1 Introduction
The cervical spondylosis(CS), a common degenerative disease, harms human life and health, affects up to twothirds of the population, and poses an serious burden on individuals and society [Matz et al.2009, Kotil and Bilge2008, Cai et al.2016, Nana Wang, Wang et al.2018]. Currently, the neck disability index [Howard Vernon] is the most commonly used tool to assess the neck dysfunction [Vernon and Mior1991], The availability of which are mainly undermined by the coarsegrained and unreasonable classification, despite that the NDI information is subjective and not accurate enough.
The surface electromyography (sEMG) is a nonstationary weak physiological signal collected by the sEMG device, and consists of the Motor Unit Action Potential Trains (MUAPTs) which is generated by motor units and superimposed on the surface of the skin [Nana Wang]. The sEMG is the CSrelated physiological signals and have the ability to reflect the neck function status closely related to CS [Wang et al.2018, Falla et al.2007, Johnston et al.2008a, Johnston et al.2008b, Madeleine et al.2016]. What’s more, the signals is nonintrusive and affordable, and the acquisition is convenient. Thus, we seek to use the sEMG data set collected from the clinical environment to provide more objective and finegrained classification of cervical function.
As a powerful modelbased clustering algorithm, the Selforganizing mapping (SOM) has strong ability of the selflearning, selforganizing, adaptive and nonlinear mapping, which is especially suitable for dealing with nonlinear reasoning, recognition, and classification task without the ground truth on the high dimensional and smallsampling data set
[Junlin Chen2017]. Thus, we seek to utilize the SOM clustering algorithm to implement the division on the sEMG data set. Despite of the advantages, the stability is critical for clinical application research. And, the stability clusters are defined in our paper as follow: the stable differences between the individuals of different categories^{1}^{1}1the samples that are assigned to a cluster by a trained SOM model can also be assigned to the same cluster by second trained SOM.. However, it is an challenging task to obtain a stability clustering results as the samples that are assigned to a group by a trained SOM model are assigned to the different group by second trained SOM, compared with the clustering result of the two trained SOM with the different parameter settings.In order to achieve it, we proposed and developed the classification framework EasiCS to obtain the relative stability clustering results, which consists of dimension reduction, clustering algorithm EasiSOM, spectral clustering algorithm EasiSC as shown in the Figure 1. To the best of our knowledge, the EasiCS is the first effort to utilize the clustering algorithm and sEMG. Compared with the seven commonly used clustering algorithms, the novelty framework EasiCS provide the best overall performance. The cervical spondylosis(CS), a common degenerative disease, harms human life and health, affects up to twothirds of the population, and poses an serious burden on individuals and society [Matz et al.2009, Kotil and Bilge2008, Cai et al.2016, Nana Wang, Wang et al.2018]. Currently, the neck disability index [Howard Vernon] is the most commonly used tool to assess the neck dysfunction [Vernon and Mior1991], The availability of which are mainly undermined by the coarsegrained and unreasonable classification, despite that the NDI information is subjective and not accurate enough.
The surface electromyography (sEMG) is a nonstationary weak physiological signal collected by the sEMG device, and consists of the Motor Unit Action Potential Trains (MUAPTs) which is generated by motor units and superimposed on the surface of the skin [Nana Wang]. The sEMG is the CSrelated physiological signals and have the ability to reflect the neck function status closely related to CS [Wang et al.2018, Falla et al.2007, Johnston et al.2008a, Johnston et al.2008b, Madeleine et al.2016]. What’s more, the signals is nonintrusive and affordable, and the acquisition is convenient. Thus, we seek to use the sEMG data set collected from the clinical environment to provide more objective and finegrained classification of cervical function.
As a powerful modelbased clustering algorithm, the Selforganizing mapping (SOM) has strong ability of the selflearning, selforganizing, adaptive and nonlinear mapping, which is especially suitable for dealing with nonlinear reasoning, recognition, and classification task without the ground truth on the high dimensional and smallsampling data set [Junlin Chen2017]. Thus, we seek to utilize the SOM clustering algorithm to implement the division on the sEMG data set. Despite of the advantages, the stability is critical for clinical application research. And, the stability clusters are defined in our paper as follow: the stable differences between the individuals of different categories. However, it is an challenging task to obtain a stability clustering results as the samples that are assigned to a group by a trained SOM model are assigned to the different group by second trained SOM, compared with the clustering result of the two trained SOM with the different parameter settings.
In order to achieve it, we proposed and developed the classification framework EasiCS to obtain the relative stability clustering results, which consists of dimension reduction, clustering algorithm EasiSOM, spectral clustering algorithm EasiSC as shown in the Figure 1. To the best of our knowledge, the EasiCS is the first effort to utilize the clustering algorithm and sEMG. Compared with the seven commonly used clustering algorithms, the novelty framework EasiCS provide the best overall performance.
The CS is a chronic musculoskeletal disorder, which is mainly accompanied by the neck pain and the disability of humanrelated functions [HoggJohnson et al.2009]. The current classification of the CS is based on clinical symptoms and cervical lesion which was in accordance with 2012 ICD9CM Diagnosis Code 721(721.0 Cervical spondylosis without myelopathy, 721.1 Cervical spondylosis with myelopathy) and the diagnostic criteria of diagnosis and treatment for CS issued by China Rehabilitation Medicine Association [gui2010]. There are many studies on CS intelligent classification: clinicalsymptomsbased method, cervicalvertebra lesionbased method, neckmusclelesionbased method, traditional Chinese medical classification.
For the clinicalsymptomsbased method, with the guidance of the knowledge engineering and expert system construction theory, the work
[Jebri et al.2015] developed the medical diagnostic expert system CSES of cervical spondylosis which use the forward reasoning as the main reasoning mechanism and production rules to represent domain expert knowledge.For the cervicalspinelesionbased method, faced with the divergences in the traditional Xray reading method, the research [Yu et al.2015] proposed the method based on maximum likelihood theory to solve the type classification of CS, and it is proved to be the effective method. For the degenerative changes of the cervical spine, the research [Jebri et al.2015]
proposed a machine learning approach to detect and localize degenerative changes in lateral Xray images of the cervical spine, obtaining the 95% accuracy.
For the neckmusclelesionbased method, the work [Zhongmin2011] have demonstrated that there are the stability and reproducibility of myoelectric activity on the surface of normal human cervical muscles, and there are significant differences of surface electromyography index between the cervical spondylosis and the healthy. The work [Nana Wang] proposed a convenient nonharm CS intelligent identify method EasiCNCSII which consists of the sEMG data acquisition and the CS identification, obtaining the best performance of 91.02% in mean accuracy, 97.14% in mean sensitivity, 81.43% in mean specificity, 0.95 in mean AUC. The research [Wang et al.2018]
proposed an intelligent method EasiDeep based on the deep learning which utilized the surface electromyography (sEMG) signal to identify CS, achieving the stateoftheart performance. It proves that sEMG contains pathological information of CS which is consistent with the work
[Falla et al.2007, Johnston et al.2008a, Johnston et al.2008b, Madeleine et al.2016].The application of clustering technology has achieved highlighted results in the bioinformatics field as well as the field of image segmentation, object and character recognition. Faced with the problem that the extent to which genomic signatures are shared across tissues is still unclear, the Katherine [Hoadley et al.2014] developed an integrative analysis to reveal a unified classification into 11 major subtypes. The research [Shen, Olshen, and Ladanyi2009] developed a joint latent variable model iCluster for integrative clustering to analyze breast and lung cancer subtype. The research [Shen et al.2012] utilized the iCluster to present an integrative subtype analysis of the TCGA glioblastoma (GBM) data set, revealing new insights through integrated subtype characterization.
2 Preliminaries
2.1 Participants
The 57 volunteers participated in the study from March 15, 2017 to July 15, 2018 in China, the female number of which is 42 and the male number of which is 15. The subjects have received a clinical diagnosis of the CS, which are in accordance with 2012 ICD9CM Diagnosis Code 721 (721.0 Cervical spondylosis without myelopathy, 721.1 Cervical spondylosis with myelopathy) and the criteria of diagnosis and treatment for CS issued by China Rehabilitation Medicine association. The 57 subjects are mainly sedentary people from 27 different occupations and involve 27 types of the CS lesion, the age of which range from 20 to 64.
2.2 Dataset
The data set are acquired from 57 volunteers above. The sEMG signal were synchronously recorded from the 6 muscles: the left sternocleidomastoid (), the left upper trapezius (), the left cervical erector spinae (), the right cervical erector spinae (), the right upper trapezius () and the right sternocleidomastoid (). The volunteers complete the 7 movements () in sequence, each movement of which is performed 3 times. The sEMG data is obtained from the muscle activated by the movement . The feature are extracted from the (), forming a sample . The detail on the is in the paper [Nana Wang]. The 3 samples are from a volunteer, and the 171 () samples is obtained from the 57 volunteers.
3 Methodology
In this section, we elaborated our proposed method EasiCS. As shown in Figure 2, the EasiCS consists of three parts: the dimensionality reduction, clustering algorithm EasiSOM, community detection EasiSC.
3.1 The dimensionality reduction: locally linear embedding
The highdimensional sEMG data decreases computational efficiency, increase storage overhead, and cause overfit [Li et al.2018, Nana Wang]
, especially for the small sample data sets. Faced with the highdimensional data, dimensionality reduction is an effective means of data preprocessing. Unlike clustering methods for local dimensionality reduction, the locally linear embedding (LLE), an unsupervised learning algorithm, computes lowdimensional, neighborhoodpreserving embeddings of highdimensional inputs and is able to learn the global structure of nonlinear manifolds
[Roweis and Saul2000].In this paper, we utilized the LLE to deal with the input according to the work[Roweis and Saul2000]. The number of neighbors and the dimension of the data set is set to 30. The is obtained. The general process is shown in the Algorithm 1. The details on calculation are in work [Roweis and Saul2000].
(1)  
(2)  
(3) 
3.2 The EasiSOM
The SelfOrganizing Map(SOM) is an excellent tool in exploratory phase of data mining, and projects input space on prototypes of a lowdimensional regular grid that can be effectively utilized to visualize and explore properties of the data [Vesanto, Alhoniemi, and others2000].
The SOM clustering results are sensitive to initial value settings, leading that there are different clusters result between two trained SOM model with the different parameter settings. And the input of the SOM contains 171 samples from the 57 subjects. A division of the 171 samples reflect the internal relations of the 57 subjects above. Although the divisions are different, we think they contain the common information that reflect the true association of 57 subjects. Thus, according to the ensemble learning, we utilize the multiple SOM algorithm to perform multiple classifications and find a set of partitions to analyze the internal commonality of the division above.
In this paper, as shown in the Algorithm 1, we developed the EasiSOM based on the SOM in our paper, which integrate the 1000 trained SOM to generate the 1000 division results. Finally, a partition set is obtained which includes 625 divisions.
3.3 The EasiSC
Next, we seek to find the internal structure of 57 entities behinds the . The network is a powerful mechanism, and has the ability to represent the complex relationship between the data [Huang et al.2018]. Complex systems with interconnected internal entities can be abstracted into networks which have extremely important structure information. The identification of the structure is of crucial importance as they may help to uncover aprior unknown functional module such as topics in information network or cybercommunities in social networks [Blondel et al.2008]. The spectral clustering algorithm is a classic clustering algorithm based on network topology.
In our work, the EasiSC based on the spectral clustering algorithm are developed to cluster the . As shown in the Algorithm 2, the each sample is treated as the network node , and the edge between the node and is represented as . The weight value between nodes is initialized to 0. If the two nodes are divided into the same class in the division, the weight value is increased by 1. The detail computation on the is shown in the Formula 4.
In order to facilitate the subsequent data analysis of 57 subjects, as the clustering results of the three samples of almost all subjects are the same, we mapped the clustering result labels of 171 samples to 57 subject as following rule: the label of a subject is defined as the labels that most samples of a subject have.
(4) 
Where the is the number of the divisions from the 625 trained SOM, and the and is the number of the 171 samples.
3.4 Algorithm
As the Algorithm 3 shown, we firstly reduce the dimensionality of the sEMG data and generate the data set . Then, the EasiSOM is trained to iteratively cluster the and generate the . Finally, the EasiSC is trained to cluster .
4 Experiments Result and Discussion
4.1 The metrics
For the lack of the ground truth (the truth label), it is generally believed that the optimal clustering partition minimizes the intracluster distance and maximizes intercluster distance. The metric [scikitlearn developers] of the Silhouette Coefficient (), Calinski Harabaz score (), Davies Bouldin score () are the widely used verification indicator to evaluate the quality of the clusters or the performance of the clustering algorithm. The large Silhouette Coefficient is, the large Calinski Harabaz score is, the smaller Davies Bouldin score is, the better the quality of the clusters are, the better the clustering algorithm perform. Thus, we utilized the indicators , and for overall cluster quality evaluation.
4.2 The Model for comparison
We compared the EasiSOM with the seven commonly used clustering models: kmeans, affinity propagation, Meanshift, spectral clustering, agglomerative clustering, gaussian mixtures and Birch on the same data set in the same clustering task as follows:

Kmeans (): The KMeans is an algorithm for clustering data points by computing the average value. It is one of the bestknown, bench marked and simplest clustering algorithms [MacQueen and others1967, Saxena et al.2017].

Affinity propagation (): Affinity propagation [Frey and Dueck2007] is a clustering algorithm based on ’information transfer’ between data points, which does not need to specify the number of clusters in advance, and can automatically generate the optimal number of clusters.

Meanshift (): it is a general nonparametric technique, which is used for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters [Comaniciu and Meer2002].

Spectral clustering (): it is a graphbased clustering method. It is simple to implement, can be solved efficiently by standard linear algebra method, and outperforms traditional clustering algorithms [Von Luxburg2007].

Agglomerative clustering (
): it is an hierarchical clustering methods and follows the bottomup approach
[Saxena et al.2017]. 
Gaussian mixtures (
): it is a parametric probability density function and commonly used as a parametric model of the probability distribution of continuous measurements or features in a biometric system
[Reynolds2015]. 
Birch (): it is a typical integrated hierarchical clustering algorithm [Zhang, Ramakrishnan, and Livny1996, Ding et al.2015], which is more suitable for the large amount of data and the large number of clusters.
4.3 The comparison of the performance of the model
N  SC  CH  DB  ICS  

56  0.4871  8.7952  0.9686  1.75%  
46  0.4547  7.8716  1.1452  2.34%  
7  0.2331  7.2309  1.1274  2.92%  
48  0.4226  7.5257  1.2397  7.60%  
56  0.4535  8.7116  0.9800  5.26%  
55  0.4848  8.7501  0.9808  3.51%  
56  0.4803  8.9374  0.9687  4.68%  
SOM  13  0.7551  2740.1569  0.3399  4.09% 
EasiCS  5  0.8220  823.1703  0.2408  1.17% 
In order to evaluate the effectiveness of the clustering algorithm, with the metric of , , , and , we compared the performance of the EasiCS with the seven commonly used models as shown in the table 1. And, the EasiCS obtained the largest 0.8220, the second largest value 823.1703, the smallest 0.2408, outperforming the seven algorithms overall.
4.3.1 The model consistency comparison
In order to evaluate the stable of the clustering algorithm, with the metric of , , , and , we compared the performance EasiCS with the SOM in the table 2. And, the EasiCS obtained the smallest 1.2635, the smallest 0.1188, the smallest 606.3688, and the smallest 0.0989. Compared with the SOM, the EasiCS have the smaller change, which means that the EasiSOM have the more stable cluster result.
0.1233  5982.5545  0.1696  
0.1188  606.3688  0.0989 
5 Conclusions
In this study, based on the relationship between cervical structure, cervical vertebrae function and CS, we developed the novelty framework based on the clustering algorithms to implement the division of the function, using the highdimensional and smallsampling of the CSrelated sEMG data, which consists of the dimension reduction, clustering algorithm EasiSOM, spectral clustering algorithm EasiSC. With the metric of the Silhouette Coefficient, the Calinski Harabaz score and the Davies Bouldin score, the EasiCS achieved the best overall performance compared with the seven commonly used clustering algorithms.
Thus, we will collect and utilize more diverse and comprehensive data to classify CS more precisely and explore the law behind the pathogenesis of CS and classification, providing more knowledge about CS prevention and treatment.
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