EasiCS: the objective and fine-grained classification method of cervical spondylosis dysfunction

The precise diagnosis is of great significance in developing precise treatment plans to restore neck function and reduce the burden posed by the cervical spondylosis (CS). However, the current available neck function assessment method are subjective and coarse-grained. In this paper, based on the relationship among CS, cervical structure, cervical vertebra function, and surface electromyography (sEMG), we seek to develop a clustering algorithms on the sEMG data set collected from the clinical environment and implement the division. We proposed and developed the framework EasiCS, which consists of dimension reduction, clustering algorithm EasiSOM, spectral clustering algorithm EasiSC. The EasiCS outperform the commonly used seven algorithms overall.

READ FULL TEXT VIEW PDF
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

08/21/2020

KCoreMotif: An Efficient Graph Clustering Algorithm for Large Networks by Exploiting k-core Decomposition and Motifs

Clustering analysis has been widely used in trust evaluation on various ...
10/24/2021

Improving Spectral Clustering Using Spectrum-Preserving Node Reduction

Spectral clustering is one of the most popular clustering methods. Howev...
08/06/2019

Hermitian matrices for clustering directed graphs: insights and applications

Graph clustering is a basic technique in machine learning, and has wides...
08/23/2021

Cube Sampled K-Prototype Clustering for Featured Data

Clustering large amount of data is becoming increasingly important in th...
01/07/2022

Probabilistic spatial clustering based on the Self Discipline Learning (SDL) model of autonomous learning

Unsupervised clustering algorithm can effectively reduce the dimension o...
10/07/2017

A New Spectral Clustering Algorithm

We present a new clustering algorithm that is based on searching for nat...
03/29/2021

Automatic Clustering in Hyrise

Physical data layout is an important performance factor for modern datab...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.

1 Introduction

The cervical spondylosis(CS), a common degenerative disease, harms human life and health, affects up to two-thirds 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 coarse-grained and unreasonable classification, despite that the NDI information is subjective and not accurate enough.

The surface electromyography (sEMG) is a non-stationary 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 CS-related 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 non-intrusive 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 fine-grained classification of cervical function.

As a powerful model-based clustering algorithm, the Self-organizing mapping (SOM) has strong ability of the self-learning, self-organizing, 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 small-sampling 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 categories111the 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 two-thirds 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 coarse-grained and unreasonable classification, despite that the NDI information is subjective and not accurate enough.

The surface electromyography (sEMG) is a non-stationary 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 CS-related 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 non-intrusive 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 fine-grained classification of cervical function.

As a powerful model-based clustering algorithm, the Self-organizing mapping (SOM) has strong ability of the self-learning, self-organizing, 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 small-sampling 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.

Figure 1: The EasiCS.

The CS is a chronic musculoskeletal disorder, which is mainly accompanied by the neck pain and the disability of human-related functions [Hogg-Johnson et al.2009]. The current classification of the CS is based on clinical symptoms and cervical lesion which was in accordance with 2012 ICD-9-CM 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: clinical-symptoms-based method, cervical-vertebra -lesion-based method, neck-muscle-lesion-based method, traditional Chinese medical classification.

For the clinical-symptoms-based 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 cervical-spine-lesion-based method, faced with the divergences in the traditional X-ray 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 X-ray images of the cervical spine, obtaining the 95% accuracy.

For the neck-muscle-lesion-based 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 non-harm 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 state-of-the-art 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 ICD-9-CM 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.

Figure 2: The EasiCS.

3.1 The dimensionality reduction: locally linear embedding

The high-dimensional 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 high-dimensional 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 low-dimensional, neighbor-hood-preserving embeddings of high-dimensional 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 Self-Organizing Map(SOM) is an excellent tool in exploratory phase of data mining, and projects input space on prototypes of a low-dimensional 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.

0:  the data set , the partition number , the number

of input neurons, the number

of output neurons, weight vector

, learning rate , learning rate threshold , neighborhood size , and the maximum number of iterations.
0:  The including the division of the data set .
1:  Initialize the iteration number , ,
, and ;
2:  for  to  do
3:     while  or  do
4:        Initialize the , , , .
5:        Calculate the winning node for each input sample ;
6:        Update the weight vector , learning rate ;
7:        
8:     end while
9:     Compute the division of the data set ;
10:     if  then
11:        Add the partition to the set .
12:     end if
13:  end for
Algorithm 1 The EasiSOM algorithm

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 a-prior unknown functional module such as topics in information network or cyber-communities 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.

0:  
0:  The partition of the ;
1:  Computer the minimum cluster number ;
2:  The maximum cluster number ;
3:  Generate weight matrix ;
4:  
5:  while  do
6:     Construct the similar matrix = ;
7:     Construct the adjacent matrix = ;
8:     Construct a standardized Laplacian matrix ;
9:     Calculate

minimum eigenvalues and eigenvectors;

10:     Use eigenvectors to transform data set to dimension ;
11:

     Use the k-means to cluster the data

obtain the .
12:     Compute the ;
13:     Add to ;
14:     Add to ;
15:     Add to ;
16:     
17:  end while
18:  Calculate the partition with the largest .
19:  Map the clustering result of 171 samples to 57 subject.
Algorithm 2 The EasiSC algorithm

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 .

0:  sEMG data set
0:  the partition
1:  Use LLE to reduct the dimension of ;
2:  Use EasiSOM to cluster ;
3:  Use EasiSC to cluster the .
Algorithm 3 The EasiCS algorithm

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 intra-cluster distance and maximizes inter-cluster distance. The metric [scikit-learn 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 K-Means is an algorithm for clustering data points by computing the average value. It is one of the best-known, 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 graph-based 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 bottom-up 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%
Table 1: The performance comparison between different clustering algorithms.

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
Table 2: The consistency comparison.

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 high-dimensional and small-sampling of the CS-related 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.

References

  • [Blondel et al.2008] Blondel, V. D.; Guillaume, J.-L.; Lambiotte, R.; and Lefebvre, E. 2008. Fast unfolding of communities in large networks. Journal of statistical mechanics: theory and experiment 2008(10):P10008.
  • [Cai et al.2016] Cai, Z.; Zhang, N.; Ma, N.; Dong, G.; Wang, S.; and Zhao, Y. 2016. Trend of the incidence of cervical spondylosis: decrease with aging in the elderly and increase with aging in the young and the adults. Int J Clin Exp Med 9(7):14329–14336.
  • [Comaniciu and Meer2002] Comaniciu, D., and Meer, P. 2002. Mean shift: A robust approach toward feature space analysis. IEEE Transactions on Pattern Analysis & Machine Intelligence (5):603–619.
  • [Ding et al.2015] Ding, S.; Wu, F.; Qian, J.; Jia, H.; and Jin, F. 2015. Research on data stream clustering algorithms. Artificial Intelligence Review 43(4):593–600.
  • [Falla et al.2007] Falla, D., .; Farina, D., .; M Kanstrup, D.; and Graven-Nielsen, T., . 2007. Muscle pain induces task-dependent changes in cervical agonist/antagonist activity. Journal of Applied Physiology 102(2):601.
  • [Frey and Dueck2007] Frey, B. J., and Dueck, D. 2007. Clustering by passing messages between data points. science 315(5814):972–976.
  • [gui2010] 2010. Guide to diagnosis and treatment of cervical spondylosis. Technical report, Chinese association of rehabilitation medicine.
  • [Hoadley et al.2014] Hoadley, K. A.; Yau, C.; Wolf, D. M.; Cherniack, A. D.; Tamborero, D.; Ng, S.; Leiserson, M. D.; Niu, B.; McLellan, M. D.; Uzunangelov, V.; et al. 2014. Multiplatform analysis of 12 cancer types reveals molecular classification within and across tissues of origin. Cell 158(4):929–944.
  • [Hogg-Johnson et al.2009] Hogg-Johnson, S.; van der Velde, G.; Carroll, L. J.; Holm, L. W.; Cassidy, J. D.; Guzman, J.; Côté, P.; Haldeman, S.; Ammendolia, C.; Carragee, E.; et al. 2009. The burden and determinants of neck pain in the general population: results of the bone and joint decade 2000–2010 task force on neck pain and its associated disorders. Journal of manipulative and physiological therapeutics 32(2):S46–S60.
  • [Howard Vernon] Howard Vernon, D. The neck disability index.
  • [Huang et al.2018] Huang, Y.; Zhan, J.; Wang, N.; Luo, C.; Wang, L.; and Ren, R. 2018. Clustering residential electricity load curves via community detection in network. arXiv preprint arXiv:1811.10356.
  • [Jebri et al.2015] Jebri, B.; Phillips, M.; Knapp, K.; Appelboam, A.; Reuben, A.; and Slabaugh, G. 2015. Detection of degenerative change in lateral projection cervical spine x-ray images. In Medical Imaging 2015: Computer-Aided Diagnosis, volume 9414, 941404. International Society for Optics and Photonics.
  • [Johnston et al.2008a] Johnston, V., .; Jull, G., .; Darnell, R., .; Jimmieson, N. L.; and Souvlis, T., . 2008a. Alterations in cervical muscle activity in functional and stressful tasks in female office workers with neck pain. European Journal of Applied Physiology 103(3):253–264.
  • [Johnston et al.2008b] Johnston, V., .; Jull, G., .; Souvlis, T., .; and Jimmieson, N. L. 2008b. Neck movement and muscle activity characteristics in female office workers with neck pain. Spine 33(5):555.
  • [Junlin Chen2017] Junlin Chen, Runmin Peng, S. L. X. C. 2017. Self-organizing feature map neural netork and k-means algorithm as a data excavation tool for obtaining geological information from regional geochemical exploration data. Geophyical and Geochemical Exploration 41(5):919–927.
  • [Kotil and Bilge2008] Kotil, K., and Bilge, T. 2008. Prospective study of anterior cervical microforaminotomy for cervical radiculopathy. Journal of Clinical Neuroscience 15(7):749–756.
  • [Li et al.2018] Li, J.; Cheng, K.; Wang, S.; Morstatter, F.; Trevino, R. P.; Tang, J.; and Liu, H. 2018. Feature selection: A data perspective. ACM Computing Surveys (CSUR) 50(6):94.
  • [MacQueen and others1967] MacQueen, J., et al. 1967. Some methods for classification and analysis of multivariate observations. In Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, volume 1, 281–297. Oakland, CA, USA.
  • [Madeleine et al.2016] Madeleine, P.; Xie, Y.; Szeto, G. P. Y.; and Samani, A. 2016. Effects of chronic neck-shoulder pain on normalized mutual information analysis of surface electromyography during functional tasks. Clinical Neurophysiology 127(9):3110–3117.
  • [Matz et al.2009] Matz, P.; Anderson, P.; Holly, L.; Groff, M.; Heary, R.; Kaiser, M.; Mummaneni, P.; Ryken, T.; Choudhri, T.; Vresilovic, E.; et al. 2009. Joint section on disorders of the spine and peripheral nerves of the american association of neurological surgeons and congress of neurological surgeons. J Neurosurg Spine 11(2):157–169.
  • [Nana Wang] Nana Wang, Xi Huang, Y. R. J. X. J. L. N. W. L. C. A convenient non-harm cervical spondylosis intelligent identity method based on machine learning. Scientific Reports.
  • [Reynolds2015] Reynolds, D. 2015. Gaussian mixture models. Encyclopedia of biometrics 827–832.
  • [Roweis and Saul2000] Roweis, S. T., and Saul, L. K. 2000. Nonlinear dimensionality reduction by locally linear embedding. science 290(5500):2323–2326.
  • [Saxena et al.2017] Saxena, A.; Prasad, M.; Gupta, A.; Bharill, N.; Patel, O. P.; Tiwari, A.; Er, M. J.; Ding, W.; and Lin, C.-T. 2017. A review of clustering techniques and developments. Neurocomputing 267:664–681.
  • [scikit-learn developers] scikit-learn developers. calinski harabaz score. https://blog.csdn.net/u010159842/article/details/78624135. Accessed December 28, 2018.
  • [Shen et al.2012] Shen, R.; Mo, Q.; Schultz, N.; Seshan, V. E.; Olshen, A. B.; Huse, J.; Ladanyi, M.; and Sander, C. 2012. Integrative subtype discovery in glioblastoma using icluster. PloS one 7(4):e35236.
  • [Shen, Olshen, and Ladanyi2009] Shen, R.; Olshen, A. B.; and Ladanyi, M. 2009. Integrative clustering of multiple genomic data types using a joint latent variable model with application to breast and lung cancer subtype analysis. Bioinformatics 25(22):2906–2912.
  • [Vernon and Mior1991] Vernon, H., and Mior, S. 1991. The neck disability index: a study of reliability and validity. Journal of manipulative and physiological therapeutics 14(7):409–415.
  • [Vesanto, Alhoniemi, and others2000] Vesanto, J.; Alhoniemi, E.; et al. 2000. Clustering of the self-organizing map.

    IEEE Transactions on neural networks

    11(3):586–600.
  • [Von Luxburg2007] Von Luxburg, U. 2007. A tutorial on spectral clustering. Statistics and computing 17(4):395–416.
  • [Wang et al.2018] Wang, N.; Cui, L.; Huang, X.; Xiang, Y.; and Xiao, J. 2018. Easicsdeep: A deep learning model for cervical spondylosis identification using surface electromyography signal. arXiv preprint arXiv:1812.04912.
  • [Yu et al.2015] Yu, X.; Liu, M.; Meng, L.; and Xiang, L. 2015. Classifying cervical spondylosis based on x-ray quantitative diagnosis. Neurocomputing 165:222–227.
  • [Zhang, Ramakrishnan, and Livny1996] Zhang, T.; Ramakrishnan, R.; and Livny, M. 1996. Birch: an efficient data clustering method for very large databases. In ACM Sigmod Record, volume 25, 103–114. ACM.
  • [Zhongmin2011] Zhongmin, Z. 2011. Study on the Symptoms and Soft Tissue Changes of Cervical Cervical Spondylosis. Ph.D. Dissertation, China Academy of Chinese Medical Sciences.