form widely applicable approximate functions, recurrent neural network RNN can predict the next character in the sequence very effectively and show excellent prediction performance [10]. Therefore, this paper adopts the lossless compression principle based on prediction to construct the cyclic neural network model as the conditional probability predictor of sequence data. After a large number of sample training, the weights of neural network model are saved. In the compression process, the saved weights of neural network model are loaded to calculate the probability distribution of characters in the data stream, and the adaptive arithmetic encoder updates the probability interval of the character and encodes the output according to the distribution and the current character to be encoded [11]. When decoding, the adaptive arithmetic encoder outputs the decompressed character sequence according to the probability distribution output by the neural network model. Through the compression results on the one-dimensional conventional data and two-dimensional array data of the actual wells in SL oilfield, as well as the comparison with the traditional compression method LZW and arithmetic coding, the effectiveness of the compression method in improving the data compression rate is verified. In order to improve the utilization efficiency of compressed data, combined with the data compression method, this paper writes the compressed data into the database and constructs a multidimensional index data query tree combined with relevant information and the unique ID randomly assigned during data writing. Compared with the traditional data query methods, the effectiveness of the data query tree strategy in improving the efficiency of data query and retrieval is verified.Through careful analysis and comparison between the idea of data compression technology and some algorithms of neural network, it is found that some neural network algorithms and ideas can meet the requirements of the above new ideas. There is a well-known algorithm in neural network, BP algorithm. BP algorithm is a very effective algorithm [12–14], and many problems can be solved by it. Rumelnart developed BP algorithm in 1985. Its basic idea is as follows:(1)
The state propagates forward, and the input mode is transmitted from the input unit to the hidden layer unit.A: The hidden layer unit is processed layer by layer and transmitted to the output unit;B: Output mode of transmission and distribution vehicle.(2)
Error backpropagation generates error signals from the actual output mode and expected output mode of the network.A: The error signal propagates back along the connection path;B: The connection weights between neurons in each layer are modified layer by layer.(3)
The network is trained repeatedly. For a given training mode, the above process is repeated until the error meets the requirements.Through a multilayer feedforward network, the input information is learned under the guidance of teacher signals. The network has not only input layer nodes and output layer nodes, but also hidden layer nodes (which can be one or more layers). For the input signal, it should first propagate forward to the hidden layer contact, after passing through the transfer function, then propagate the output information of the hidden layer node to the output node, and finally give the output result. The transfer function of hidden layer nodes usually selects sigmoid function, such asfx=1/1+e−x, which is used because of its nonlinearity and flexibility. BP model has become one of the important models of neural network. Its network topology is shown in Figure 2.Figure 2
BP network topology.The working principle of BP network is as follows:(1)
Define tokenk is the sample sequence;Yk is the output sample;Y^k is the actual output of the network;Oik is the output of unit i;Wij is the connection weight from unit i to unit j;netjk is the total input of unit j;ξ is the error set;η>0 is the learning factor.(2)
Weight correction formula:(1)ΔkWij=ηξjkOik.(3)
Error adjustment formula of output layer unit:(2)ξjk=Y^k−Ykf′netjk,wheref is the translation function.(4)
Error adjustment formula of hidden layer element:(3)ξjk=f′netjk∑ξmk⋅Wmj,wherem is the order of the neuron located in the above layer.Since the neural network can obtain the mapping between input and specified output through learning, if the number of hidden layer units is much less than the number of input layers, a mapping between input and output is established. Then, a relatively small number of hidden layer units can represent more output layer units [15]. This is the basic idea of the combination of neural network and data compression; that is, choose the BP network structure with as few hidden units as possible, take the possible binary number set (such as ASCII A codeword of characters) as input, or learn the file to be compressed directly, select the ASCII T code of a certain length string according to the scanning order as the input mode, and specify its output signal as its own and learn. At the end of the study, you can compress it. Scan the compressed file from beginning to end, input the characters or strings in turn according to the learning mode, and get the intermediate results of the hidden layer unit according to the network weight and output function after learning. Save the intermediate result sequentially, and you get a mapping file of the original file. Because the hidden layer unit is far less than the number of units in the input layer, the size of the mapping file is much smaller than the original file, achieving the compression effect. The compressed features of the image are stored in the hidden layer. This leads to the higher compression ration when the number of hidden neurons is smaller. The output layer ultimately results in the decomposed image to the external environment. When decompressing, because of the good stability of the BP network, the value of the mapping file is taken as the intermediate result of the hidden layer unit of the BP network, which is led to the output layer under the action of the original BP network, and the same output result as the original file is obtained, which achieves the effect of restoration. Based on this idea, the BP algorithm flow is modified to achieve the purpose of data compression.


## 3. Theory Model and Algorithm

### 3.1. RNN Probabilistic Predictor Model

In this paper, two-layer multi-input and multioutput gated cyclic unit (GRU) is used as RNN model to prevent gradient dispersion and weakening dependence on distant characters in the sequence. The neural network architecture is shown in Figure3.Figure 3
RNN probability predictor model.In the input layer, the EMBEDDING layer is added to map the input character to the m-dimensional vector space according to the single-layer neural network and the position of the character in the dictionary to characterize the score of the character in the M dimensions, so that the mutually independent input string vectors become internally related relationship vectors, which can be used to find the deep relationship between the input string vectors. This relationship is always updated in the backpropagation process of network model training. Therefore, after multiple epochs, this relationship can become relatively mature, which can correctly express the relationship between each input string, and the trained vector can better adapt to the task of data compression [16]. The number of GRU units in each layer is the length of the input character sequence N; at time t, each GRU unit outputs a 1,M dimension vector, and M is the output dimension of the GRU unit. In the second layer GRU, each GRU generates output to form a 1,N,M dimensional vector. At this time, the flatten layer is added to connect the 1,N,M dimensional vectors in series to form a 1,N×M dimensional vector, followed by the full connection layer FC with two activation functions: RELU and softmax. The number of neurons in the uppermost full connection layer is the number of character types K in the whole compressed data stream; in this way, the model can output the probability distribution of all categories of characters for the next adaptive arithmetic coding.GRU, as an extended RNN network unit structure with gated cycle unit, uses update gate and reset gate to solve the gradient dispersion problem in standard RNN while retaining long-term sequence information [17, 18]. The update gate adds the current input character information and the output information of the previous GRU unit after linear transformation, respectively, and transforms the output to 0∼1 through the sigmoid activation function to help the model determine the memory information of the previous step and the amount of information that the current input character information needs to continue to transfer. Similarly, the reset gate adds the current input character information and the output information of the previous GRU unit, respectively, after linear transformation and sends it to the sigmoid function to determine the information to be retained and forgotten. During the calculation of the current memory content, the reset gate is used to determine the elements to be retained and forgotten in the output of the previous GRU unit in the form of gating. Finally, the update gate is used to add the information that the output of the previous GRU unit is retained to the final memory and the information that the current memory content is retained to the final memory, that is, the final output content of the current GRU unit [19].


### 3.2. THE Proposed Model

With the rapid development of modern society, we are in an information explosion society. Data is the specific form of information. The huge amount of data makes storage and transmission very inconvenient. Therefore, many data compression technologies have been proposed. For example, the methods used for image data compression and coding include predictive coding, transform coding, and neural network-based methods. The methods used for ECG data compression include direct data processing method, transformation method, and neural network method.In order to compress data, a method based on neural networks automatically retrieves feature information that is concealed in the data. This technology has become increasingly popular because of its adaptive capabilities, parallel processing, rebuilt image, good waveform quality, and anti-interference. However, on the one hand, data compression must achieve the highest feasible data compression ratio while, at the same time, ensuring that as little effective information is lost as possible. ECG data compression can only be achieved with a local optimal solution if the present objective function neural network is still used, and the neural network is easy to go into local minima. A multiobjective data compression method built on a neural network is the focus of this paper, which applies the theory of multiple objective function optimization to the approach. Neural network learns under the guidance of multiple objective function, automatically adjusts neural network structural parameters (connection weights and biases), and extracts feature information hidden in data, which not only reaches highest compression ratio, but ensures that effective information is not lost or minimized as much as possible. An optimization neural network for multiobjective optimization is studied first, and then a multitarget data compression approach is proposed based on this model. Finally, a neural network-based multitarget ECG data compression method is shown. Experiments have shown that neural network-based multitarget data compression is both feasible and advanced.In a large number of engineering applications, there are often multiple objective functions as evaluation indexes. In this way, the simultaneous optimization of multiobjective functions can be described by the following mathematical problems:(4)minx⟶∈Xfx⟶=f1x⟶,f2x⟶,…,fmx⟶.Here,fx⟶=f1x⟶,f2x⟶,…,fmx⟶ is the multiobjective vector criterion function, x⟶ is the n-dimensional Euclidean space vector, and X is the constraint set.In multiobjective optimization problems, the concept of noninferior solution is generally used to describe the solution of vector function optimization. The so-called feasible decision vector,x⟶′∈X, is a noninferior solution; that is, there is no x⟶′∈X, so that the noninferior solution of fx⟶≤fx⟶′ multiobjective optimization problem (4) can be obtained by(5)minx⟶∈X∑i=1mWi⋅fix⟶,where Wi>0 and ∑i=1mWi=1. Under the convex constraints, x⟶ is totally decided by the Wi=wi1,wi2,…,wim. Thus, the multiobjective convex optimization problem can be solved by the optimization of the weighted and scalar problem (5).If the feedforward neural network is used to solve the above multiobjective optimization problem, the neural network is to minimize the energy function in the following form:(6)E=∑i=1mWi⋅fix⟶.According to (6), the learning equation of multiobjective optimization is derived as(7)dωijdt=−μ∑k=1mωk∂fkx⟶∂ωij,where μ is the learning rate of neural network, and fkx⟶k=1,2,…,m is the objective function, which is determined by the specific problem; wij is the connection weight between neuron i and neuron j and wk>0,∑k=1nwk=1.Data compression is also a multiobjective optimization problem; that is, useful information is required to lose as little or no data as possible. The data compression ratio is as high as possible. As an index to evaluate data compression, normalized RMS error (PRD) and correlation coefficient (CC) are used.(8)PRD=1/N∑i=1Nri−r⟶2−oi−o⟶21/N∑i=1Noi−o⟶2,CC=1/N∑i=1Noi−o⟶⋅ri−r⟶1/N∑i=1oi−o⟶2⋅1/N∑i=1Nri−r⟶2,where o is the value of sampling point i of the original waveform, ri is the value of sampling point i of the recovered waveform, o⟶ is the average value of each sampling point of the original waveform, and r⟶ is the average value of each sampling point of the recovered waveform.The error included inside the waveform is represented by PRD, while the accuracy of the recovered waveform is represented by CC. So, the multiobjective optimization neural network for data compression has the goal of minimizing the energy function, which can be written as(9)E=W1⋅Nd+W2⋅PPD+W3⋅1−CC,where Nd represents the number of neurons in the hidden layer, PRD represents the normalized RMS error, and CC represents the correlation coefficient. In multiobjective ECG data compression, the weight of compression ratio, the normalized RMS error, and the correlation coefficient are represented by W1, W2 and W3, respectively.According to (9), the first represents the structural optimization of neural network, which aims to improve the data compression ratio; the second represents the error contained in the waveform, which aims to reduce the total error of data recovery; and the third represents the correctness of waveform recovery, which is concerned with reducing the recovery error of each sampling point in each sampling point in (9). (9) may be used to obtain the learning equation for a neural network, which is denoted as follows:(10)dωijdt=−μ⋅∂E∂ωij=−μ⋅w1⋅∂Nd∂wij+W2⋅∂PRD∂wij+W3⋅−∂CC∂wij,where an is the learning rate of neural network, and W1, W2 and W3 are positive numbers less than 1, and W1+W2+W3=1.The structure of the neural network for multiobjective data compression is shown in Figure4. It is a three-layer feedforward neural network, including input layer, hidden layer, and output layer. The input of neurons in the input layer is sampling data; the hidden layer neuron automatically adjusts its connection weight and bias value with the input layer neuron according to the characteristic change of the data and extracts the characteristic information hidden in the data. According to the data feature information extracted by the hidden neuron, the output layer neuron obtains the offset value by automatically adjusting its connection weight with the hidden layer neuron and reconstructs the image or waveform after data compression.Figure 4
The neural network structure used for electrocardiogram data compression.


### 3.3. Compression and Decompression Strategy

In the compression strategy, for the initialn characters, the uniform a priori probability distribution is selected, and the adaptive arithmetic encoder is used for coding and compression. Then, the character is input into the RNN probability predictor loaded with the trained network model weight to obtain the probability distribution of each character. The adaptive arithmetic encoder obtains the probability distribution of each character according to the probability distribution and the N + 1 character value. Update the original character probability distribution and cumulative frequency to obtain a new probability interval for each character. Repeat this process, and finally lock the probability interval of character C1 to obtain the encoded data stream. The decompression process is symmetrical to the compression process, which is the inverse process of compression. The adaptive arithmetic encoder first decodes the first n characters using the uniform a priori probability distribution and then decodes the subsequent characters according to the character probability distribution obtained by the RNN probability predictor. Here, the arithmetic decoder also needs to update the character probability distribution every time to obtain a new character probability interval and decode the characters corresponding to the probability interval according to the probability interval in which the real number represented by the compressed data stream falls. In the decompression process, the RNN probability predictor also uses the trained network model weights, which can produce the same probability estimation as the compression process.


## 3.1. RNN Probabilistic Predictor Model

In this paper, two-layer multi-input and multioutput gated cyclic unit (GRU) is used as RNN model to prevent gradient dispersion and weakening dependence on distant characters in the sequence. The neural network architecture is shown in Figure3.Figure 3
RNN probability predictor model.In the input layer, the EMBEDDING layer is added to map the input character to the m-dimensional vector space according to the single-layer neural network and the position of the character in the dictionary to characterize the score of the character in the M dimensions, so that the mutually independent input string vectors become internally related relationship vectors, which can be used to find the deep relationship between the input string vectors. This relationship is always updated in the backpropagation process of network model training. Therefore, after multiple epochs, this relationship can become relatively mature, which can correctly express the relationship between each input string, and the trained vector can better adapt to the task of data compression [16]. The number of GRU units in each layer is the length of the input character sequence N; at time t, each GRU unit outputs a 1,M dimension vector, and M is the output dimension of the GRU unit. In the second layer GRU, each GRU generates output to form a 1,N,M dimensional vector. At this time, the flatten layer is added to connect the 1,N,M dimensional vectors in series to form a 1,N×M dimensional vector, followed by the full connection layer FC with two activation functions: RELU and softmax. The number of neurons in the uppermost full connection layer is the number of character types K in the whole compressed data stream; in this way, the model can output the probability distribution of all categories of characters for the next adaptive arithmetic coding.GRU, as an extended RNN network unit structure with gated cycle unit, uses update gate and reset gate to solve the gradient dispersion problem in standard RNN while retaining long-term sequence information [17, 18]. The update gate adds the current input character information and the output information of the previous GRU unit after linear transformation, respectively, and transforms the output to 0∼1 through the sigmoid activation function to help the model determine the memory information of the previous step and the amount of information that the current input character information needs to continue to transfer. Similarly, the reset gate adds the current input character information and the output information of the previous GRU unit, respectively, after linear transformation and sends it to the sigmoid function to determine the information to be retained and forgotten. During the calculation of the current memory content, the reset gate is used to determine the elements to be retained and forgotten in the output of the previous GRU unit in the form of gating. Finally, the update gate is used to add the information that the output of the previous GRU unit is retained to the final memory and the information that the current memory content is retained to the final memory, that is, the final output content of the current GRU unit [19].


## 3.2. THE Proposed Model

With the rapid development of modern society, we are in an information explosion society. Data is the specific form of information. The huge amount of data makes storage and transmission very inconvenient. Therefore, many data compression technologies have been proposed. For example, the methods used for image data compression and coding include predictive coding, transform coding, and neural network-based methods. The methods used for ECG data compression include direct data processing method, transformation method, and neural network method.In order to compress data, a method based on neural networks automatically retrieves feature information that is concealed in the data. This technology has become increasingly popular because of its adaptive capabilities, parallel processing, rebuilt image, good waveform quality, and anti-interference. However, on the one hand, data compression must achieve the highest feasible data compression ratio while, at the same time, ensuring that as little effective information is lost as possible. ECG data compression can only be achieved with a local optimal solution if the present objective function neural network is still used, and the neural network is easy to go into local minima. A multiobjective data compression method built on a neural network is the focus of this paper, which applies the theory of multiple objective function optimization to the approach. Neural network learns under the guidance of multiple objective function, automatically adjusts neural network structural parameters (connection weights and biases), and extracts feature information hidden in data, which not only reaches highest compression ratio, but ensures that effective information is not lost or minimized as much as possible. An optimization neural network for multiobjective optimization is studied first, and then a multitarget data compression approach is proposed based on this model. Finally, a neural network-based multitarget ECG data compression method is shown. Experiments have shown that neural network-based multitarget data compression is both feasible and advanced.In a large number of engineering applications, there are often multiple objective functions as evaluation indexes. In this way, the simultaneous optimization of multiobjective functions can be described by the following mathematical problems:(4)minx⟶∈Xfx⟶=f1x⟶,f2x⟶,…,fmx⟶.Here,fx⟶=f1x⟶,f2x⟶,…,fmx⟶ is the multiobjective vector criterion function, x⟶ is the n-dimensional Euclidean space vector, and X is the constraint set.In multiobjective optimization problems, the concept of noninferior solution is generally used to describe the solution of vector function optimization. The so-called feasible decision vector,x⟶′∈X, is a noninferior solution; that is, there is no x⟶′∈X, so that the noninferior solution of fx⟶≤fx⟶′ multiobjective optimization problem (4) can be obtained by(5)minx⟶∈X∑i=1mWi⋅fix⟶,where Wi>0 and ∑i=1mWi=1. Under the convex constraints, x⟶ is totally decided by the Wi=wi1,wi2,…,wim. Thus, the multiobjective convex optimization problem can be solved by the optimization of the weighted and scalar problem (5).If the feedforward neural network is used to solve the above multiobjective optimization problem, the neural network is to minimize the energy function in the following form:(6)E=∑i=1mWi⋅fix⟶.According to (6), the learning equation of multiobjective optimization is derived as(7)dωijdt=−μ∑k=1mωk∂fkx⟶∂ωij,where μ is the learning rate of neural network, and fkx⟶k=1,2,…,m is the objective function, which is determined by the specific problem; wij is the connection weight between neuron i and neuron j and wk>0,∑k=1nwk=1.Data compression is also a multiobjective optimization problem; that is, useful information is required to lose as little or no data as possible. The data compression ratio is as high as possible. As an index to evaluate data compression, normalized RMS error (PRD) and correlation coefficient (CC) are used.(8)PRD=1/N∑i=1Nri−r⟶2−oi−o⟶21/N∑i=1Noi−o⟶2,CC=1/N∑i=1Noi−o⟶⋅ri−r⟶1/N∑i=1oi−o⟶2⋅1/N∑i=1Nri−r⟶2,where o is the value of sampling point i of the original waveform, ri is the value of sampling point i of the recovered waveform, o⟶ is the average value of each sampling point of the original waveform, and r⟶ is the average value of each sampling point of the recovered waveform.The error included inside the waveform is represented by PRD, while the accuracy of the recovered waveform is represented by CC. So, the multiobjective optimization neural network for data compression has the goal of minimizing the energy function, which can be written as(9)E=W1⋅Nd+W2⋅PPD+W3⋅1−CC,where Nd represents the number of neurons in the hidden layer, PRD represents the normalized RMS error, and CC represents the correlation coefficient. In multiobjective ECG data compression, the weight of compression ratio, the normalized RMS error, and the correlation coefficient are represented by W1, W2 and W3, respectively.According to (9), the first represents the structural optimization of neural network, which aims to improve the data compression ratio; the second represents the error contained in the waveform, which aims to reduce the total error of data recovery; and the third represents the correctness of waveform recovery, which is concerned with reducing the recovery error of each sampling point in each sampling point in (9). (9) may be used to obtain the learning equation for a neural network, which is denoted as follows:(10)dωijdt=−μ⋅∂E∂ωij=−μ⋅w1⋅∂Nd∂wij+W2⋅∂PRD∂wij+W3⋅−∂CC∂wij,where an is the learning rate of neural network, and W1, W2 and W3 are positive numbers less than 1, and W1+W2+W3=1.The structure of the neural network for multiobjective data compression is shown in Figure4. It is a three-layer feedforward neural network, including input layer, hidden layer, and output layer. The input of neurons in the input layer is sampling data; the hidden layer neuron automatically adjusts its connection weight and bias value with the input layer neuron according to the characteristic change of the data and extracts the characteristic information hidden in the data. According to the data feature information extracted by the hidden neuron, the output layer neuron obtains the offset value by automatically adjusting its connection weight with the hidden layer neuron and reconstructs the image or waveform after data compression.Figure 4
The neural network structure used for electrocardiogram data compression.


## 3.3. Compression and Decompression Strategy

In the compression strategy, for the initialn characters, the uniform a priori probability distribution is selected, and the adaptive arithmetic encoder is used for coding and compression. Then, the character is input into the RNN probability predictor loaded with the trained network model weight to obtain the probability distribution of each character. The adaptive arithmetic encoder obtains the probability distribution of each character according to the probability distribution and the N + 1 character value. Update the original character probability distribution and cumulative frequency to obtain a new probability interval for each character. Repeat this process, and finally lock the probability interval of character C1 to obtain the encoded data stream. The decompression process is symmetrical to the compression process, which is the inverse process of compression. The adaptive arithmetic encoder first decodes the first n characters using the uniform a priori probability distribution and then decodes the subsequent characters according to the character probability distribution obtained by the RNN probability predictor. Here, the arithmetic decoder also needs to update the character probability distribution every time to obtain a new character probability interval and decode the characters corresponding to the probability interval according to the probability interval in which the real number represented by the compressed data stream falls. In the decompression process, the RNN probability predictor also uses the trained network model weights, which can produce the same probability estimation as the compression process.


## 4. Experimental Methods

### 4.1. Mobile Communication Data Compression Performance Index

This paper compresses mobile communication data based on big data technology. Data compression technology can be applied in many fields, so the conditions are different in many aspects. Measuring the quality of data compression technology and performance indicators is mainly based on three parts: compression ratio, reconstruction quality, and compression and decompression speed.(1)
Compression Ratio. Compression ratio is also described as compression multiple, which is mainly used to measure the quality of performance indicators of compression methods. First, setR to represent the compression ratio, and the expression can be obtained as follows:(11)R=Total data before compressionTotal data after compression.The BPH as a unit of the compression ratio represents a 1-bit equilibrium within the data after compression instead of theR bit before compression.(2)
Reconstruction Quality. When conducting reconstruction, the quality of reconstruction is usually evaluated based on subjective evaluation, but in communication data according on the following indicators as follows:The energy loss:(12)η=∑iNxi−xi∗2log10∧∑ixi2.The mean square error:(13)RMSE=1N∑ixi−xi∗2.The signal-to-noise ratio:(14)SNP=∑iNxi2∑iNxi−xi∗2.From the above formula, it can be concluded thatxi describes the input communication data, xi∗ describes the corresponding reconstruction data, and N describes the length of the input data, η describes the lost energy, RMSE describes the mean square deviation, and SNP describes the signal-to-noise ratio.(3)
The speed of compression and decompression and the speed of decompression are the primary indexes to judge the compression method. The compression method can be divided into symmetrical and subsymmetrical compression forms according to whether the compression process occurs in real time. For symmetric compression, the process is in real time and in progress. For asymmetric compression, only decompression occurs in real time, and compression is not in progress. The speed in the compression process is closely related to the compression algorithm. The compression speed can be used as the average compression cycle of each byte.


### 4.2. Results and Discussion

In order to verify the efficiency and practicability of this method, the simulation experiment platform is in Windows XP and MATLAB 7 0 language program, Intel Pentium 40 GHz, 256 MB memory, and iris data is used as the data set sample, which contains 180 sample points, with 4 characteristic attributes in each sample, 3 clustering categories, and 50 sample points in each category.The methods in this paper are compared with those in literature [1, 2], and the specific contents are shown in Table 1.Table 1
Comparison of compression time.
Data volume (MB)Compression time (S)Text methodLiterature [1]Literature [2]50216161003211315054626200650312508605930096767It can be concluded from Table1 that the decompression and compression speed of the method proposed in this paper is higher, faster than the other two competing methods, can save a lot of running time, and has obvious advantages.For mobile communication data, there will be more business transactions every day. The full table compression for billing bill format can reach 1 : 4. If the compression format is optimized, the compression ratio will increase to 1 : 10.In the compressed billing library, the production table is 1.2 g and takes 6 minutes. Compressing the database of 1t according to the operation will take up to 1H. If the monthly traffic reaches 3T, the service idle time is about 12h, and then the compression of the total historical traffic of this month can be completed.Before and after mobile communication data compression, its query speed has been greatly improved; that is, the ratio is 3 : 1. In normal use, its performance will be improved by about 60%. Its specific compression performance is shown in Figure5.Figure 5
Compression results performance. (a) Storage occupation comparison chart. (b) Degree of compression.
(a)(b)It is obvious from Figure5 that the mobile communication data compression method proposed in this paper can complete the task of data compression more quickly and meet the actual needs in many aspects of data compression speed compared with other methods; at the same time, it can also deal with the fluctuation of abnormal data and promote the accuracy and accuracy of data under the condition of effectively ensuring a certain compression ratio. The accuracy is greatly improved, and the problem of large redundant information in the compression algorithm is effectively alleviated.


## 4.1. Mobile Communication Data Compression Performance Index

This paper compresses mobile communication data based on big data technology. Data compression technology can be applied in many fields, so the conditions are different in many aspects. Measuring the quality of data compression technology and performance indicators is mainly based on three parts: compression ratio, reconstruction quality, and compression and decompression speed.(1)
Compression Ratio. Compression ratio is also described as compression multiple, which is mainly used to measure the quality of performance indicators of compression methods. First, setR to represent the compression ratio, and the expression can be obtained as follows:(11)R=Total data before compressionTotal data after compression.The BPH as a unit of the compression ratio represents a 1-bit equilibrium within the data after compression instead of theR bit before compression.(2)
Reconstruction Quality. When conducting reconstruction, the quality of reconstruction is usually evaluated based on subjective evaluation, but in communication data according on the following indicators as follows:The energy loss:(12)η=∑iNxi−xi∗2log10∧∑ixi2.The mean square error:(13)RMSE=1N∑ixi−xi∗2.The signal-to-noise ratio:(14)SNP=∑iNxi2∑iNxi−xi∗2.From the above formula, it can be concluded thatxi describes the input communication data, xi∗ describes the corresponding reconstruction data, and N describes the length of the input data, η describes the lost energy, RMSE describes the mean square deviation, and SNP describes the signal-to-noise ratio.(3)
The speed of compression and decompression and the speed of decompression are the primary indexes to judge the compression method. The compression method can be divided into symmetrical and subsymmetrical compression forms according to whether the compression process occurs in real time. For symmetric compression, the process is in real time and in progress. For asymmetric compression, only decompression occurs in real time, and compression is not in progress. The speed in the compression process is closely related to the compression algorithm. The compression speed can be used as the average compression cycle of each byte.


## 4.2. Results and Discussion

In order to verify the efficiency and practicability of this method, the simulation experiment platform is in Windows XP and MATLAB 7 0 language program, Intel Pentium 40 GHz, 256 MB memory, and iris data is used as the data set sample, which contains 180 sample points, with 4 characteristic attributes in each sample, 3 clustering categories, and 50 sample points in each category.The methods in this paper are compared with those in literature [1, 2], and the specific contents are shown in Table 1.Table 1
Comparison of compression time.
Data volume (MB)Compression time (S)Text methodLiterature [1]Literature [2]50216161003211315054626200650312508605930096767It can be concluded from Table1 that the decompression and compression speed of the method proposed in this paper is higher, faster than the other two competing methods, can save a lot of running time, and has obvious advantages.For mobile communication data, there will be more business transactions every day. The full table compression for billing bill format can reach 1 : 4. If the compression format is optimized, the compression ratio will increase to 1 : 10.In the compressed billing library, the production table is 1.2 g and takes 6 minutes. Compressing the database of 1t according to the operation will take up to 1H. If the monthly traffic reaches 3T, the service idle time is about 12h, and then the compression of the total historical traffic of this month can be completed.Before and after mobile communication data compression, its query speed has been greatly improved; that is, the ratio is 3 : 1. In normal use, its performance will be improved by about 60%. Its specific compression performance is shown in Figure5.Figure 5
Compression results performance. (a) Storage occupation comparison chart. (b) Degree of compression.
(a)(b)It is obvious from Figure5 that the mobile communication data compression method proposed in this paper can complete the task of data compression more quickly and meet the actual needs in many aspects of data compression speed compared with other methods; at the same time, it can also deal with the fluctuation of abnormal data and promote the accuracy and accuracy of data under the condition of effectively ensuring a certain compression ratio. The accuracy is greatly improved, and the problem of large redundant information in the compression algorithm is effectively alleviated.


## 5. Conclusion

The proposed idea of using neural network to realize data compression is a breakthrough in itself. It will certainly drive the development of a new field of research. This method has also prompted people to take more consideration of the compression of their own compression results, have a new understanding of the compression limit, and create a new world of compression theory. Data compression technology is one of the hot technologies urgently needed in the modern information society, and there are still many aspects worth studying. Now, not only the above methods, but also many new theories and technologies are emerging one after another. Wavelet transform and fractal compression have become new hotspots of data compression. The data compression technology combined with neural network mentioned above will also occupy a place and will continue to promote the intelligence and automation of information processing on this basis. According to the multiobjective optimization theory, this paper studies the multiobjective data compression algorithm based on neural network, which has been successfully applied to ECG data compression and achieved satisfactory results. When processing or analyzing big data, the growth of data shows a straight-line upward trend, and further compression of big data becomes particularly important. In this paper, wavelet transform is used for processing, and then reconstruction is carried out according to MDL function. Finally, a method with high-precision compression effect and high reconstruction accuracy is obtained. Experimental results show that, compared with other methods, the proposed method has significant advantages in performance index, compression time and compression effect, high efficiency, and high-quality robustness.



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*Source: 2885735-2022-04-14.xml*