# RFID Data Analysis and Evaluation Based on Big Data and Data Clustering

Authors: Lihua Lv
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

The era people live in is the era of big data, and massive data carry a large amount of information. This study aims to analyze RFID data based on big data and clustering algorithms. In this study, a RFID data extraction technology based on joint Kalman filter fusion is proposed. In the system, the proposed data extraction technology can effectively read RFID tags. The data are recorded, and the KM-KL clustering algorithm is proposed for RFID data, which combines the advantages of the K-means algorithm. The improved KM-KL clustering algorithm can effectively analyze and evaluate RFID data. The experimental results of this study prove that the recognition error rate of the RFID data extraction technology based on the joint Kalman filter fusion is only 2.7%. The improved KM-KL clustering algorithm also has better performance than the traditional algorithm.


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## Body

## 1. Introduction

Since human society entered the information age, information technology-related industries have rapidly developed, driving changes in many fields such as computers, communications, and data storage. With the advent of this change, the main content of people's daily work has gradually changed to the processing of various data information. With the support of software and hardware technology, a huge amount of data in various forms has become an important part of people’s lives. However, these massive data information often have no obvious structural characteristics at first glance, and traditional methods and ideas are difficult to achieve the purpose of fully understanding and understanding them. Coupled with the huge amount of data and rich types of data, traditional statistical methods cannot fully extract effective information, and it becomes more difficult to obtain valuable information in the data. On top of this predicament, data mining technology has received extensive attention. With the help of data mining technology, people can extract originally hidden, unknown, and valuable information from a large amount of disorganized data. By using it in other fields, the value of information has been fully reflected. Data mining technology is a multidisciplinary field technology, which has rapidly developed under the huge demand for information data processing technology in the past ten years.This study mainly analyzes the reasonable solution to the problem of time and space requirements and tries to propose an effective clustering scheme for RFID data. Compared with previous studies, this study mainly has the following two innovations: (1) based on big data technology, the RFID data extraction technology has been improved, and the RFID data extraction technology based on joint Kalman filter fusion is proposed. (2) An improved KM-KL clustering algorithm is proposed.


### 1.1. Related Work

RFID technology is one of the important technologies of the internet of things and big data. It realizes the transmission between things, and a large amount of data is generated during the transmission process. There are many research studies at home and abroad. Wang and Jiang proposed an OCT prediction method utilizing a combination of order and real-time shop floor RFID data. It uses accurate RFID data to describe the real-time load situation of the job shop and tries to mine the mapping relationship between RFID data and OCT from historical data [1]. Fazzinga et al. investigated a method for interpreting RFID data in the context of object tracking. It consists of converting readings generated by RFID-tracked moving objects into semantic locations on a map by exploiting some integrity constraints [2]. Martinus et al. created a system for supermarket shopping research that enables people to scan items themselves and quickly pay. They focus on using RFID technology in the system [3]. Microcontrolled devices were studied by Novikov et al., and their aim was to develop a personal portable effective dose dosimeter with an RFID data channel without built-in power supply [4]. In the process of analysis, cluster analysis is often used for massive RFID data. Yunoh et al. focused on the analysis of fatigue strain signals based on clustering and classification methods. They grouped the feature extraction using the K-means clustering method to obtain the appropriate number of datasets. The classification process is performed by using an artificial neural network (ANN) for optimal pattern recognition. Experiments show that their algorithm is about 92% accurate [5]. Wang et al. predict natural disasters by modeling meteorological disasters. They clustered natural disasters through the detention analysis method, summarized the characteristics of each weather system, and designed disaster control projects based on this. Their experiments show that control engineering has a high centrality with the occurrence of disasters, and engineering implementation can reduce disasters [6]. Chen used MATLAB software to perform statistical analysis and cluster analysis on the daily PM_(2.5) concentrations observed in Shanghai in 2014. The results show that the PM_(2.5) concentration in spring and winter is higher than that in summer and autumn, and the annual distribution of PM_(2.5) concentration is U-shaped [7]. Balik et al. compared health indicators and health expenditures in 28 European Union (EU) countries, 6 EU candidate countries, and 3 European Free Trade Association (EFTA) countries using a cluster analysis method. As a result of the cluster analysis, the countries were divided into 3 clusters, the first cluster including Turkey had the lowest average per capita public, private, and out-of-pocket health expenditure of the three clusters [8]. It can be easily seen from the related research that the research on RFID technology is more on its application level than on data analysis, so the cluster analysis for RFID data is rarely studied.


## 1.1. Related Work

RFID technology is one of the important technologies of the internet of things and big data. It realizes the transmission between things, and a large amount of data is generated during the transmission process. There are many research studies at home and abroad. Wang and Jiang proposed an OCT prediction method utilizing a combination of order and real-time shop floor RFID data. It uses accurate RFID data to describe the real-time load situation of the job shop and tries to mine the mapping relationship between RFID data and OCT from historical data [1]. Fazzinga et al. investigated a method for interpreting RFID data in the context of object tracking. It consists of converting readings generated by RFID-tracked moving objects into semantic locations on a map by exploiting some integrity constraints [2]. Martinus et al. created a system for supermarket shopping research that enables people to scan items themselves and quickly pay. They focus on using RFID technology in the system [3]. Microcontrolled devices were studied by Novikov et al., and their aim was to develop a personal portable effective dose dosimeter with an RFID data channel without built-in power supply [4]. In the process of analysis, cluster analysis is often used for massive RFID data. Yunoh et al. focused on the analysis of fatigue strain signals based on clustering and classification methods. They grouped the feature extraction using the K-means clustering method to obtain the appropriate number of datasets. The classification process is performed by using an artificial neural network (ANN) for optimal pattern recognition. Experiments show that their algorithm is about 92% accurate [5]. Wang et al. predict natural disasters by modeling meteorological disasters. They clustered natural disasters through the detention analysis method, summarized the characteristics of each weather system, and designed disaster control projects based on this. Their experiments show that control engineering has a high centrality with the occurrence of disasters, and engineering implementation can reduce disasters [6]. Chen used MATLAB software to perform statistical analysis and cluster analysis on the daily PM_(2.5) concentrations observed in Shanghai in 2014. The results show that the PM_(2.5) concentration in spring and winter is higher than that in summer and autumn, and the annual distribution of PM_(2.5) concentration is U-shaped [7]. Balik et al. compared health indicators and health expenditures in 28 European Union (EU) countries, 6 EU candidate countries, and 3 European Free Trade Association (EFTA) countries using a cluster analysis method. As a result of the cluster analysis, the countries were divided into 3 clusters, the first cluster including Turkey had the lowest average per capita public, private, and out-of-pocket health expenditure of the three clusters [8]. It can be easily seen from the related research that the research on RFID technology is more on its application level than on data analysis, so the cluster analysis for RFID data is rarely studied.


## 2. RFID Technology

Wireless identification technology, also known as radio-frequency identification technology, is often referred to as RFID (radio-frequency identification) technology. This communication technology originated from the identification application of British fighter jets during World War II and has been commercialized since the 1960s. In particular, the promotion and application of the US Food and Drug Administration (FDA) and Walmart supermarkets, such as real-time detection of fresh commodities in supermarkets, intelligent price tag system, inventory control system, and intelligent shopping cart, have greatly expanded the application market of RFID technology in the world [9, 10].The RFID system is generally composed of three parts: reader (Reader), electronic label (Tag), and application software. The tag can be divided into two parts: an antenna and a special chip, and the chip is attached with a unique identification code, indicating the basic information attached to the object. The principle is that the reader transmits the emitted radio-frequency signal to the electronic tag by means of electromagnetic or inductive coupling, so as to drive the electronic tag circuit to transmit its internal data to the reader. The reader accepts and interprets the relevant data in sequence and uses the software system for relevant processing [11]. Radio-frequency identification has the characteristics of noncontact, not affected by environmental factors, a large amount of stored information, readable and writable, fast recognition speed, long recognition distance, and anticollision function. It can process multiple radio-frequency cards at the same time, and the two identification methods of RFID are shown in Figure 1:Figure 1
RFID (radio-frequency identification) technology.The peculiar way in which RFID devices acquire data leads to serious uncertainty in their data [12, 13]. There are three main reasons for the uncertainty of RFID data, namely, missing reading, overreading, and dirty data. Compared with the three, multireading and dirty data phenomena are more contingent and less likely to occur. The phenomenon of missing reading is relatively common, which is the main factor leading to the uncertainty of RFID data.


### 2.1. The Principle of Antong Data Collection

Because RFID technology has the advantages of fast and real time, it also has extensive analysis in the field of its data collection. The RFID data acquisition system generally includes three parts: the target with the electrical label, the RFID base station, and the information center. The system composition is shown in Figure2:Figure 2
Composition of RFID traffic data collection system.Based on the working principle of RFID technology, the RFID data acquisition system performs radio-frequency identification on the target equipped with electronic tags and transmits the identification data to the traffic information center. Its working principle is as follows: (1) the system enters the acquisition state from the dormant state and (2) determines whether to stop the acquisition by judging the stop flag bit of reading the radio-frequency tag. If there is no stop command, the system starts to read the target information. (3) The RFID base station judges whether a tag enters the radio-frequency field through radio-frequency technology. (4) After sending the request, the mark is selected to confirm whether to detect the specific target. (5) After the verification is passed, the resident writer starts to read the tag carried by the target and returns and transmits the read response data to the information center after the operation is successful. The workflow of the RFID data acquisition system is shown in Figure3:Figure 3
RFID traffic data collection system operation process.


### 2.2. Joint Kalman Filter Fusion of RFID Technology and Coil Technology

For the fusion methods of multisensor information of the same detection section, the fusion methods suitable for dynamic traffic parameters mainly include joint filter fusion, centralized filter fusion, and neural network-based fusion methods.The basic structure of the joint Kalman filter adopts the method of two-stage processing of data and scattered filtering. The combined filter consists of the main filter and several subfilters.The structure diagram of the joint Kalman filtering algorithm used in this study is shown in Figure4:Figure 4
Structure diagram of joint Kalman filter.In the structure of the joint Kalman filter in Figure4, the subfilter first performs independent filtering, transmits the filtering result to the main filter, and at the same time completes the optimal fusion of the collected information.Among them, the state formula and measurement formula of the filter are equations (1) and (2), respectively:(1)Xik=Φk,k−1⋅Xik−1+Wik−1,(2)Yik=Hik⋅Xik+Vik.where Wik−1 is the noise of the dynamic model, and its covariance is Qik−1. Vik is the observation noise, and its covariance is Rik. Since the traffic volume collected by the coil sensor is slightly smaller than the actual value, this study improves the joint Kalman filter. In this study, a sensor with a known acquisition error is selected as the reference sensor, and the method of the first comparison and then fusion is adopted. Its filtering formula is shown in equations (3) and (4):(3)Xik+1=Φk+1,k⋅Xik,(4)pik+1,k=Φk+1,kPikΦTk+1,k+Qik.The main filter does not perform filtering but directly performs data fusion. The fusion method is shown in equations (5) and (6):(5)Xg=Pg∑i=1n,mPi−1Xi,(6)Pg=∑i=1n,mPi−1−1;i=1,2.When the main filter is fused, it feeds back information to the subfilters according to the fusion result, where the feedback factors are shown in equations (7) and (8):(7)βi=p1−1+p2−1−1⋅pi−1,(8)pi−1k=βi⋅pg−1k.When the condition ofQ1 < Q2 is not satisfied, it can be seen from equations (5) to (7) that β1+β1=1. Xg=β1X1+β2X2, that is, the fusion result Xg will take a value between X1 and X2, and change between the two values as the feedback factor changes. At the same time, the subfilters are fed back according to the fusion result, and the information is redistributed to improve the fusion accuracy.Compared with the centralized Kalman filter and artificial neural network, the joint Kalman filter has the advantages of flexible design, a simple algorithm, better fault tolerance, and more suitable for real-time systems.In this study, the dataQ1 collected by RFID technology and the data Q2 collected by the coil sensor are directly combined with Kalman filtering (hereinafter referred to as general fusion). At the same time, it compares the size of Q1 and Q2 and then fuses them according to the fusion method (hereinafter referred to as improved fusion), as shown in Figure 5.Figure 5
Traffic fusion results of the joint Kalman filter algorithm.As can be seen from Figure5, when the traffic volume collected by the RFID technology and the coil sensor is smaller than the actual value, the fusion effect is poor. When the traffic volume collected by RFID technology is smaller than that of the coil sensor, the traffic volume collected by the coil sensor is directly taken as the fusion value. The fusion curve coincides with the traffic volume change curve collected by the coil sensor, which significantly improves the accuracy of the fusion result.It can be seen from Table1 that in dataset 1, the error of the improved fusion is the same as that of the general fusion, so the improved fusion method in this study has certain applicable conditions. That is, when the traffic volume collected by RFID technology is smaller than the traffic volume collected by the known small sensor or larger than the traffic volume collected by the known large sensor, the improved fusion proposed in this study produces better results. From dataset 2 and dataset 3, it can be seen that the relative error is significantly reduced by using the improved method in this study for fusion.Table 1
Comparison of average relative errors (unit: %).
DataTraditional RFID technologyCoil sensorGeneral fusionImprove fusion18.526.270.970.97210.044.937.234.639.565.785.722.74Average9.375.664.642.77


## 2.1. The Principle of Antong Data Collection

Because RFID technology has the advantages of fast and real time, it also has extensive analysis in the field of its data collection. The RFID data acquisition system generally includes three parts: the target with the electrical label, the RFID base station, and the information center. The system composition is shown in Figure2:Figure 2
Composition of RFID traffic data collection system.Based on the working principle of RFID technology, the RFID data acquisition system performs radio-frequency identification on the target equipped with electronic tags and transmits the identification data to the traffic information center. Its working principle is as follows: (1) the system enters the acquisition state from the dormant state and (2) determines whether to stop the acquisition by judging the stop flag bit of reading the radio-frequency tag. If there is no stop command, the system starts to read the target information. (3) The RFID base station judges whether a tag enters the radio-frequency field through radio-frequency technology. (4) After sending the request, the mark is selected to confirm whether to detect the specific target. (5) After the verification is passed, the resident writer starts to read the tag carried by the target and returns and transmits the read response data to the information center after the operation is successful. The workflow of the RFID data acquisition system is shown in Figure3:Figure 3
RFID traffic data collection system operation process.


## 2.2. Joint Kalman Filter Fusion of RFID Technology and Coil Technology

For the fusion methods of multisensor information of the same detection section, the fusion methods suitable for dynamic traffic parameters mainly include joint filter fusion, centralized filter fusion, and neural network-based fusion methods.The basic structure of the joint Kalman filter adopts the method of two-stage processing of data and scattered filtering. The combined filter consists of the main filter and several subfilters.The structure diagram of the joint Kalman filtering algorithm used in this study is shown in Figure4:Figure 4
Structure diagram of joint Kalman filter.In the structure of the joint Kalman filter in Figure4, the subfilter first performs independent filtering, transmits the filtering result to the main filter, and at the same time completes the optimal fusion of the collected information.Among them, the state formula and measurement formula of the filter are equations (1) and (2), respectively:(1)Xik=Φk,k−1⋅Xik−1+Wik−1,(2)Yik=Hik⋅Xik+Vik.where Wik−1 is the noise of the dynamic model, and its covariance is Qik−1. Vik is the observation noise, and its covariance is Rik. Since the traffic volume collected by the coil sensor is slightly smaller than the actual value, this study improves the joint Kalman filter. In this study, a sensor with a known acquisition error is selected as the reference sensor, and the method of the first comparison and then fusion is adopted. Its filtering formula is shown in equations (3) and (4):(3)Xik+1=Φk+1,k⋅Xik,(4)pik+1,k=Φk+1,kPikΦTk+1,k+Qik.The main filter does not perform filtering but directly performs data fusion. The fusion method is shown in equations (5) and (6):(5)Xg=Pg∑i=1n,mPi−1Xi,(6)Pg=∑i=1n,mPi−1−1;i=1,2.When the main filter is fused, it feeds back information to the subfilters according to the fusion result, where the feedback factors are shown in equations (7) and (8):(7)βi=p1−1+p2−1−1⋅pi−1,(8)pi−1k=βi⋅pg−1k.When the condition ofQ1 < Q2 is not satisfied, it can be seen from equations (5) to (7) that β1+β1=1. Xg=β1X1+β2X2, that is, the fusion result Xg will take a value between X1 and X2, and change between the two values as the feedback factor changes. At the same time, the subfilters are fed back according to the fusion result, and the information is redistributed to improve the fusion accuracy.Compared with the centralized Kalman filter and artificial neural network, the joint Kalman filter has the advantages of flexible design, a simple algorithm, better fault tolerance, and more suitable for real-time systems.In this study, the dataQ1 collected by RFID technology and the data Q2 collected by the coil sensor are directly combined with Kalman filtering (hereinafter referred to as general fusion). At the same time, it compares the size of Q1 and Q2 and then fuses them according to the fusion method (hereinafter referred to as improved fusion), as shown in Figure 5.Figure 5
Traffic fusion results of the joint Kalman filter algorithm.As can be seen from Figure5, when the traffic volume collected by the RFID technology and the coil sensor is smaller than the actual value, the fusion effect is poor. When the traffic volume collected by RFID technology is smaller than that of the coil sensor, the traffic volume collected by the coil sensor is directly taken as the fusion value. The fusion curve coincides with the traffic volume change curve collected by the coil sensor, which significantly improves the accuracy of the fusion result.It can be seen from Table1 that in dataset 1, the error of the improved fusion is the same as that of the general fusion, so the improved fusion method in this study has certain applicable conditions. That is, when the traffic volume collected by RFID technology is smaller than the traffic volume collected by the known small sensor or larger than the traffic volume collected by the known large sensor, the improved fusion proposed in this study produces better results. From dataset 2 and dataset 3, it can be seen that the relative error is significantly reduced by using the improved method in this study for fusion.Table 1
Comparison of average relative errors (unit: %).
DataTraditional RFID technologyCoil sensorGeneral fusionImprove fusion18.526.270.970.97210.044.937.234.639.565.785.722.74Average9.375.664.642.77


## 3. Analysis and Result

### 3.1. Cluster Analysis

Pattern recognition is to study the automatic processing and interpretation of patterns through the use of mathematical techniques by computers, and the environment and objects are collectively referred to as “patterns.” With the development of computer technology, it is possible for human beings to study the complex information processing process. An important form of the process is the recognition of the environment and objects by the living body. In the field of pattern recognition and statistical analysis, cluster analysis has always been the focus and research direction of the academic community. So far, a large number of theories and methods have been proposed, and remarkable research results have been achieved. After a long period of research and development, clustering analysis can be divided as follows [14, 15]:


#### 3.1.1. Partition-Based Approach

The typical algorithm is the K-means algorithm and its characteristics are summarized in Table1, so it will not be repeated here.


#### 3.1.2. Hierarchical Approach

Hierarchical clustering methods use top-down splitting or bottom-up agglomeration to represent datasets in a hierarchical tree structure. Each object is first treated as a separate cluster, and these clusters are merged into larger and larger clusters until a given end condition is met. This clustering method is a bottom-up agglomerative clustering method. Divisive hierarchical clustering is just the opposite, where all objects are first grouped into one large cluster. Then, it is gradually divided into smaller and smaller clusters according to the similarity, until the end condition is satisfied.


#### 3.1.3. Density-Based Methods

Density-based methods are divided into different clusters according to different aggregation densities in data object sets, and clusters with similar densities are divided into one cluster. However, its calculation is large, usually isOn2. In addition, based on the density, the setting of parameters has a great influence on the performance of the algorithm, and there is no good solution at present, which mainly depends on the user's experience to select parameters.


#### 3.1.4. Grid-Based Approach

Grid-based clustering method divides the data space into a certain number of ultrarectangular grid cells according to the partition parameters, maps the data objects to the corresponding grid cells, and then merges the adjacent grid cells into a connected region, that is, a cluster. Grid-based clustering method has good scalability for the size of datasets, can handle large-scale datasets, and can find clusters with arbitrary shapes. Grid-based clustering method is usually combined with the density-based clustering method [16].


#### 3.1.5. Model-Based Approach

The model-based clustering method is to use a specific model for cluster analysis and try to optimize the fit between the actual data and the model. Neural network-based clustering methods and statistical learning-based clustering methods are two types of model-based clustering methods. Among the neural network models commonly used in cluster analysis are the self-organizing map (SOM) model [17], the adaptive resonance theory model [18], and the learning vector quantization (LVQ) model. The EM clustering algorithm based on the Gaussian mixture model is a typical clustering method based on statistical learning [19].


#### 3.1.6. Fuzzy Clustering Method

The clustering method described above can be regarded as hard clustering. Different from hard clustering, fuzzy clustering is a soft clustering method. Fuzzy C-means clustering algorithm [20] is a popular fuzzy clustering algorithm at present, which transforms the clustering problem into an optimization problem and uses an iterative method to solve it. It has a simple design, good clustering performance, and wide application. However, the algorithm is sensitive to the initial conditions, easily falls into local optimum, requires a large amount of computation, and has a low resolution for objects in the overlapping area of class boundaries.Table2 summarizes the clustering methods commonly used at present, and the advantages and disadvantages of each method, in which NCA means to determine the number of classes sensitive to initial values and outliers in advance.Table 2
Types of clustering methods.
TypeAdvantageInsufficientBased on partition methodWide application, fast convergence, incremental clustering, and suitability for large-scale dataIt is necessary to determine the NCA, which is sensitive to initial values and outliers, so as to find circular clustersHierarchy-based methodIt does not need to determine the NCA and can find clusters of any shape, which is suitable for data of any attribute and has strong clustering abilityNo backtracking, no exchange of data objects between classes, no full processing of large-scale data, and no incremental clusteringDensity-based methodIt does not need to determine the NCA, can find clusters of different shapes, can detect outliers, and has good adaptability to large datasetsIt is very sensitive to parameters. For datasets with uneven density distribution, the quality of clustering results is not high


### 3.2. Partition-Based Clustering Algorithm—KM-KL Algorithm

#### 3.2.1. The Basic Concept of KM-KL Algorithm

In the traditional partition-based clustering algorithm, the set of uncertain objects is divided into given K clusters according to their mutual distances. The KM-KL algorithm in this study follows the idea of the traditional partition-based clustering algorithm and divides the uncertain dataset O containingn uncertain objects into k clusters. They are denoted as C1,L,Ck, respectively, use the symbol Ci as the center point of each cluster, and use the center point to represent the cluster Ci. In the partition-based clustering algorithm, the following properties are included as follows:(1)
All clusters belong to the uncertain dataset, that isCi⊆O1≤i≤k.(2)
Each cluster contains at least one data record, that isCi≠φ.(3)
Each data record belongs to one cluster and belongs to only one cluster, that is, when equation (9) is satisfied, equation (10) can be satisfied:(9)Ui=1kCi=O,i≠j,(10)Ci∩Cj=φ.On the basis of traditional partition-based clustering, the KM-KL algorithm in this study uses KL divergence as a similarity measure.The algorithm divides uncertain objects intok clusters and selects an optimal cluster center point for each cluster to minimize the sum of the overall KL divergence. In the clustering algorithm, in the division formed by a clustering process, the sum of the KL divergence among all objects is shown in the following:(11)TKL=∑i=1k∑p∈CiDPCi.This formula is used to measure the quality of the clustering. The larger the TKL value, the worse the quality of this clustering is, and the smaller the TKL value is, the better the quality of this clustering is. In equation (11), DPCi represents the KL distance from the object P to the cluster center point Ci, which is used to assign the object to each cluster.(12)∑p∈CiDPCi.Formula (12) represents the sum of the KL distances from each object P in the cluster Ci to the cluster center point Ci, according to which the structure of the cluster Ci can be adjusted.


#### 3.2.2. KM-KL Algorithm Description

The KM-KL algorithm in this study is an extension of the K-medoids algorithm using KL divergence as a similarity measure. This algorithm clusters uncertain data on probabilistic similarity [11–22]. The algorithm is divided into two parts, the initial clustering division stage and the center replacement stage.(1) Initializing the clustering stage. In the initial clustering and division stage, the algorithm selects k cluster center points one by one to initialize the clustering and division of other objects. The first center point C1 selects the object with the smallest sum of KL divergence of other objects in the uncertain object set O, that is, formula:(13)C1=argmin∑P′∈ODP′P,The remainingk − 1 center points are iteratively selected. At the i-th iteration, the algorithm selects the object Ci that minimizes TKL. When it is calculated that P′ will be allocated to the cluster with P as the new cluster center point, the contribution of this allocation to reducing TKL is shown in the following:(14)max0,minj=1i−1DP′Cj−DP′CjFrom formula (14), it can be calculated the sum of the reduction in TKL by the division of all unselected objects in this round, which is expressed as DECP. In the KM-KL algorithm, the center point selected by the i-th iteration is the object with the largest DECP, that is, formula:(15)Ci=argmaxP∈OC1,…,Ci−1DECP.This ensures that the initial cluster center point selected at each time is optimal, because this selection can minimize the dissimilarity between clusters. The initial clustering division phase ends when allk cluster center points are selected and then enters the second phase of the algorithm, the center replacement phase.(2) Center replacement stage. In the center replacement stage, the algorithm iteratively replaces the cluster center points with all noncenter points in the cluster and selects the optimal cluster center point to improve the clustering quality. Every time redistribution occurs, it records the TKL reduction value after redistribution and selects the object with the largest value as the new cluster center, as shown in the following:(16)Pmax=argmaxP∈OC1,…,Ci−1DECP.At this time, if it isDECPmax, it means that this round of exchange improves the clustering effect. Otherwise, the algorithm ends and the final clustering is generated. The example shown in Figure 6 is used to illustrate the KM-KL algorithm flow.Figure 6
Data objects and their KL divergence.
(a)(b)As shown in Figure6, Figure 6(a) shows the distribution of the uncertain object set. Supposing that the uncertain objects a1, a2, and a3 satisfy the same distribution, it forms a cluster. The uncertain objects b1, b2, and b3 satisfy another distribution and it forms another cluster, which is the clustering result of the benchmark. Figure 6(b) shows the KL divergence between uncertain objects and the initialized TKL value. Due to the asymmetry of KL divergence, in Figure 6(a), for example, the divergence from a1 to a2 is not equal to the divergence from a2 to a1. At this time, the KM-KL algorithm is used to cluster the uncertain objects in Figure 6(a), and the input parameter k is equal to 2.Finally, the KM-KL algorithm forms two clusters {a1, a2, a3} and {b2, b1, b3} with a1 and b2 as the center points, respectively, and the division is the optimal division.


### 3.3. Algorithm Performance Test and Effectiveness Analysis

The experimental platform is configured as follows: Intel(R) processor, 2.94 GHz main frequency, 2G memory, using Windows7 operating system. The experimental program is written in C++ language, compiled and run on VS2010, and simulated by MATLAB.This study generates datasets on discrete and continuous domains, respectively. In the continuous domain, an uncertain object is a sample taken from a continuous distribution, and in the discrete domain, the dataset is transformed from a continuous model. The continuous domain is discretized using a meshing method, dividing each dimension into two equal parts, thus dividing the d-dimensional data space into the same 2D cells. The probability of an object in a certain unit is the sum of the probabilities of all sample points of the object in this unit. The value range of the data is [0, 1]d. Three different probability distributions will be used in this study, namely, uniform distribution, Gaussian distribution, and inverse Gaussian distribution, which is generated by Gaussian distribution, as shown in Figure7.Figure 7
Three different distributions. (a) Evenly distribution. (b) Normal distribution. (c) Inverse Gaussian distribution.
(a)(b)(c)The experiments in this study are mainly divided into three parts: first, the effect of the clustering algorithm using KL divergence is analyzed. Second, it shows the improvement of the computational efficiency of the clustering algorithm in this study after using an efficient implementation method and an improved fast Gaussian transform. Finally, experiments show the scalability of the algorithm on large datasets.In classical partition-based and density-based clustering algorithms, KL divergence and geometric distance are used as similarity measures, respectively, to compare clustering quality. Among the partition-based clustering algorithms, the UK-means algorithm using geometric distance (denoted as UK) and the KM-KL and RKM-KL algorithms proposed in this study are compared. Among the density-based clustering algorithms, the FDBSCAN algorithm using geometric distance (denoted as FD) and the DB-KL algorithm in this study are compared.In the experiment, the base number of objects is set ton = 100 by default, each object contains s = 100 sample points, the data dimension d = 4, and the default setting of clustering produces k = 6 clusters. For the density-based algorithm, k is not used as a parameter, and the parameters’ density threshold μ and distance radius ε need to be set here. Among them, the density threshold is μ=5 according to the recommendation, and the distance radius ε is continuously adjusted in the experiment so that the z FD and DB-KL can produce clustering results’ approximate to k clusters.Since the complexity of the density-based algorithm DB-KL exponentially increases with respect to the number of data objects, the algorithm is not suitable for a large number of data objects. The scalability of the RKM-KL algorithm is mainly tested here. The dataset defaults to 4 dimensions and contains 10 clusters.Figures8 and 9 show the effect of the RKM-KL algorithm and the RKM-KL-FGT algorithm on the clustering quality of the algorithm when the data object cardinality is large and the number of object samples is large. It can be seen that when the object cardinality is large or the number of samples is large, the algorithm has a similar quality trend as when the amount of data is small. Moreover, as in the previous experimental analysis, the clustering quality of the RKM-KL-FGT algorithm will be reduced to a certain extent compared to the RKM-KL algorithm.Figure 8
Accuracy when using large datasets on continuous domains.Figure 9
Coverage when using large datasets on continuous domains.Figure10 shows the running time of the RKM-KL algorithm and the RKM-KL-FGT algorithm when the dataset is large. It can be seen that the running time of the RKM-KL algorithm linearly increases as the cardinality of the data objects increases. The RKM-KL-FGT algorithm uses an improved fast Gaussian transform to obtain approximations, so the running time of the algorithm is shorter, and the running time smoothly increases with the increase in cardinality. However, since the calculation of the sum of KL-divergence squarely increases with respect to the number of samples of the object, the calculation time of the algorithm RKM-KL rapidly increases with the increase in the sample data volume. While the computation time of the RKM-KL-FGT algorithm is almost unaffected (it grows linearly), obviously, RKM-KL-FGT is more effective when the amount of data is large.Figure 10
Running time when using large datasets on continuous domains.


## 3.1. Cluster Analysis

Pattern recognition is to study the automatic processing and interpretation of patterns through the use of mathematical techniques by computers, and the environment and objects are collectively referred to as “patterns.” With the development of computer technology, it is possible for human beings to study the complex information processing process. An important form of the process is the recognition of the environment and objects by the living body. In the field of pattern recognition and statistical analysis, cluster analysis has always been the focus and research direction of the academic community. So far, a large number of theories and methods have been proposed, and remarkable research results have been achieved. After a long period of research and development, clustering analysis can be divided as follows [14, 15]:


### 3.1.1. Partition-Based Approach

The typical algorithm is the K-means algorithm and its characteristics are summarized in Table1, so it will not be repeated here.


### 3.1.2. Hierarchical Approach

Hierarchical clustering methods use top-down splitting or bottom-up agglomeration to represent datasets in a hierarchical tree structure. Each object is first treated as a separate cluster, and these clusters are merged into larger and larger clusters until a given end condition is met. This clustering method is a bottom-up agglomerative clustering method. Divisive hierarchical clustering is just the opposite, where all objects are first grouped into one large cluster. Then, it is gradually divided into smaller and smaller clusters according to the similarity, until the end condition is satisfied.


### 3.1.3. Density-Based Methods

Density-based methods are divided into different clusters according to different aggregation densities in data object sets, and clusters with similar densities are divided into one cluster. However, its calculation is large, usually isOn2. In addition, based on the density, the setting of parameters has a great influence on the performance of the algorithm, and there is no good solution at present, which mainly depends on the user's experience to select parameters.


### 3.1.4. Grid-Based Approach

Grid-based clustering method divides the data space into a certain number of ultrarectangular grid cells according to the partition parameters, maps the data objects to the corresponding grid cells, and then merges the adjacent grid cells into a connected region, that is, a cluster. Grid-based clustering method has good scalability for the size of datasets, can handle large-scale datasets, and can find clusters with arbitrary shapes. Grid-based clustering method is usually combined with the density-based clustering method [16].


### 3.1.5. Model-Based Approach

The model-based clustering method is to use a specific model for cluster analysis and try to optimize the fit between the actual data and the model. Neural network-based clustering methods and statistical learning-based clustering methods are two types of model-based clustering methods. Among the neural network models commonly used in cluster analysis are the self-organizing map (SOM) model [17], the adaptive resonance theory model [18], and the learning vector quantization (LVQ) model. The EM clustering algorithm based on the Gaussian mixture model is a typical clustering method based on statistical learning [19].


### 3.1.6. Fuzzy Clustering Method

The clustering method described above can be regarded as hard clustering. Different from hard clustering, fuzzy clustering is a soft clustering method. Fuzzy C-means clustering algorithm [20] is a popular fuzzy clustering algorithm at present, which transforms the clustering problem into an optimization problem and uses an iterative method to solve it. It has a simple design, good clustering performance, and wide application. However, the algorithm is sensitive to the initial conditions, easily falls into local optimum, requires a large amount of computation, and has a low resolution for objects in the overlapping area of class boundaries.Table2 summarizes the clustering methods commonly used at present, and the advantages and disadvantages of each method, in which NCA means to determine the number of classes sensitive to initial values and outliers in advance.Table 2
Types of clustering methods.
TypeAdvantageInsufficientBased on partition methodWide application, fast convergence, incremental clustering, and suitability for large-scale dataIt is necessary to determine the NCA, which is sensitive to initial values and outliers, so as to find circular clustersHierarchy-based methodIt does not need to determine the NCA and can find clusters of any shape, which is suitable for data of any attribute and has strong clustering abilityNo backtracking, no exchange of data objects between classes, no full processing of large-scale data, and no incremental clusteringDensity-based methodIt does not need to determine the NCA, can find clusters of different shapes, can detect outliers, and has good adaptability to large datasetsIt is very sensitive to parameters. For datasets with uneven density distribution, the quality of clustering results is not high


## 3.1.1. Partition-Based Approach

The typical algorithm is the K-means algorithm and its characteristics are summarized in Table1, so it will not be repeated here.


## 3.1.2. Hierarchical Approach

Hierarchical clustering methods use top-down splitting or bottom-up agglomeration to represent datasets in a hierarchical tree structure. Each object is first treated as a separate cluster, and these clusters are merged into larger and larger clusters until a given end condition is met. This clustering method is a bottom-up agglomerative clustering method. Divisive hierarchical clustering is just the opposite, where all objects are first grouped into one large cluster. Then, it is gradually divided into smaller and smaller clusters according to the similarity, until the end condition is satisfied.


## 3.1.3. Density-Based Methods

Density-based methods are divided into different clusters according to different aggregation densities in data object sets, and clusters with similar densities are divided into one cluster. However, its calculation is large, usually isOn2. In addition, based on the density, the setting of parameters has a great influence on the performance of the algorithm, and there is no good solution at present, which mainly depends on the user's experience to select parameters.


## 3.1.4. Grid-Based Approach

Grid-based clustering method divides the data space into a certain number of ultrarectangular grid cells according to the partition parameters, maps the data objects to the corresponding grid cells, and then merges the adjacent grid cells into a connected region, that is, a cluster. Grid-based clustering method has good scalability for the size of datasets, can handle large-scale datasets, and can find clusters with arbitrary shapes. Grid-based clustering method is usually combined with the density-based clustering method [16].


## 3.1.5. Model-Based Approach

The model-based clustering method is to use a specific model for cluster analysis and try to optimize the fit between the actual data and the model. Neural network-based clustering methods and statistical learning-based clustering methods are two types of model-based clustering methods. Among the neural network models commonly used in cluster analysis are the self-organizing map (SOM) model [17], the adaptive resonance theory model [18], and the learning vector quantization (LVQ) model. The EM clustering algorithm based on the Gaussian mixture model is a typical clustering method based on statistical learning [19].


## 3.1.6. Fuzzy Clustering Method

The clustering method described above can be regarded as hard clustering. Different from hard clustering, fuzzy clustering is a soft clustering method. Fuzzy C-means clustering algorithm [20] is a popular fuzzy clustering algorithm at present, which transforms the clustering problem into an optimization problem and uses an iterative method to solve it. It has a simple design, good clustering performance, and wide application. However, the algorithm is sensitive to the initial conditions, easily falls into local optimum, requires a large amount of computation, and has a low resolution for objects in the overlapping area of class boundaries.Table2 summarizes the clustering methods commonly used at present, and the advantages and disadvantages of each method, in which NCA means to determine the number of classes sensitive to initial values and outliers in advance.Table 2
Types of clustering methods.
TypeAdvantageInsufficientBased on partition methodWide application, fast convergence, incremental clustering, and suitability for large-scale dataIt is necessary to determine the NCA, which is sensitive to initial values and outliers, so as to find circular clustersHierarchy-based methodIt does not need to determine the NCA and can find clusters of any shape, which is suitable for data of any attribute and has strong clustering abilityNo backtracking, no exchange of data objects between classes, no full processing of large-scale data, and no incremental clusteringDensity-based methodIt does not need to determine the NCA, can find clusters of different shapes, can detect outliers, and has good adaptability to large datasetsIt is very sensitive to parameters. For datasets with uneven density distribution, the quality of clustering results is not high


## 3.2. Partition-Based Clustering Algorithm—KM-KL Algorithm

### 3.2.1. The Basic Concept of KM-KL Algorithm

In the traditional partition-based clustering algorithm, the set of uncertain objects is divided into given K clusters according to their mutual distances. The KM-KL algorithm in this study follows the idea of the traditional partition-based clustering algorithm and divides the uncertain dataset O containingn uncertain objects into k clusters. They are denoted as C1,L,Ck, respectively, use the symbol Ci as the center point of each cluster, and use the center point to represent the cluster Ci. In the partition-based clustering algorithm, the following properties are included as follows:(1)
All clusters belong to the uncertain dataset, that isCi⊆O1≤i≤k.(2)
Each cluster contains at least one data record, that isCi≠φ.(3)
Each data record belongs to one cluster and belongs to only one cluster, that is, when equation (9) is satisfied, equation (10) can be satisfied:(9)Ui=1kCi=O,i≠j,(10)Ci∩Cj=φ.On the basis of traditional partition-based clustering, the KM-KL algorithm in this study uses KL divergence as a similarity measure.The algorithm divides uncertain objects intok clusters and selects an optimal cluster center point for each cluster to minimize the sum of the overall KL divergence. In the clustering algorithm, in the division formed by a clustering process, the sum of the KL divergence among all objects is shown in the following:(11)TKL=∑i=1k∑p∈CiDPCi.This formula is used to measure the quality of the clustering. The larger the TKL value, the worse the quality of this clustering is, and the smaller the TKL value is, the better the quality of this clustering is. In equation (11), DPCi represents the KL distance from the object P to the cluster center point Ci, which is used to assign the object to each cluster.(12)∑p∈CiDPCi.Formula (12) represents the sum of the KL distances from each object P in the cluster Ci to the cluster center point Ci, according to which the structure of the cluster Ci can be adjusted.


### 3.2.2. KM-KL Algorithm Description

The KM-KL algorithm in this study is an extension of the K-medoids algorithm using KL divergence as a similarity measure. This algorithm clusters uncertain data on probabilistic similarity [11–22]. The algorithm is divided into two parts, the initial clustering division stage and the center replacement stage.(1) Initializing the clustering stage. In the initial clustering and division stage, the algorithm selects k cluster center points one by one to initialize the clustering and division of other objects. The first center point C1 selects the object with the smallest sum of KL divergence of other objects in the uncertain object set O, that is, formula:(13)C1=argmin∑P′∈ODP′P,The remainingk − 1 center points are iteratively selected. At the i-th iteration, the algorithm selects the object Ci that minimizes TKL. When it is calculated that P′ will be allocated to the cluster with P as the new cluster center point, the contribution of this allocation to reducing TKL is shown in the following:(14)max0,minj=1i−1DP′Cj−DP′CjFrom formula (14), it can be calculated the sum of the reduction in TKL by the division of all unselected objects in this round, which is expressed as DECP. In the KM-KL algorithm, the center point selected by the i-th iteration is the object with the largest DECP, that is, formula:(15)Ci=argmaxP∈OC1,…,Ci−1DECP.This ensures that the initial cluster center point selected at each time is optimal, because this selection can minimize the dissimilarity between clusters. The initial clustering division phase ends when allk cluster center points are selected and then enters the second phase of the algorithm, the center replacement phase.(2) Center replacement stage. In the center replacement stage, the algorithm iteratively replaces the cluster center points with all noncenter points in the cluster and selects the optimal cluster center point to improve the clustering quality. Every time redistribution occurs, it records the TKL reduction value after redistribution and selects the object with the largest value as the new cluster center, as shown in the following:(16)Pmax=argmaxP∈OC1,…,Ci−1DECP.At this time, if it isDECPmax, it means that this round of exchange improves the clustering effect. Otherwise, the algorithm ends and the final clustering is generated. The example shown in Figure 6 is used to illustrate the KM-KL algorithm flow.Figure 6
Data objects and their KL divergence.
(a)(b)As shown in Figure6, Figure 6(a) shows the distribution of the uncertain object set. Supposing that the uncertain objects a1, a2, and a3 satisfy the same distribution, it forms a cluster. The uncertain objects b1, b2, and b3 satisfy another distribution and it forms another cluster, which is the clustering result of the benchmark. Figure 6(b) shows the KL divergence between uncertain objects and the initialized TKL value. Due to the asymmetry of KL divergence, in Figure 6(a), for example, the divergence from a1 to a2 is not equal to the divergence from a2 to a1. At this time, the KM-KL algorithm is used to cluster the uncertain objects in Figure 6(a), and the input parameter k is equal to 2.Finally, the KM-KL algorithm forms two clusters {a1, a2, a3} and {b2, b1, b3} with a1 and b2 as the center points, respectively, and the division is the optimal division.


## 3.2.1. The Basic Concept of KM-KL Algorithm

In the traditional partition-based clustering algorithm, the set of uncertain objects is divided into given K clusters according to their mutual distances. The KM-KL algorithm in this study follows the idea of the traditional partition-based clustering algorithm and divides the uncertain dataset O containingn uncertain objects into k clusters. They are denoted as C1,L,Ck, respectively, use the symbol Ci as the center point of each cluster, and use the center point to represent the cluster Ci. In the partition-based clustering algorithm, the following properties are included as follows:(1)
All clusters belong to the uncertain dataset, that isCi⊆O1≤i≤k.(2)
Each cluster contains at least one data record, that isCi≠φ.(3)
Each data record belongs to one cluster and belongs to only one cluster, that is, when equation (9) is satisfied, equation (10) can be satisfied:(9)Ui=1kCi=O,i≠j,(10)Ci∩Cj=φ.On the basis of traditional partition-based clustering, the KM-KL algorithm in this study uses KL divergence as a similarity measure.The algorithm divides uncertain objects intok clusters and selects an optimal cluster center point for each cluster to minimize the sum of the overall KL divergence. In the clustering algorithm, in the division formed by a clustering process, the sum of the KL divergence among all objects is shown in the following:(11)TKL=∑i=1k∑p∈CiDPCi.This formula is used to measure the quality of the clustering. The larger the TKL value, the worse the quality of this clustering is, and the smaller the TKL value is, the better the quality of this clustering is. In equation (11), DPCi represents the KL distance from the object P to the cluster center point Ci, which is used to assign the object to each cluster.(12)∑p∈CiDPCi.Formula (12) represents the sum of the KL distances from each object P in the cluster Ci to the cluster center point Ci, according to which the structure of the cluster Ci can be adjusted.


## 3.2.2. KM-KL Algorithm Description

The KM-KL algorithm in this study is an extension of the K-medoids algorithm using KL divergence as a similarity measure. This algorithm clusters uncertain data on probabilistic similarity [11–22]. The algorithm is divided into two parts, the initial clustering division stage and the center replacement stage.(1) Initializing the clustering stage. In the initial clustering and division stage, the algorithm selects k cluster center points one by one to initialize the clustering and division of other objects. The first center point C1 selects the object with the smallest sum of KL divergence of other objects in the uncertain object set O, that is, formula:(13)C1=argmin∑P′∈ODP′P,The remainingk − 1 center points are iteratively selected. At the i-th iteration, the algorithm selects the object Ci that minimizes TKL. When it is calculated that P′ will be allocated to the cluster with P as the new cluster center point, the contribution of this allocation to reducing TKL is shown in the following:(14)max0,minj=1i−1DP′Cj−DP′CjFrom formula (14), it can be calculated the sum of the reduction in TKL by the division of all unselected objects in this round, which is expressed as DECP. In the KM-KL algorithm, the center point selected by the i-th iteration is the object with the largest DECP, that is, formula:(15)Ci=argmaxP∈OC1,…,Ci−1DECP.This ensures that the initial cluster center point selected at each time is optimal, because this selection can minimize the dissimilarity between clusters. The initial clustering division phase ends when allk cluster center points are selected and then enters the second phase of the algorithm, the center replacement phase.(2) Center replacement stage. In the center replacement stage, the algorithm iteratively replaces the cluster center points with all noncenter points in the cluster and selects the optimal cluster center point to improve the clustering quality. Every time redistribution occurs, it records the TKL reduction value after redistribution and selects the object with the largest value as the new cluster center, as shown in the following:(16)Pmax=argmaxP∈OC1,…,Ci−1DECP.At this time, if it isDECPmax, it means that this round of exchange improves the clustering effect. Otherwise, the algorithm ends and the final clustering is generated. The example shown in Figure 6 is used to illustrate the KM-KL algorithm flow.Figure 6
Data objects and their KL divergence.
(a)(b)As shown in Figure6, Figure 6(a) shows the distribution of the uncertain object set. Supposing that the uncertain objects a1, a2, and a3 satisfy the same distribution, it forms a cluster. The uncertain objects b1, b2, and b3 satisfy another distribution and it forms another cluster, which is the clustering result of the benchmark. Figure 6(b) shows the KL divergence between uncertain objects and the initialized TKL value. Due to the asymmetry of KL divergence, in Figure 6(a), for example, the divergence from a1 to a2 is not equal to the divergence from a2 to a1. At this time, the KM-KL algorithm is used to cluster the uncertain objects in Figure 6(a), and the input parameter k is equal to 2.Finally, the KM-KL algorithm forms two clusters {a1, a2, a3} and {b2, b1, b3} with a1 and b2 as the center points, respectively, and the division is the optimal division.


## 3.3. Algorithm Performance Test and Effectiveness Analysis

The experimental platform is configured as follows: Intel(R) processor, 2.94 GHz main frequency, 2G memory, using Windows7 operating system. The experimental program is written in C++ language, compiled and run on VS2010, and simulated by MATLAB.This study generates datasets on discrete and continuous domains, respectively. In the continuous domain, an uncertain object is a sample taken from a continuous distribution, and in the discrete domain, the dataset is transformed from a continuous model. The continuous domain is discretized using a meshing method, dividing each dimension into two equal parts, thus dividing the d-dimensional data space into the same 2D cells. The probability of an object in a certain unit is the sum of the probabilities of all sample points of the object in this unit. The value range of the data is [0, 1]d. Three different probability distributions will be used in this study, namely, uniform distribution, Gaussian distribution, and inverse Gaussian distribution, which is generated by Gaussian distribution, as shown in Figure7.Figure 7
Three different distributions. (a) Evenly distribution. (b) Normal distribution. (c) Inverse Gaussian distribution.
(a)(b)(c)The experiments in this study are mainly divided into three parts: first, the effect of the clustering algorithm using KL divergence is analyzed. Second, it shows the improvement of the computational efficiency of the clustering algorithm in this study after using an efficient implementation method and an improved fast Gaussian transform. Finally, experiments show the scalability of the algorithm on large datasets.In classical partition-based and density-based clustering algorithms, KL divergence and geometric distance are used as similarity measures, respectively, to compare clustering quality. Among the partition-based clustering algorithms, the UK-means algorithm using geometric distance (denoted as UK) and the KM-KL and RKM-KL algorithms proposed in this study are compared. Among the density-based clustering algorithms, the FDBSCAN algorithm using geometric distance (denoted as FD) and the DB-KL algorithm in this study are compared.In the experiment, the base number of objects is set ton = 100 by default, each object contains s = 100 sample points, the data dimension d = 4, and the default setting of clustering produces k = 6 clusters. For the density-based algorithm, k is not used as a parameter, and the parameters’ density threshold μ and distance radius ε need to be set here. Among them, the density threshold is μ=5 according to the recommendation, and the distance radius ε is continuously adjusted in the experiment so that the z FD and DB-KL can produce clustering results’ approximate to k clusters.Since the complexity of the density-based algorithm DB-KL exponentially increases with respect to the number of data objects, the algorithm is not suitable for a large number of data objects. The scalability of the RKM-KL algorithm is mainly tested here. The dataset defaults to 4 dimensions and contains 10 clusters.Figures8 and 9 show the effect of the RKM-KL algorithm and the RKM-KL-FGT algorithm on the clustering quality of the algorithm when the data object cardinality is large and the number of object samples is large. It can be seen that when the object cardinality is large or the number of samples is large, the algorithm has a similar quality trend as when the amount of data is small. Moreover, as in the previous experimental analysis, the clustering quality of the RKM-KL-FGT algorithm will be reduced to a certain extent compared to the RKM-KL algorithm.Figure 8
Accuracy when using large datasets on continuous domains.Figure 9
Coverage when using large datasets on continuous domains.Figure10 shows the running time of the RKM-KL algorithm and the RKM-KL-FGT algorithm when the dataset is large. It can be seen that the running time of the RKM-KL algorithm linearly increases as the cardinality of the data objects increases. The RKM-KL-FGT algorithm uses an improved fast Gaussian transform to obtain approximations, so the running time of the algorithm is shorter, and the running time smoothly increases with the increase in cardinality. However, since the calculation of the sum of KL-divergence squarely increases with respect to the number of samples of the object, the calculation time of the algorithm RKM-KL rapidly increases with the increase in the sample data volume. While the computation time of the RKM-KL-FGT algorithm is almost unaffected (it grows linearly), obviously, RKM-KL-FGT is more effective when the amount of data is large.Figure 10
Running time when using large datasets on continuous domains.


## 4. Conclusions

The application of RFID technology has been relatively mature, and there are applications in many places. Especially after these years of development, RFID technology has relatively mature applications in many aspects, such as supermarkets, express delivery, logistics, and other industries. In this study, the massive data generated by RFID technology are analyzed and clustered to mine effective information and reduce system running time. This study starts from the relevant background of big data and computer science and introduces the relevant research background of RFID technology. Subsequently, this study will introduce the RFID technology in detail, from the definition to the calculation process. In this study, the cluster analysis is introduced in detail, and an improved KM-KL algorithm is proposed, which is proved to be very effective. However, there are also shortcomings in this study, that is, the data extraction is too extensive, and subsequent research can conduct specific analysis on the data of a certain industry, such as logistics data.



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*Source: 3432688-2022-03-26.xml*