# Multilevel Information Granule Construction Model Based on Large Data Environment and Its Application in Time Series

Authors: Dongxian Yu; Jian Xiao
Journal: Mobile Information Systems
 (2022)

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## Abstract

Considering the uneven distribution of time series data in time windows, this paper designs an information granulation method based on the idea of “multigranularity,” and uses multilayer information granularity to construct the prediction model of time series. Firstly, a multigranularity time series model is established by applying binary relation on the time axis of time series data, and an evaluation effect function of time series data mining is introduced for the purpose of forecasting tasks. Based on this function, the optimal time granularity of prediction is found. In view of the uncertainty of time series, a multidimensional matrix model of attributes of sequence data is constructed, and the clustering category information of each attribute is obtained by clustering operation on the matrix model. Finally, the clustered data are classified by machine learning method to obtain classification knowledge. Prediction is achieved by classifying knowledge. Finally, the ICU data were used to predict the life and death of ICU patients to test the predictive effect of granular computing on time series data. The experimental results show the following: (1) the proposed method is superior to the traditional time series analysis and modeling methods. (2) When EM clustering algorithm, optimal time granularity and ID3 decision tree algorithm are used, the prediction rate of ICU mortality can reach 92.13% by using ICU time series data.


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## Body

## 1. Introduction

Time series data exist in many fields such as nature, finance, medicine, and so on. It objectively records the important information of the observed system at every time point. As the output of the observed system, time series often implies some specific laws and potential characteristics of the system. Therefore, time series analysis and modeling has been widely studied. Early researchers used the linear system theory, black box methodology, and fuzzy set theory to analyze and model time series and obtained many classical time series models, such as AR series model [1], artificial neural network model [2], Bayesian model [3], and fuzzy time series model [4]. These models have been applied in various fields and achieved good results. However, in the context of today’s big data era, time series are characterized by high-dimensional data representation, massive data, and complexity of data structure, which makes some traditional time series analysis and modeling methods cannot fully meet the practical application needs. The main manifestations are as follows: (1) the traditional time series analysis and modeling methods are essentially “numerical” centered, when the data sample size is huge, and the “interpretability” of the time series model constructed by the traditional time series modeling methods will be greatly reduced. (2) Traditional models cannot deal with the relationship between the dimensions of complex time series, which leads to poor results in dealing with complex time series data. (3) The models constructed by traditional time series analysis and modeling methods are all output in the form of specific “digital values.” Such output is difficult to understand and recognize in large data environments. Therefore, many researchers have tried other methods to deal with time series in large data environments. In reference [5], the convolution neural network is introduced to the mining of time series data. Reference [6] proposes the use of recurrent neural network (RNN) to solve the prediction and repair of complex time series. Bettini et al. [7] proposed for the first time that the size of time interval in time series should be regarded as time granularity. Time granularity function is used to express multiple description levels in time series and then mining frequent association patterns at different levels. Ruan et al., combined the granulation of fuzzy information with support vector machine, proposed a time series model of fuzzy granular support vector machine [8]. In these studies, the introduction of granular computing into time series analysis is the main research.Granular computing is a natural model to simulate human thinking and solving large-scale complex problems. It improves computing efficiency by granulating complex data and replacing samples with information granules. In granular computing, the transformation of deterministic information and uncertain information can be achieved by changing granularity; the data scale of original data can be reduced by abstract summary representation of the finest granular raw data by granular structure; and the time efficiency of solution can be improved by establishing domain-oriented granular structure. At present, there are many research results on time series analysis using granular computing. In [9], Hryniewicz and Kaczmarek integrated information granules into the Bayesian posterior estimation process, proposed a Bayesian probability prediction model of time series based on granular computing. In [10], M. Y. Chen and B. T. Chen used the discrete iteration method based on entropy to degranulate the domain of fuzzy time series, and based on this, we constructed a hybrid fuzzy time prediction model to predict stock prices. Documents [11] Al-Hmouz et al. construct information particles in space by collecting amplitude and amplitude changes through time windows, and experiment with a series of time series data sets. Lu et al. transformed the original time series into granular time series, used different window widths to control the size of granulation, and analyzed the influence of granulation window size and granulation degree on the prediction results through experiments. In [13], Wang et al. applied the improved fuzzy C-means clustering algorithm and information granulation to the long-term prediction of time series. In [8], Ruan et al. combined the granulation of fuzzy information with support vector machines (SVM) to predict large-scale data rapidly by using FGSVM (fuzzy granular support vector machines). In [14], Vairavan et al. proposed the method of granulation of multigranularity information to analyze the trend of data transformation. Geometric models were constructed by using the topological grouping structure of moving objects in two-dimensional or high-dimensional space. The transformation trend of time-varying data was detected by adjusting granularity, support size and duration. Although there are many achievements in the research of time series analysis and modeling methods based on granular computing, some of these studies reduce the scale of time series data through information granules and some simplify the calculation through information granules. They only take advantage of some characteristics of granular computing and lack systematic methods for time series analysis and modeling based on granular computing. In addition, many studies use “single information granule,” that is, when granulating time series, only one granulation level is considered. This cannot reasonably reflect the different viewing angles of users. The information granulation of time series data at different granularity levels will help us to analyze and observe time series data from different levels according to the needs of the problem.Therefore, this paper proposes to improve the processing of time series data through granular computing in three aspects. Firstly, according to the high dimension of time series data, the ICU time series are granulated at different granularity levels, and the multigranularity time series model is established to reduce the original data scale. Aiming at the uncertainty of time series, the multidimensional matrix model is constructed on the basis of the multigranularity time series model. In order to reduce the difficulty of time series data processing, the multidimensional matrix model processing is divided into two steps. Firstly, the matrix model is clustered to get the clustering category information of each attribute. Then, the clustered data are classified by the machine learning method. Finally, this paper tests the predictive effect of the proposed method by using ICU data to predict the life and death of ICU patients. The experimental results show that when EM clustering algorithm, optimal time granularity, and ID3 decision tree algorithm are used, the prediction rate of ICU mortality can reach 92.13% by using ICU time series data.


## 2. Time Series Prediction Model Based on Multilayer Information Granules

### 2.1. Granule Computation

#### 2.1.1. Granular Computing Framework

Granular computing is a very active research field in computer science in recent ten years. By abstracting and dividing complex problems into several simpler ones, it helps to better analyze and solve problems. In the framework of granular computing, according to the actual problem itself, the problem information is granulated into information granules, which are calculated, processed, and returned to the results of processing. Figure1 shows the basic framework of granular computing.Figure 1
Basic framework for granular computing.In Figure1, information granule is the basic element of granular computing, which is a set of elements aggregated according to indistinguishability, similarity, similarity or functionality. In granular computing, the main task is to construct, represent, and process information granules. Information granules can be divided into different sizes, that is, the “information granularity” of information granules. For example, people can use different time intervals to granulate information and deduce information granules of different sizes (year, month, day, etc.). The size of information granules deduced implies the level of “information granularity” used in information granulation. Therefore, information granules are hierarchical, and the information granules generated at different granularity levels can be transformed into each other, as shown in Figure 2.Figure 2
Information granules and information granularity.In the process of granulation, there are two directions: construction and decomposition. Construction refers to how finer or lower grains are merged into coarser or upper grains. Convert “thinner” and “more special” information granules into “coarser” and “more general” information granules; on the contrary, decompose the coarser or upper granules into finer lower granules. That is to say, “coarser” and “more general” information granules are further refined into “thinner” and “more special” information granules. At present, the specific methods of granulation include fuzzy information granulation [15], rough set approximation [16], quotient space method [17], clustering-based granulation [18] and cloud model method [19–21].


#### 2.1.2. Basic Terms in Granular Computing

(1) Representation of Information Granules. Referring to the representation of topological space in quotient space, the information granules are formally described by triples, namely,(1)IG=KVS,GM,VM,where KVS (key value pair set) represents the feature subvector describing the information granule, i.e., KVS=key1,value1>,…,<keyn,valuen (i = 1, 2, …, n) and Valuei represents the value taken by a feature named Keyi in the information granule.GM (granularity measure) denotes the granularity measure of the information granule, i.e., the degree of granularity of the information granule. Its formula is [22](2)GMπ=∑i=1mXiUlog|Xi|Among them,π=X1,X2,…,Xm is a division of the universe U, and Xi is a subset of U. When the granularity is the finest, that is, each granule is a single point set, there is GMπ=0; when the granularity is the thickest, that is, the whole universe is a granule. GMπ=log|U| VM (value measure) represents the value measure of the information granule. Its determination is mainly from three aspects: granularity measurement, uncertainty, and domain knowledge.(2) Representation of Granular Layer. The granular layer (layer) consists of all information granules based on a certain granulation criterion and the relationship between them. The granular layer can be formally expressed as a binary group, that is, a binary group.(3)Layer=IGS,Intra−LR,where IGS (information granule set) represents a set of information granules in the granular layer, which can be expressed as IGS=IG1,IG2,…,IGM; intra-LR (intralayer relationships) represents possible relationships between information granules in the granular layer. If the information granule IGp and IGq is related to the existence, then Intra−LR=E/E=IGp,IGq,IGp,IGq∈IGS.(3) Representation of Granular Structure. The granular structure in MGrIKR is a topological structure consisting of multiple granular layers obtained by different granulation criteria, the relationship between information granules in different granular layers and the relationship between information granules in the same granular layer. Therefore, the granular structure GS (granular structure) can be expressed in tuple form:(4)GS=LS,Inter−LRAmong them,LS=Layer1,...,Layerm−1,Layerm represents a set of m granular layers Layer Set,LS, in which the granular layer Layerj is a granular layer in the granular structure. Inter-LR (interlayer relationships) denotes the set of transformation relations between two layers of Layerj and Layerk information granules, Inter−LR which can be expressed as(5)Inter−LR=rp|rpLayerj,Layerk⋅j,k=1,...,m.Among them,r < denotes the satisfied partial order relationship between Layerj and Layerk information granules, which can be the relationship between information granules in adjacent two granular layers, or the relationship between information granules across layers.


### 2.2. Framework for Time Series Analysis, Processing, and Modeling Based on Granular Computing

Sequential data in the era of large data have the characteristics of huge scale, dynamic and instability. Therefore, researchers have proposed a processing framework for time series data based on granular computing to simulate human granulation cognitive mechanism as shown in Figure3.Figure 3
Data sequence processing framework based on granular computing.


#### 2.2.1. Rational Information Granulation of Time Series

In order to reduce the scale of time series data, it replaces the original time series in a simple and clear form. Firstly, it divides the time series into several time windows and then granulates the data on each time window to transform the original time series into a time-related “information granule” sequence (granular time series). Suppose for a time seriesx=x1,x2,…,xn, firstly, the time series is divided into a P-time window T1,T2,…,Tk, and then the data on each time window Tii=1,…,k are granulated to form information granules λii=1,2,…p. Thus, the original time series X is transformed into corresponding granular time series λ=λ1,λ2,…λp by granulation of information.


#### 2.2.2. Time Series Analysis and Interpretation Based on Information Granulation

Time series analysis and interpretation takes “granular time series” as the research object. Semantic labels describing the dynamic characteristics of information granules are used as basic elements to describe each element in granular time series. It is assumed that there exists a set of granular semantic tagsL=L1,L2,…,Lh, in which ≤ p. This stage is to realize how to describe granular information λi with elements in the set L of semantic tags. Researchers have used fuzzy sets to achieve this, that is, to assign corresponding semantics to information granules λi: “Yes, λi is Lj, its matching degree is ϕij.” Some researchers also use clustering algorithm to divide P information granules into granular semantic tag set L according to their similarity.


#### 2.2.3. Time Series Modeling Based on Information Granulation

Time series modeling is to transfer domain knowledge by means of information granules and capture the main relational features of time series by logical association language. Because the granular model of time series is user-oriented, the output of the model can be understood and recognized by users, thus helping users to make reasonable decisions. Its input and output are information granules on the corresponding time window of time series. It is assumed that time series granular model describes the dynamic relationship between information granulesλj,…λi−2,λi−1,λi formed by time series in time windows Tj,…Ti−2,Ti−1,Ti.


### 2.3. Time Series Prediction Model Based on Multilayer Information Granules

Considering the data presented by time series in time window, the distribution of time series is mostly uneven. The information granules constructed by single information granularity may not capture the essential characteristics of data. Therefore, in order to reasonably granulate the information of time series data, this paper designs an information granulation method based on the idea of “multi-granularity.” Different information granularity levels are used to granulate the time series data on a time window to obtain information granularity at different information granularity levels. Finally, a time series prediction model based on multilevel information granules is proposed to predict ICU patient data. The basic flow of the prediction process is shown in Figure4.Figure 4
Forecasting process of the forecasting model.Specific steps are as follows: firstly, this paper establishes a multigranularity time series model by applying binary relationship on the time axis of time series data and introduces the evaluation effect function of time series data mining (the function of judging the accuracy of prediction) as the goal of prediction task. Based on this function, the optimal time granularity of prediction is found. In view of the uncertainty of time series, a multidimensional matrix model is constructed, and then the clustering category information of each attribute is obtained by clustering operation. Finally, the clustered data are classified by machine learning method to obtain classification knowledge. Forecasting can be achieved by classifying knowledge.


#### 2.3.1. Establishment of Multigranularity Time Series Model

In the research of time series prediction, the time domainUT is generally considered as a line segment. Therefore, this paper uses the form of the time axis to represent the time domain and assumes that the starting point of the time domain is a origin of the time axis, which is recorded as t0. The multigranularity time series ∑UT,AT,TS is defined as TS with multiple optional time granularities (indicating that AT values can be more than one) in a given time domain UT.General analysis is based on the different attributes of objects in the universe to analyze their values and describe them in the form of two-dimensional tables. In this paper, we slice the multidimensional time series and analyze one of its atomic points. The time series are divided intot0, t1, …, Tn, and the analysis of tI time points is studied. From this, a multigranularity time series model TGSUT,A,∗T,R of ICU is constructed, UT which is a time domain, A=AN∪AT, AN is a set of related attributes; AT is a set of time granularity attributes, and ∗ T is a set of time granularity atx∈AT attributes obtained by equivalence partition UTatx of R to UT formed according to different time granularity AT.


#### 2.3.2. Finding the Optimal Time Granularity for Prediction

Because the granularity is variable in constructing multigranularity time series model, the model can be used to predict different prediction effects. Therefore, in order to evaluate the performance of prediction based on different time grains in a given time domain, this paper uses the time series data mining evaluation functionFati∈AT to try to find the best time granularity in the model. The process of solving the optimal time granularity is shown in Figure 5.Figure 5
The process of finding the optimal time granularity.There are two stages:(i)
Optimal time granular search based on time domain.Assuming the time domainUT, the alternative I is based on the equivalence partition I=k1,k2,k3 of time granules, the evaluation effect function Fati∈AT of time series data mining, the diagnostic accuracy λ and the minimum time granularity amin. Firstly, according to the evaluation function, a partition is selected from the candidate I partition to get the granularity ati as the next time granularity set TGi.(iii)
Optimal time granular fine search based on time domain.The prediction results under eachTGi condition are evaluated in turn, and the algorithm ends if the accuracy is less than λ or less than the prescribed minimum time granularity amin. Otherwise, according to the current TGi time granule, the best time granule expression sequence is selected to further classify the time granule under the current granularity into I categories, and the results are calculated according to the precursor-successor relationship of the time granule. Finally, the optimal time granularity and its time granularity are recorded as OPT.


#### 2.3.3. Constructing Multidimensional Matrix Model of Indicator Attributes

Time series data include data of many different indicators, which have been collected throughout the time domain. These data have high latitude and time series. In order to obtain an effective data source, it is necessary to sample the original time series data. TS, which is commonly used in practice, is also a limited set. It is expressed asTS=t1,v1,t2,v2,…, where ti denotes sampling time, vi denotes sampling value, and there is a certain functional relationship between Ti and vi, vi = f (ti). From a large number of time series data records, it is found that these records are some interval sampling uncertain time series. Therefore, in order to transform it into deterministic time series, this paper intends to use the blank strategy and data interpolation to determine the uncertain time series, respectively. Then, the matrix model is used to describe the time series data of time series data indicators. Matrix M, which consists of time series corresponding to all indexes of time series TSdjai data, is defined as a multidimensional matrix model of indexes as follows:(6)M=TSd1a1TSd1a2...TSd1anTSd2a1TSd2a2...TSd2an............TSdma1TSd2a2...TSdman.Among them,TSdjai=<ft1,ft2,…fth>djai the first index representing the time series of Article J has time series. Mij represents the time series corresponding to the jth index of the first time series. Meeting conditions ∃rst.ftrdiai=φ∩ftrdiajorftrdiai≠φ∩ftrdiaj=φ.It can also be seen from formula (1) that the index multimatrix model is a set of super-high dimensional time series.


#### 2.3.4. Classification by Clustering

The index multidimensional matrix model is clustered to obtain the clustering core sequence based on the index data and the two-dimensional table corresponding to the physiological index and the clustering result. The specific steps are as follows:Input: Data training set DS, initial clustering centerH=h1,h2,…,hh, similarity function F(x, y). Convergence coefficient is θ.Step 1: calculate the distance betweenX and y of any time series according to F(x, y). Where F(x, y) is expressed as(7)Fx,y=∑i=148|lw|dx_i_max−dy_i_max2+dx_i_min−dy_i_min2∑i=148|lw|dx_i_min+dy_i_min/22+dx_i_min−dy_i_min/22.dx_i_max It represents the maximum value in the i time granule of sequence x and dx_i_min represents the minimum value in the i time granule of sequence X.Step 2: update the clustering center. The newly generatedK clustering centers are not more than θ according to F(x, y). Then output the clustering result of DS, otherwise continue iterating.In this paper,K-means clustering algorithm and x-means clustering algorithm are used.(i)
K-means clustering algorithmThe idea of K-means algorithm is simple. For a given sample set, the sample set is divided into K clusters according to the distance between samples. Let the points in the cluster be as close as possible, and let the distance between the clusters be as large as possible. Mathematical expressions are used to minimize the mean varianceE if the cluster is divided into C1,C2,…,Ck.(8)E=∑i=1k∑x∈Ci||x−μi||22,whereμi is the mean vector of Ci, the expression is(9)μi=1Ci∑x∈Cix.(ii)
X-means algorithmX-means algorithm is an improvement of K-means algorithm. The main aspects of improvement are as follows:(a)
Using kd-tree to accelerate each iteration of the original K-means(b)
Users specify the scope of K and select the optimal K according to BIC score(c)
Each iteration only takes 2-means.X-means algorithm steps: user inputKmin, Kmax, data set D.(1)
RunningKmin-means.(2)
Run 2-means on each cluster.(3)
According to BIC score (calculated only on this cluster, i.e. the BIC score when only the clustering data are divided into one and two categories), it is decided whether or not to divide the clustering into two categories.(4)
IfK < Kmax, proceed to Step 2, otherwise the result will be returned.(5)
Clustering data classification using machine learning method.The two-dimensional information table of clustering results is used to obtain classification knowledge by corresponding machine learning method. Then, the prediction is realized by matching the learned classification knowledge in the test set data. In this paper, SVM algorithm, ID3 algorithm and PNN (probability neural networks) algorithm are used for classification.(iii)
SVM algorithmSupport vector machine (SVM) is a classification algorithm. It can improve the generalization ability of learning machine by seeking the smallest structured risk, and minimize the empirical risk and confidence range, so as to achieve the goal of obtaining good statistical rules in the case of fewer statistical samples. Generally speaking, it is a two-class classification model. Its basic model is defined as a linear classifier with the largest spacing in the feature space. That is to say, the learning strategy of support vector machine is to maximize the spacing, which can eventually be transformed into a solution of a convex quadratic programming problem.(iv)
ID3 algorithmThe core of ID3 algorithm is that when selecting attributes at all levels of decision tree nodes, information gain is used as the criterion to select attributes, so that when testing at each nonleaf node, the maximum category information about the tested record can be obtained. The specific method is to detect all attributes, select the attributes with the greatest information gain to generate decision tree nodes, establish branches from different values of the attributes, and then recursively call the method to establish branches of decision tree nodes for each subset until all subsets contain only the same category of data. Finally, a decision tree is obtained, which can be used to classify new samples.(v)
PNN algorithmPNN is a simple and widely used neural network. It is a radial neural network. On the basis of RBF network, PNN combines density function estimation and Bayesian decision theory. It consists of input layer, hidden layer, summation layer and output layer. The input layer receives the values from the training samples and transfers the data to the hidden layer. Implicit layer mainly accepts input samples from input layer, calculates the distance between input vector and center, and finally returns a scalar value. Vectors are input into the hidden layer. The input/output relationship determined by thej neuron of type I mode in the hidden layer is defined as follows:(10)φijx=12π1/2σdex−xijx−xijT/σ2.I = 1, 2, …, M, M is the total number of classes in the training sample. d is the dimension of the sample space data and xij is the jth center of the class i sample. The summation layer weights and averages the output of the hidden neurons belonging to the same class in the hidden layer:(11)vi=∑j=1LφijL.v
i represents the output of Class i, and L represents the number of neurons in Class i. The number of neurons in summation layer is the same as that in category M.Output layer selection and the largest class in the layer as output categoryy=arg maxvi.


## 2.1. Granule Computation

### 2.1.1. Granular Computing Framework

Granular computing is a very active research field in computer science in recent ten years. By abstracting and dividing complex problems into several simpler ones, it helps to better analyze and solve problems. In the framework of granular computing, according to the actual problem itself, the problem information is granulated into information granules, which are calculated, processed, and returned to the results of processing. Figure1 shows the basic framework of granular computing.Figure 1
Basic framework for granular computing.In Figure1, information granule is the basic element of granular computing, which is a set of elements aggregated according to indistinguishability, similarity, similarity or functionality. In granular computing, the main task is to construct, represent, and process information granules. Information granules can be divided into different sizes, that is, the “information granularity” of information granules. For example, people can use different time intervals to granulate information and deduce information granules of different sizes (year, month, day, etc.). The size of information granules deduced implies the level of “information granularity” used in information granulation. Therefore, information granules are hierarchical, and the information granules generated at different granularity levels can be transformed into each other, as shown in Figure 2.Figure 2
Information granules and information granularity.In the process of granulation, there are two directions: construction and decomposition. Construction refers to how finer or lower grains are merged into coarser or upper grains. Convert “thinner” and “more special” information granules into “coarser” and “more general” information granules; on the contrary, decompose the coarser or upper granules into finer lower granules. That is to say, “coarser” and “more general” information granules are further refined into “thinner” and “more special” information granules. At present, the specific methods of granulation include fuzzy information granulation [15], rough set approximation [16], quotient space method [17], clustering-based granulation [18] and cloud model method [19–21].


### 2.1.2. Basic Terms in Granular Computing

(1) Representation of Information Granules. Referring to the representation of topological space in quotient space, the information granules are formally described by triples, namely,(1)IG=KVS,GM,VM,where KVS (key value pair set) represents the feature subvector describing the information granule, i.e., KVS=key1,value1>,…,<keyn,valuen (i = 1, 2, …, n) and Valuei represents the value taken by a feature named Keyi in the information granule.GM (granularity measure) denotes the granularity measure of the information granule, i.e., the degree of granularity of the information granule. Its formula is [22](2)GMπ=∑i=1mXiUlog|Xi|Among them,π=X1,X2,…,Xm is a division of the universe U, and Xi is a subset of U. When the granularity is the finest, that is, each granule is a single point set, there is GMπ=0; when the granularity is the thickest, that is, the whole universe is a granule. GMπ=log|U| VM (value measure) represents the value measure of the information granule. Its determination is mainly from three aspects: granularity measurement, uncertainty, and domain knowledge.(2) Representation of Granular Layer. The granular layer (layer) consists of all information granules based on a certain granulation criterion and the relationship between them. The granular layer can be formally expressed as a binary group, that is, a binary group.(3)Layer=IGS,Intra−LR,where IGS (information granule set) represents a set of information granules in the granular layer, which can be expressed as IGS=IG1,IG2,…,IGM; intra-LR (intralayer relationships) represents possible relationships between information granules in the granular layer. If the information granule IGp and IGq is related to the existence, then Intra−LR=E/E=IGp,IGq,IGp,IGq∈IGS.(3) Representation of Granular Structure. The granular structure in MGrIKR is a topological structure consisting of multiple granular layers obtained by different granulation criteria, the relationship between information granules in different granular layers and the relationship between information granules in the same granular layer. Therefore, the granular structure GS (granular structure) can be expressed in tuple form:(4)GS=LS,Inter−LRAmong them,LS=Layer1,...,Layerm−1,Layerm represents a set of m granular layers Layer Set,LS, in which the granular layer Layerj is a granular layer in the granular structure. Inter-LR (interlayer relationships) denotes the set of transformation relations between two layers of Layerj and Layerk information granules, Inter−LR which can be expressed as(5)Inter−LR=rp|rpLayerj,Layerk⋅j,k=1,...,m.Among them,r < denotes the satisfied partial order relationship between Layerj and Layerk information granules, which can be the relationship between information granules in adjacent two granular layers, or the relationship between information granules across layers.


## 2.1.1. Granular Computing Framework

Granular computing is a very active research field in computer science in recent ten years. By abstracting and dividing complex problems into several simpler ones, it helps to better analyze and solve problems. In the framework of granular computing, according to the actual problem itself, the problem information is granulated into information granules, which are calculated, processed, and returned to the results of processing. Figure1 shows the basic framework of granular computing.Figure 1
Basic framework for granular computing.In Figure1, information granule is the basic element of granular computing, which is a set of elements aggregated according to indistinguishability, similarity, similarity or functionality. In granular computing, the main task is to construct, represent, and process information granules. Information granules can be divided into different sizes, that is, the “information granularity” of information granules. For example, people can use different time intervals to granulate information and deduce information granules of different sizes (year, month, day, etc.). The size of information granules deduced implies the level of “information granularity” used in information granulation. Therefore, information granules are hierarchical, and the information granules generated at different granularity levels can be transformed into each other, as shown in Figure 2.Figure 2
Information granules and information granularity.In the process of granulation, there are two directions: construction and decomposition. Construction refers to how finer or lower grains are merged into coarser or upper grains. Convert “thinner” and “more special” information granules into “coarser” and “more general” information granules; on the contrary, decompose the coarser or upper granules into finer lower granules. That is to say, “coarser” and “more general” information granules are further refined into “thinner” and “more special” information granules. At present, the specific methods of granulation include fuzzy information granulation [15], rough set approximation [16], quotient space method [17], clustering-based granulation [18] and cloud model method [19–21].


## 2.1.2. Basic Terms in Granular Computing

(1) Representation of Information Granules. Referring to the representation of topological space in quotient space, the information granules are formally described by triples, namely,(1)IG=KVS,GM,VM,where KVS (key value pair set) represents the feature subvector describing the information granule, i.e., KVS=key1,value1>,…,<keyn,valuen (i = 1, 2, …, n) and Valuei represents the value taken by a feature named Keyi in the information granule.GM (granularity measure) denotes the granularity measure of the information granule, i.e., the degree of granularity of the information granule. Its formula is [22](2)GMπ=∑i=1mXiUlog|Xi|Among them,π=X1,X2,…,Xm is a division of the universe U, and Xi is a subset of U. When the granularity is the finest, that is, each granule is a single point set, there is GMπ=0; when the granularity is the thickest, that is, the whole universe is a granule. GMπ=log|U| VM (value measure) represents the value measure of the information granule. Its determination is mainly from three aspects: granularity measurement, uncertainty, and domain knowledge.(2) Representation of Granular Layer. The granular layer (layer) consists of all information granules based on a certain granulation criterion and the relationship between them. The granular layer can be formally expressed as a binary group, that is, a binary group.(3)Layer=IGS,Intra−LR,where IGS (information granule set) represents a set of information granules in the granular layer, which can be expressed as IGS=IG1,IG2,…,IGM; intra-LR (intralayer relationships) represents possible relationships between information granules in the granular layer. If the information granule IGp and IGq is related to the existence, then Intra−LR=E/E=IGp,IGq,IGp,IGq∈IGS.(3) Representation of Granular Structure. The granular structure in MGrIKR is a topological structure consisting of multiple granular layers obtained by different granulation criteria, the relationship between information granules in different granular layers and the relationship between information granules in the same granular layer. Therefore, the granular structure GS (granular structure) can be expressed in tuple form:(4)GS=LS,Inter−LRAmong them,LS=Layer1,...,Layerm−1,Layerm represents a set of m granular layers Layer Set,LS, in which the granular layer Layerj is a granular layer in the granular structure. Inter-LR (interlayer relationships) denotes the set of transformation relations between two layers of Layerj and Layerk information granules, Inter−LR which can be expressed as(5)Inter−LR=rp|rpLayerj,Layerk⋅j,k=1,...,m.Among them,r < denotes the satisfied partial order relationship between Layerj and Layerk information granules, which can be the relationship between information granules in adjacent two granular layers, or the relationship between information granules across layers.


## 2.2. Framework for Time Series Analysis, Processing, and Modeling Based on Granular Computing

Sequential data in the era of large data have the characteristics of huge scale, dynamic and instability. Therefore, researchers have proposed a processing framework for time series data based on granular computing to simulate human granulation cognitive mechanism as shown in Figure3.Figure 3
Data sequence processing framework based on granular computing.


### 2.2.1. Rational Information Granulation of Time Series

In order to reduce the scale of time series data, it replaces the original time series in a simple and clear form. Firstly, it divides the time series into several time windows and then granulates the data on each time window to transform the original time series into a time-related “information granule” sequence (granular time series). Suppose for a time seriesx=x1,x2,…,xn, firstly, the time series is divided into a P-time window T1,T2,…,Tk, and then the data on each time window Tii=1,…,k are granulated to form information granules λii=1,2,…p. Thus, the original time series X is transformed into corresponding granular time series λ=λ1,λ2,…λp by granulation of information.


### 2.2.2. Time Series Analysis and Interpretation Based on Information Granulation

Time series analysis and interpretation takes “granular time series” as the research object. Semantic labels describing the dynamic characteristics of information granules are used as basic elements to describe each element in granular time series. It is assumed that there exists a set of granular semantic tagsL=L1,L2,…,Lh, in which ≤ p. This stage is to realize how to describe granular information λi with elements in the set L of semantic tags. Researchers have used fuzzy sets to achieve this, that is, to assign corresponding semantics to information granules λi: “Yes, λi is Lj, its matching degree is ϕij.” Some researchers also use clustering algorithm to divide P information granules into granular semantic tag set L according to their similarity.


### 2.2.3. Time Series Modeling Based on Information Granulation

Time series modeling is to transfer domain knowledge by means of information granules and capture the main relational features of time series by logical association language. Because the granular model of time series is user-oriented, the output of the model can be understood and recognized by users, thus helping users to make reasonable decisions. Its input and output are information granules on the corresponding time window of time series. It is assumed that time series granular model describes the dynamic relationship between information granulesλj,…λi−2,λi−1,λi formed by time series in time windows Tj,…Ti−2,Ti−1,Ti.


## 2.2.1. Rational Information Granulation of Time Series

In order to reduce the scale of time series data, it replaces the original time series in a simple and clear form. Firstly, it divides the time series into several time windows and then granulates the data on each time window to transform the original time series into a time-related “information granule” sequence (granular time series). Suppose for a time seriesx=x1,x2,…,xn, firstly, the time series is divided into a P-time window T1,T2,…,Tk, and then the data on each time window Tii=1,…,k are granulated to form information granules λii=1,2,…p. Thus, the original time series X is transformed into corresponding granular time series λ=λ1,λ2,…λp by granulation of information.


## 2.2.2. Time Series Analysis and Interpretation Based on Information Granulation

Time series analysis and interpretation takes “granular time series” as the research object. Semantic labels describing the dynamic characteristics of information granules are used as basic elements to describe each element in granular time series. It is assumed that there exists a set of granular semantic tagsL=L1,L2,…,Lh, in which ≤ p. This stage is to realize how to describe granular information λi with elements in the set L of semantic tags. Researchers have used fuzzy sets to achieve this, that is, to assign corresponding semantics to information granules λi: “Yes, λi is Lj, its matching degree is ϕij.” Some researchers also use clustering algorithm to divide P information granules into granular semantic tag set L according to their similarity.


## 2.2.3. Time Series Modeling Based on Information Granulation

Time series modeling is to transfer domain knowledge by means of information granules and capture the main relational features of time series by logical association language. Because the granular model of time series is user-oriented, the output of the model can be understood and recognized by users, thus helping users to make reasonable decisions. Its input and output are information granules on the corresponding time window of time series. It is assumed that time series granular model describes the dynamic relationship between information granulesλj,…λi−2,λi−1,λi formed by time series in time windows Tj,…Ti−2,Ti−1,Ti.


## 2.3. Time Series Prediction Model Based on Multilayer Information Granules

Considering the data presented by time series in time window, the distribution of time series is mostly uneven. The information granules constructed by single information granularity may not capture the essential characteristics of data. Therefore, in order to reasonably granulate the information of time series data, this paper designs an information granulation method based on the idea of “multi-granularity.” Different information granularity levels are used to granulate the time series data on a time window to obtain information granularity at different information granularity levels. Finally, a time series prediction model based on multilevel information granules is proposed to predict ICU patient data. The basic flow of the prediction process is shown in Figure4.Figure 4
Forecasting process of the forecasting model.Specific steps are as follows: firstly, this paper establishes a multigranularity time series model by applying binary relationship on the time axis of time series data and introduces the evaluation effect function of time series data mining (the function of judging the accuracy of prediction) as the goal of prediction task. Based on this function, the optimal time granularity of prediction is found. In view of the uncertainty of time series, a multidimensional matrix model is constructed, and then the clustering category information of each attribute is obtained by clustering operation. Finally, the clustered data are classified by machine learning method to obtain classification knowledge. Forecasting can be achieved by classifying knowledge.


### 2.3.1. Establishment of Multigranularity Time Series Model

In the research of time series prediction, the time domainUT is generally considered as a line segment. Therefore, this paper uses the form of the time axis to represent the time domain and assumes that the starting point of the time domain is a origin of the time axis, which is recorded as t0. The multigranularity time series ∑UT,AT,TS is defined as TS with multiple optional time granularities (indicating that AT values can be more than one) in a given time domain UT.General analysis is based on the different attributes of objects in the universe to analyze their values and describe them in the form of two-dimensional tables. In this paper, we slice the multidimensional time series and analyze one of its atomic points. The time series are divided intot0, t1, …, Tn, and the analysis of tI time points is studied. From this, a multigranularity time series model TGSUT,A,∗T,R of ICU is constructed, UT which is a time domain, A=AN∪AT, AN is a set of related attributes; AT is a set of time granularity attributes, and ∗ T is a set of time granularity atx∈AT attributes obtained by equivalence partition UTatx of R to UT formed according to different time granularity AT.


### 2.3.2. Finding the Optimal Time Granularity for Prediction

Because the granularity is variable in constructing multigranularity time series model, the model can be used to predict different prediction effects. Therefore, in order to evaluate the performance of prediction based on different time grains in a given time domain, this paper uses the time series data mining evaluation functionFati∈AT to try to find the best time granularity in the model. The process of solving the optimal time granularity is shown in Figure 5.Figure 5
The process of finding the optimal time granularity.There are two stages:(i)
Optimal time granular search based on time domain.Assuming the time domainUT, the alternative I is based on the equivalence partition I=k1,k2,k3 of time granules, the evaluation effect function Fati∈AT of time series data mining, the diagnostic accuracy λ and the minimum time granularity amin. Firstly, according to the evaluation function, a partition is selected from the candidate I partition to get the granularity ati as the next time granularity set TGi.(iii)
Optimal time granular fine search based on time domain.The prediction results under eachTGi condition are evaluated in turn, and the algorithm ends if the accuracy is less than λ or less than the prescribed minimum time granularity amin. Otherwise, according to the current TGi time granule, the best time granule expression sequence is selected to further classify the time granule under the current granularity into I categories, and the results are calculated according to the precursor-successor relationship of the time granule. Finally, the optimal time granularity and its time granularity are recorded as OPT.


### 2.3.3. Constructing Multidimensional Matrix Model of Indicator Attributes

Time series data include data of many different indicators, which have been collected throughout the time domain. These data have high latitude and time series. In order to obtain an effective data source, it is necessary to sample the original time series data. TS, which is commonly used in practice, is also a limited set. It is expressed asTS=t1,v1,t2,v2,…, where ti denotes sampling time, vi denotes sampling value, and there is a certain functional relationship between Ti and vi, vi = f (ti). From a large number of time series data records, it is found that these records are some interval sampling uncertain time series. Therefore, in order to transform it into deterministic time series, this paper intends to use the blank strategy and data interpolation to determine the uncertain time series, respectively. Then, the matrix model is used to describe the time series data of time series data indicators. Matrix M, which consists of time series corresponding to all indexes of time series TSdjai data, is defined as a multidimensional matrix model of indexes as follows:(6)M=TSd1a1TSd1a2...TSd1anTSd2a1TSd2a2...TSd2an............TSdma1TSd2a2...TSdman.Among them,TSdjai=<ft1,ft2,…fth>djai the first index representing the time series of Article J has time series. Mij represents the time series corresponding to the jth index of the first time series. Meeting conditions ∃rst.ftrdiai=φ∩ftrdiajorftrdiai≠φ∩ftrdiaj=φ.It can also be seen from formula (1) that the index multimatrix model is a set of super-high dimensional time series.


### 2.3.4. Classification by Clustering

The index multidimensional matrix model is clustered to obtain the clustering core sequence based on the index data and the two-dimensional table corresponding to the physiological index and the clustering result. The specific steps are as follows:Input: Data training set DS, initial clustering centerH=h1,h2,…,hh, similarity function F(x, y). Convergence coefficient is θ.Step 1: calculate the distance betweenX and y of any time series according to F(x, y). Where F(x, y) is expressed as(7)Fx,y=∑i=148|lw|dx_i_max−dy_i_max2+dx_i_min−dy_i_min2∑i=148|lw|dx_i_min+dy_i_min/22+dx_i_min−dy_i_min/22.dx_i_max It represents the maximum value in the i time granule of sequence x and dx_i_min represents the minimum value in the i time granule of sequence X.Step 2: update the clustering center. The newly generatedK clustering centers are not more than θ according to F(x, y). Then output the clustering result of DS, otherwise continue iterating.In this paper,K-means clustering algorithm and x-means clustering algorithm are used.(i)
K-means clustering algorithmThe idea of K-means algorithm is simple. For a given sample set, the sample set is divided into K clusters according to the distance between samples. Let the points in the cluster be as close as possible, and let the distance between the clusters be as large as possible. Mathematical expressions are used to minimize the mean varianceE if the cluster is divided into C1,C2,…,Ck.(8)E=∑i=1k∑x∈Ci||x−μi||22,whereμi is the mean vector of Ci, the expression is(9)μi=1Ci∑x∈Cix.(ii)
X-means algorithmX-means algorithm is an improvement of K-means algorithm. The main aspects of improvement are as follows:(a)
Using kd-tree to accelerate each iteration of the original K-means(b)
Users specify the scope of K and select the optimal K according to BIC score(c)
Each iteration only takes 2-means.X-means algorithm steps: user inputKmin, Kmax, data set D.(1)
RunningKmin-means.(2)
Run 2-means on each cluster.(3)
According to BIC score (calculated only on this cluster, i.e. the BIC score when only the clustering data are divided into one and two categories), it is decided whether or not to divide the clustering into two categories.(4)
IfK < Kmax, proceed to Step 2, otherwise the result will be returned.(5)
Clustering data classification using machine learning method.The two-dimensional information table of clustering results is used to obtain classification knowledge by corresponding machine learning method. Then, the prediction is realized by matching the learned classification knowledge in the test set data. In this paper, SVM algorithm, ID3 algorithm and PNN (probability neural networks) algorithm are used for classification.(iii)
SVM algorithmSupport vector machine (SVM) is a classification algorithm. It can improve the generalization ability of learning machine by seeking the smallest structured risk, and minimize the empirical risk and confidence range, so as to achieve the goal of obtaining good statistical rules in the case of fewer statistical samples. Generally speaking, it is a two-class classification model. Its basic model is defined as a linear classifier with the largest spacing in the feature space. That is to say, the learning strategy of support vector machine is to maximize the spacing, which can eventually be transformed into a solution of a convex quadratic programming problem.(iv)
ID3 algorithmThe core of ID3 algorithm is that when selecting attributes at all levels of decision tree nodes, information gain is used as the criterion to select attributes, so that when testing at each nonleaf node, the maximum category information about the tested record can be obtained. The specific method is to detect all attributes, select the attributes with the greatest information gain to generate decision tree nodes, establish branches from different values of the attributes, and then recursively call the method to establish branches of decision tree nodes for each subset until all subsets contain only the same category of data. Finally, a decision tree is obtained, which can be used to classify new samples.(v)
PNN algorithmPNN is a simple and widely used neural network. It is a radial neural network. On the basis of RBF network, PNN combines density function estimation and Bayesian decision theory. It consists of input layer, hidden layer, summation layer and output layer. The input layer receives the values from the training samples and transfers the data to the hidden layer. Implicit layer mainly accepts input samples from input layer, calculates the distance between input vector and center, and finally returns a scalar value. Vectors are input into the hidden layer. The input/output relationship determined by thej neuron of type I mode in the hidden layer is defined as follows:(10)φijx=12π1/2σdex−xijx−xijT/σ2.I = 1, 2, …, M, M is the total number of classes in the training sample. d is the dimension of the sample space data and xij is the jth center of the class i sample. The summation layer weights and averages the output of the hidden neurons belonging to the same class in the hidden layer:(11)vi=∑j=1LφijL.v
i represents the output of Class i, and L represents the number of neurons in Class i. The number of neurons in summation layer is the same as that in category M.Output layer selection and the largest class in the layer as output categoryy=arg maxvi.


## 2.3.1. Establishment of Multigranularity Time Series Model

In the research of time series prediction, the time domainUT is generally considered as a line segment. Therefore, this paper uses the form of the time axis to represent the time domain and assumes that the starting point of the time domain is a origin of the time axis, which is recorded as t0. The multigranularity time series ∑UT,AT,TS is defined as TS with multiple optional time granularities (indicating that AT values can be more than one) in a given time domain UT.General analysis is based on the different attributes of objects in the universe to analyze their values and describe them in the form of two-dimensional tables. In this paper, we slice the multidimensional time series and analyze one of its atomic points. The time series are divided intot0, t1, …, Tn, and the analysis of tI time points is studied. From this, a multigranularity time series model TGSUT,A,∗T,R of ICU is constructed, UT which is a time domain, A=AN∪AT, AN is a set of related attributes; AT is a set of time granularity attributes, and ∗ T is a set of time granularity atx∈AT attributes obtained by equivalence partition UTatx of R to UT formed according to different time granularity AT.


## 2.3.2. Finding the Optimal Time Granularity for Prediction

Because the granularity is variable in constructing multigranularity time series model, the model can be used to predict different prediction effects. Therefore, in order to evaluate the performance of prediction based on different time grains in a given time domain, this paper uses the time series data mining evaluation functionFati∈AT to try to find the best time granularity in the model. The process of solving the optimal time granularity is shown in Figure 5.Figure 5
The process of finding the optimal time granularity.There are two stages:(i)
Optimal time granular search based on time domain.Assuming the time domainUT, the alternative I is based on the equivalence partition I=k1,k2,k3 of time granules, the evaluation effect function Fati∈AT of time series data mining, the diagnostic accuracy λ and the minimum time granularity amin. Firstly, according to the evaluation function, a partition is selected from the candidate I partition to get the granularity ati as the next time granularity set TGi.(iii)
Optimal time granular fine search based on time domain.The prediction results under eachTGi condition are evaluated in turn, and the algorithm ends if the accuracy is less than λ or less than the prescribed minimum time granularity amin. Otherwise, according to the current TGi time granule, the best time granule expression sequence is selected to further classify the time granule under the current granularity into I categories, and the results are calculated according to the precursor-successor relationship of the time granule. Finally, the optimal time granularity and its time granularity are recorded as OPT.


## 2.3.3. Constructing Multidimensional Matrix Model of Indicator Attributes

Time series data include data of many different indicators, which have been collected throughout the time domain. These data have high latitude and time series. In order to obtain an effective data source, it is necessary to sample the original time series data. TS, which is commonly used in practice, is also a limited set. It is expressed asTS=t1,v1,t2,v2,…, where ti denotes sampling time, vi denotes sampling value, and there is a certain functional relationship between Ti and vi, vi = f (ti). From a large number of time series data records, it is found that these records are some interval sampling uncertain time series. Therefore, in order to transform it into deterministic time series, this paper intends to use the blank strategy and data interpolation to determine the uncertain time series, respectively. Then, the matrix model is used to describe the time series data of time series data indicators. Matrix M, which consists of time series corresponding to all indexes of time series TSdjai data, is defined as a multidimensional matrix model of indexes as follows:(6)M=TSd1a1TSd1a2...TSd1anTSd2a1TSd2a2...TSd2an............TSdma1TSd2a2...TSdman.Among them,TSdjai=<ft1,ft2,…fth>djai the first index representing the time series of Article J has time series. Mij represents the time series corresponding to the jth index of the first time series. Meeting conditions ∃rst.ftrdiai=φ∩ftrdiajorftrdiai≠φ∩ftrdiaj=φ.It can also be seen from formula (1) that the index multimatrix model is a set of super-high dimensional time series.


## 2.3.4. Classification by Clustering

The index multidimensional matrix model is clustered to obtain the clustering core sequence based on the index data and the two-dimensional table corresponding to the physiological index and the clustering result. The specific steps are as follows:Input: Data training set DS, initial clustering centerH=h1,h2,…,hh, similarity function F(x, y). Convergence coefficient is θ.Step 1: calculate the distance betweenX and y of any time series according to F(x, y). Where F(x, y) is expressed as(7)Fx,y=∑i=148|lw|dx_i_max−dy_i_max2+dx_i_min−dy_i_min2∑i=148|lw|dx_i_min+dy_i_min/22+dx_i_min−dy_i_min/22.dx_i_max It represents the maximum value in the i time granule of sequence x and dx_i_min represents the minimum value in the i time granule of sequence X.Step 2: update the clustering center. The newly generatedK clustering centers are not more than θ according to F(x, y). Then output the clustering result of DS, otherwise continue iterating.In this paper,K-means clustering algorithm and x-means clustering algorithm are used.(i)
K-means clustering algorithmThe idea of K-means algorithm is simple. For a given sample set, the sample set is divided into K clusters according to the distance between samples. Let the points in the cluster be as close as possible, and let the distance between the clusters be as large as possible. Mathematical expressions are used to minimize the mean varianceE if the cluster is divided into C1,C2,…,Ck.(8)E=∑i=1k∑x∈Ci||x−μi||22,whereμi is the mean vector of Ci, the expression is(9)μi=1Ci∑x∈Cix.(ii)
X-means algorithmX-means algorithm is an improvement of K-means algorithm. The main aspects of improvement are as follows:(a)
Using kd-tree to accelerate each iteration of the original K-means(b)
Users specify the scope of K and select the optimal K according to BIC score(c)
Each iteration only takes 2-means.X-means algorithm steps: user inputKmin, Kmax, data set D.(1)
RunningKmin-means.(2)
Run 2-means on each cluster.(3)
According to BIC score (calculated only on this cluster, i.e. the BIC score when only the clustering data are divided into one and two categories), it is decided whether or not to divide the clustering into two categories.(4)
IfK < Kmax, proceed to Step 2, otherwise the result will be returned.(5)
Clustering data classification using machine learning method.The two-dimensional information table of clustering results is used to obtain classification knowledge by corresponding machine learning method. Then, the prediction is realized by matching the learned classification knowledge in the test set data. In this paper, SVM algorithm, ID3 algorithm and PNN (probability neural networks) algorithm are used for classification.(iii)
SVM algorithmSupport vector machine (SVM) is a classification algorithm. It can improve the generalization ability of learning machine by seeking the smallest structured risk, and minimize the empirical risk and confidence range, so as to achieve the goal of obtaining good statistical rules in the case of fewer statistical samples. Generally speaking, it is a two-class classification model. Its basic model is defined as a linear classifier with the largest spacing in the feature space. That is to say, the learning strategy of support vector machine is to maximize the spacing, which can eventually be transformed into a solution of a convex quadratic programming problem.(iv)
ID3 algorithmThe core of ID3 algorithm is that when selecting attributes at all levels of decision tree nodes, information gain is used as the criterion to select attributes, so that when testing at each nonleaf node, the maximum category information about the tested record can be obtained. The specific method is to detect all attributes, select the attributes with the greatest information gain to generate decision tree nodes, establish branches from different values of the attributes, and then recursively call the method to establish branches of decision tree nodes for each subset until all subsets contain only the same category of data. Finally, a decision tree is obtained, which can be used to classify new samples.(v)
PNN algorithmPNN is a simple and widely used neural network. It is a radial neural network. On the basis of RBF network, PNN combines density function estimation and Bayesian decision theory. It consists of input layer, hidden layer, summation layer and output layer. The input layer receives the values from the training samples and transfers the data to the hidden layer. Implicit layer mainly accepts input samples from input layer, calculates the distance between input vector and center, and finally returns a scalar value. Vectors are input into the hidden layer. The input/output relationship determined by thej neuron of type I mode in the hidden layer is defined as follows:(10)φijx=12π1/2σdex−xijx−xijT/σ2.I = 1, 2, …, M, M is the total number of classes in the training sample. d is the dimension of the sample space data and xij is the jth center of the class i sample. The summation layer weights and averages the output of the hidden neurons belonging to the same class in the hidden layer:(11)vi=∑j=1LφijL.v
i represents the output of Class i, and L represents the number of neurons in Class i. The number of neurons in summation layer is the same as that in category M.Output layer selection and the largest class in the layer as output categoryy=arg maxvi.


## 3. Experiment

### 3.1. Experimental Data

In this paper, the data provided by the PhysicoNet website of the National Institutes of Health are used. The data included 575 ICU data from Coronary Care, 871 ICU data from Cardiac Surgery, 1482 ICU data from Recovery Unit and 4000 ICU data from Medical and Surgical. Various physiological indicators were used in all the data. Different physiological indicators also have a certain percentage of missing values in these case records. Of these cases, 13.86% died and 86.14% survived. Because of the unbalanced distribution of data sets, the focus of this classifier is whether death samples can be correctly identified.


### 3.2. Physiological Indicators and Setting of Experimental Parameters

According to the frequency and importance of physiological indicators in different ICUs, and the short average sampling interval of these indicators. Ten candidate physiological attributes (HR, urine, WBC, temp, PH, PaO2, PaCO2, NIDias ABP, dias ABP, and sys ABP) were selected from many indicators. In this paper, the data ratio of training set and test set is set to 7 : 3. The minimum time granularity is set to 0.25 hours, and the minimum prediction accuracy is 75%.


### 3.3. Experimental Scheme

In the early stage of this paper, the missing data is filled by simple blank interpolation. After determining the time series of ICU data, two different clustering methods (K-means algorithm and GMM maximum expectation EM algorithm) are used to cluster the sequence. Finally, different machine methods (SVM algorithm, ID3, and PNN) are used to classify and predict the sequence. Therefore, three experimental schemes are adopted in this paper.Scheme 1: clustering algorithm uses K-means algorithm, and then uses three different machine classification algorithms, using different time granularity for prediction.Scheme 2: clustering algorithm adopts EM algorithm, and then three different machine classification algorithms are used to predict with different time granularity.Scheme 3: clustering algorithm adopts EM algorithm, then three different machine classification algorithms are used, respectively, and the optimal time granularity is used to predict.


## 3.1. Experimental Data

In this paper, the data provided by the PhysicoNet website of the National Institutes of Health are used. The data included 575 ICU data from Coronary Care, 871 ICU data from Cardiac Surgery, 1482 ICU data from Recovery Unit and 4000 ICU data from Medical and Surgical. Various physiological indicators were used in all the data. Different physiological indicators also have a certain percentage of missing values in these case records. Of these cases, 13.86% died and 86.14% survived. Because of the unbalanced distribution of data sets, the focus of this classifier is whether death samples can be correctly identified.


## 3.2. Physiological Indicators and Setting of Experimental Parameters

According to the frequency and importance of physiological indicators in different ICUs, and the short average sampling interval of these indicators. Ten candidate physiological attributes (HR, urine, WBC, temp, PH, PaO2, PaCO2, NIDias ABP, dias ABP, and sys ABP) were selected from many indicators. In this paper, the data ratio of training set and test set is set to 7 : 3. The minimum time granularity is set to 0.25 hours, and the minimum prediction accuracy is 75%.


## 3.3. Experimental Scheme

In the early stage of this paper, the missing data is filled by simple blank interpolation. After determining the time series of ICU data, two different clustering methods (K-means algorithm and GMM maximum expectation EM algorithm) are used to cluster the sequence. Finally, different machine methods (SVM algorithm, ID3, and PNN) are used to classify and predict the sequence. Therefore, three experimental schemes are adopted in this paper.Scheme 1: clustering algorithm uses K-means algorithm, and then uses three different machine classification algorithms, using different time granularity for prediction.Scheme 2: clustering algorithm adopts EM algorithm, and then three different machine classification algorithms are used to predict with different time granularity.Scheme 3: clustering algorithm adopts EM algorithm, then three different machine classification algorithms are used, respectively, and the optimal time granularity is used to predict.


## 4. Result Analysis

### 4.1. Analysis of Experimental Results of Schemes 1 and 2

The experimental results of schemes 1 and 2 are shown in Figure6.Figure 6
Prediction results of schemes 1 and 2. (a) Comparison of the prediction effect of scheme 1. (b) Comparison of the prediction effect of scheme 2.
(a)
(b)In Figure6, three different machine classification methods (SVM, ID3, PNN) are used to predict the results at four different time granularities (1 hour, 2 hours, 4 hours, 8 hours). As can be seen from Figure 6, both scheme 1 and scheme 2 have the best prediction effect when using ID3 algorithm, and PNN algorithm has the worst prediction effect. When using the same machine learning method, different time granularity is selected, and the prediction effect is also quite different. When choosing the time granularity of 4 hours, the prediction effect of different machine learning methods is generally the best. The prediction rates of SVM method, ID3 method and PNN method in scheme 1 were 72.31%, 72.38% and 72.21%, respectively. The prediction rates of SVM method, ID3 method and PNN method in scheme 2 were 74.92%, 75.88% and 74.21%, respectively. The comparison of the forecasting effect between scheme 1 and scheme 2 is shown in Figure 7.Figure 7
Comparison of the predicted results of schemes 1 and 2.As can be seen from Figure7, the blue line represents the prediction effect of Scheme 2 and the red line represents the prediction effect of Scheme 1. In scheme 2, the predictive effect of all machine learning methods has increased in general. It is shown that the clustering algorithm EM can not only reduce the dimension, but also improve the distinguishability of various physiological index attributes for life and death results by comparing K-means algorithm.


### 4.2. Experimental Results of Scheme 3

In experiment 3, the given time domain was assumed to be January (30 ∗ 24 hours). For the initial equivalence of the time domain, it is divided intoI = {1, 2, 4}, where the meaning of 1, 2, 4 represents the equivalence of 1, 2 and 4 for a given time domain. Only the predictive effect of death samples is considered here. The threshold of prediction accuracy of death samples is 75% and the minimum time granularity is 0.25 hours. Then the initial equivalence partition is refined according to the value of mining evaluation effect function. The experimental results of Experiment 3 are shown in Table 1 and Figure 8.Table 1
Predicted results of Scheme 3.
Equivalent partition set
Machine method
Mining the maximum value of evaluation effect function (%)
Function maximum corresponds to time granule
L1 = {1, 2, 4}
SVM
4.39
180 hours
ID3
5.13
PNN
2.23
L2 = {1, 2, 4, 8}
SVM
28.84
90 hours
ID3
28.91
PNN
21.38
L3 = {1, 2, 4, 8, 16, 32}
SVM
49.21
45 hours
ID3
49.32
PNN
43.82
L4 = {1, 2, 4, 8, 16, 32, 64, 128, 256}
SVM
86.61
5.625 hours
ID3
92.13
PNN
83.43Figure 8
Comparisons of prediction results of different machine classifications with optimal time granule.As can be seen from Table1, when the time granularity is equal to 5.625 hours, i.e. 128 equal parts in the time domain, the value of the evaluation function in the prediction model is more than 75% regardless of the machine classification method used. Therefore, 5.625 hours is the optimal time granule. From Figure 8, we can use the optimal time granule prediction algorithm, which basically reaches about 85%. The highest prediction algorithm is ID3 algorithm, which has a prediction rate of 92.13%. It is obvious that the prediction effect of scheme 1 is better than that of scheme 1 and scheme 2. Secondly, as can be seen from Figure 8, the speed of finding the best time granule based on the time domain proposed in this paper is also faster. Basically, the best time granule was found after four cycles.


### 4.3. Comparisons of Prediction Results between Traditional Time Series Analysis Processing Algorithms and Granular Computing

In order to judge the validity of the proposed method, this paper compares the predictive effect of the traditional time series analysis on the same data set. Fourier transform is used here. Firstly, the original time series is filtered and reduced by discrete Fourier transform and wavelet transform, respectively. Then the data mining algorithm is used to mine the preprocessed time series. The data mining algorithms used here are SVM, ID3, and PNN. The data contains 575 ICU data from Coronary Care and 871 ICU data from Cardiac Surgery. There were 1482 ICU data from Recovery Unit and 4000 ICU data from Medical and Surgical. The prediction results of traditional time series analysis are shown in Table2.Table 2
Predictive effect of different mining algorithms for traditional time series analysis.
Fourier change
Wavelet transform
Data set source/number (example)
SVM
ID3
PNN
Data set source/number (example)
SVM
ID3
PNN
Coronary care/575
54.83
57.23
54.23
Coronary care/575
60.83
64.23
54.23
Cardiac surgery/871
58.23
63.87
53.22
Cardiac surgery/871
62.23
63.87
62.22
Recovery unit/1482
67.25
68.26
66.53
Recovery unit/1482
61.25
62.26
59.53
Medical and surgical/4000
54.87
56.91
52.19
Medical and surgical/4000
69.87
73.21
65.13
Average value
58.795
61.5675
56.5425
Average value
63.545
65.8925
60.2775From Table2, we can see that the effect of using Fourier transform or wavelet transform to analyze time series data is basically below 65%. Their prediction results are compared with those of the first three schemes as shown in Figure 9. It is obvious that the prediction effect of time series data based on multilayer information granule construction model is better than that of Fourier transform and wavelet transform.Figure 9
Comparison of the predictive effect between the traditional time series analysis modeling method and the proposed method.


## 4.1. Analysis of Experimental Results of Schemes 1 and 2

The experimental results of schemes 1 and 2 are shown in Figure6.Figure 6
Prediction results of schemes 1 and 2. (a) Comparison of the prediction effect of scheme 1. (b) Comparison of the prediction effect of scheme 2.
(a)
(b)In Figure6, three different machine classification methods (SVM, ID3, PNN) are used to predict the results at four different time granularities (1 hour, 2 hours, 4 hours, 8 hours). As can be seen from Figure 6, both scheme 1 and scheme 2 have the best prediction effect when using ID3 algorithm, and PNN algorithm has the worst prediction effect. When using the same machine learning method, different time granularity is selected, and the prediction effect is also quite different. When choosing the time granularity of 4 hours, the prediction effect of different machine learning methods is generally the best. The prediction rates of SVM method, ID3 method and PNN method in scheme 1 were 72.31%, 72.38% and 72.21%, respectively. The prediction rates of SVM method, ID3 method and PNN method in scheme 2 were 74.92%, 75.88% and 74.21%, respectively. The comparison of the forecasting effect between scheme 1 and scheme 2 is shown in Figure 7.Figure 7
Comparison of the predicted results of schemes 1 and 2.As can be seen from Figure7, the blue line represents the prediction effect of Scheme 2 and the red line represents the prediction effect of Scheme 1. In scheme 2, the predictive effect of all machine learning methods has increased in general. It is shown that the clustering algorithm EM can not only reduce the dimension, but also improve the distinguishability of various physiological index attributes for life and death results by comparing K-means algorithm.


## 4.2. Experimental Results of Scheme 3

In experiment 3, the given time domain was assumed to be January (30 ∗ 24 hours). For the initial equivalence of the time domain, it is divided intoI = {1, 2, 4}, where the meaning of 1, 2, 4 represents the equivalence of 1, 2 and 4 for a given time domain. Only the predictive effect of death samples is considered here. The threshold of prediction accuracy of death samples is 75% and the minimum time granularity is 0.25 hours. Then the initial equivalence partition is refined according to the value of mining evaluation effect function. The experimental results of Experiment 3 are shown in Table 1 and Figure 8.Table 1
Predicted results of Scheme 3.
Equivalent partition set
Machine method
Mining the maximum value of evaluation effect function (%)
Function maximum corresponds to time granule
L1 = {1, 2, 4}
SVM
4.39
180 hours
ID3
5.13
PNN
2.23
L2 = {1, 2, 4, 8}
SVM
28.84
90 hours
ID3
28.91
PNN
21.38
L3 = {1, 2, 4, 8, 16, 32}
SVM
49.21
45 hours
ID3
49.32
PNN
43.82
L4 = {1, 2, 4, 8, 16, 32, 64, 128, 256}
SVM
86.61
5.625 hours
ID3
92.13
PNN
83.43Figure 8
Comparisons of prediction results of different machine classifications with optimal time granule.As can be seen from Table1, when the time granularity is equal to 5.625 hours, i.e. 128 equal parts in the time domain, the value of the evaluation function in the prediction model is more than 75% regardless of the machine classification method used. Therefore, 5.625 hours is the optimal time granule. From Figure 8, we can use the optimal time granule prediction algorithm, which basically reaches about 85%. The highest prediction algorithm is ID3 algorithm, which has a prediction rate of 92.13%. It is obvious that the prediction effect of scheme 1 is better than that of scheme 1 and scheme 2. Secondly, as can be seen from Figure 8, the speed of finding the best time granule based on the time domain proposed in this paper is also faster. Basically, the best time granule was found after four cycles.


## 4.3. Comparisons of Prediction Results between Traditional Time Series Analysis Processing Algorithms and Granular Computing

In order to judge the validity of the proposed method, this paper compares the predictive effect of the traditional time series analysis on the same data set. Fourier transform is used here. Firstly, the original time series is filtered and reduced by discrete Fourier transform and wavelet transform, respectively. Then the data mining algorithm is used to mine the preprocessed time series. The data mining algorithms used here are SVM, ID3, and PNN. The data contains 575 ICU data from Coronary Care and 871 ICU data from Cardiac Surgery. There were 1482 ICU data from Recovery Unit and 4000 ICU data from Medical and Surgical. The prediction results of traditional time series analysis are shown in Table2.Table 2
Predictive effect of different mining algorithms for traditional time series analysis.
Fourier change
Wavelet transform
Data set source/number (example)
SVM
ID3
PNN
Data set source/number (example)
SVM
ID3
PNN
Coronary care/575
54.83
57.23
54.23
Coronary care/575
60.83
64.23
54.23
Cardiac surgery/871
58.23
63.87
53.22
Cardiac surgery/871
62.23
63.87
62.22
Recovery unit/1482
67.25
68.26
66.53
Recovery unit/1482
61.25
62.26
59.53
Medical and surgical/4000
54.87
56.91
52.19
Medical and surgical/4000
69.87
73.21
65.13
Average value
58.795
61.5675
56.5425
Average value
63.545
65.8925
60.2775From Table2, we can see that the effect of using Fourier transform or wavelet transform to analyze time series data is basically below 65%. Their prediction results are compared with those of the first three schemes as shown in Figure 9. It is obvious that the prediction effect of time series data based on multilayer information granule construction model is better than that of Fourier transform and wavelet transform.Figure 9
Comparison of the predictive effect between the traditional time series analysis modeling method and the proposed method.


## 5. Conclusion

With the rapid development of network, the era of big data has come. Among them, time series data is very common in various fields. This kind of data mining and knowledge discovery is of great significance. Time series data is different from ordinary data. In addition to time-related, it also has high-dimensional, uncertain and dynamic characteristics. These characteristics lead to the use of traditional mining methods for data mining is not very good. Therefore, this paper uses granular computing to deal with it according to its characteristics, and uses ICU data to predict the life and death of ICU patients to test the predictive effect of granular computing on time series data. The main work of this paper is as follows:(1)
In this paper, a multigranularity time series model is established by applying binary relation on the time axis of time series data, and an evaluation effect function of time series data mining is introduced for the purpose of forecasting tasks. Based on this function, the optimal time granularity of prediction is found. According to the uncertainties of time series, an index multidimensional matrix model is constructed, and then the clustering category information of each attribute is obtained by clustering operation. Finally, the clustered data are classified by machine learning method to obtain classification knowledge. Prediction is achieved by classifying knowledge.(2)
The experimental results show that EM clustering algorithm is better than K-means in improving the discriminability of all kinds of physiological indicators for life and death results; the optimal time granularity can improve the prediction rate; ID3 decision-making algorithm is better than SVM and PNN algorithm in data mining for time series data. In addition, the prediction of time series data based on the multilayer information granule construction model is better than the traditional time series analysis method.



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*Source: 9465551-2022-03-12.xml*