A Novel Density Based Clustering Algorithm by Incorporating Mahalanobis Distance

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1 Receive: November 20, A Novel Density Base Clustering Algorithm by Incorporating Mahalanobis Distance Margaret Sangeetha 1 * Velumani Paikkaramu 2 Rajakumar Thankappan Chellan 3 1 Department of Computer Science, Manonmaniam Sunaranar University, Tirunelveli, Inia 2 Department of Computer Science, The M.D.T Hinu College, Tirunelveli, Inia 3 Department of Computer Science, St. Xavier s College, Tirunelveli, Inia * Corresponing author s margaret.msu@gmail.com Abstract: Data clustering is one of the active research areas, which aims to group relate ata together. The process of ata clustering improves the ata organization an enhances the user experience as well. For this sake, several clustering algorithms are propose in the literature. However, a constant eman for a better clustering algorithm is still a basic requirement. Unerstaning the necessity, this paper proposes a ensity base clustering algorithm which is base on Density Base Spatial Clustering of Applications with Noise (DBSCAN) algorithm. The main rawback of DBSCAN algorithm is it requires two important parameters as initial input. It is really ifficult to fix the values for these parameters, as it requires some prior knowlege about the ataset. This requirement is overthrown by the propose clustering algorithm by selecting the parameters automatically. The automate selection of parameters is achieve by analysing the ataset an it varies from ataset to ataset. This way of parameter selection improves the quality of service an prouce effective clusters. The experimental results show that the propose approach outperforms the DBSCAN algorithm in terms of purity, F-measure an entropy. Keywors: Density base clustering, Data clustering, Clustering algorithm. 1. Introuction Data is the lifebloo of toay s worl an the collecte ata are store in voluminous atabases. The ata must be store in an organize fashion, such that the require ata can easily be locate. Data analysis is one of the most essential necessities in all omains, such that the worth of the applications can be enhance. Data analysis can be performe better, when the relate ata are store together. The concept of ata clustering hits the scene at this juncture. The major goal of ata clustering is to group similar ata together. The term ata can be auio, vieo, text, numeric an so on. The relate ata are groupe together, so as to form ifferent clusters. This makes sense that entities within the cluster show maximum egree of similarity an the entities of ifferent clusters show minimal egree of similarity. This makes the ata processing easier an helps to enhance the performance of the application. Owing to its avantages, ata clustering is utilize in almost all omains such as healthcare, finance, business oriente, ata retrieval, image processing applications an so on. For instance, healthcare applications utilize clustering to group patients with similar symptoms or egree of severity [1]. The business oriente applications cluster the customers, who share the same buying habits [2]. Though the concept of clustering brings in numerous merits to an application, it is extremely ifficult to achieve better clusters. A clustering algorithm has to hanle several tough challenges such as the selection of better features, istance measures [3] an ealing with noise [4]. Apart from this, a goo clustering algorithm must be scalable, capable of hanling noise an to fin clusters without consiering the shape [5]. The clustering algorithms can be broaly ivie into partitional, hierarchical, ensity an gri base clustering [6].

2 Receive: November 20, Each an every kin of clustering approach has its own merits an emerits. This work focuses on ensity base clustering, which clusters the ata base on the ensity. In this kin of clustering, the size of the cluster improves till the count of neighbouring points is greater or equal to the threshol. The threshol is chosen by the user an the cluster oes not have any shape constraints. This feature makes the ensity base clustering popular. Taking all these points into account, this paper intens to present a clustering algorithm that is base on Density Base Spatial Clustering of Applications with Noise (DBSCAN) algorithm. The DBSCAN algorithm is introuce by Martin Ester et.al. in the late 90 s [7] an is claime as the best ensity base clustering algorithms. The main objective of this article is to present a clustering algorithm, which is an enhancement of DBSCAN algorithm. There are two important parameters associate with DBSCAN algorithm, which are epsilon ( ε) an minimum number of points (min_pts ). The ε value enotes the maximum istance between two ata points an the min_pts enote the minimal number of points for builing a cluster. The traitional DBSCAN algorithm employs static value for ε an utilizes Eucliean istance as the istance measure. The propose algorithm enhances the traitional DBSCAN algorithm an the contributions of this work are liste below. The propose clustering algorithm fixes the ε value by itself. The value of ε is chosen by calculating the istance between the points an the count of points in a particular raius. This way of automatic selection of ε simplifies the entire clustering process an improves the performance. Manual choice of ε is tiresome an may fail, in certain cases. The propose work analyses the ata istribution an fixes the value of ε, which makes the clustering process effective. The traitional DBSCAN algorithm utilizes Eucliean istance as the similarity measure. However, the major rawback of Eucliean istance is its sensitiveness to the geometrical shape of clusters. The propose algorithm employs Mahalanobis istance, because of its insensitivity to cluster shape The performance of the propose approach is analyse in terms of F-measure, entropy an purity. Aitionally, the propose approach stuies the performances of Manhattan an Minkowski similarity measures. The remainer of this paper is organize as follows. Section 2 reviews the relate literature with respect to ensity base clustering algorithm. The propose approach is elaborate in section 3 along with the overview of the work. Section 4 analyses the performance of the propose approach an iscusses the attaine results. At last, section 5 presents the conclusive points of the propose approach. 2. Review of literature This section presents the state-of-the-art relate literature with respect to ensity base clustering algorithm. In [8], an effective ensity base clustering framework is propose. This work separates the core an the non-core points by means of a neighbourhoo ensity estimation moel. Initially, the core points are treate by the clustering algorithm, followe by which the non-core points are treate. However, this work chooses the clustering parameters manually an consumes more time. The work propose in [9] introuces a clustering algorithm, which can treat the ata points an outliers separately. Initially, a ensity base clustering algorithm is employe to istinguish between the core points an the outliers in all the clusters. However, the main goal of this article is to etect outliers. A ensity base clustering algorithm for location base services is propose in [10]. This approach clusters the nearby locations with respect to a query location an returns the user with a set nearby points. A clustering algorithm base on ominant set is presente in [11]. This work prouces the initial set of clusters by combining the ominant set algorithm an the histogram equalization transformation. The so prouce clusters are then refine with the ensity information of the ata points. This work involves computational an space complexity. A ensity peak base semi-supervise clustering algorithm is propose in [12], which exploits the label information. Initially, a ensity base clustering algorithm is employe to etect the ensity peaks. This is followe by the introuction of a graph base algorithm to assign the class label, by utilizing the see information. The label information of the see points is again utilize to form clusters, which increases the time consumption further. In [13], a ensity base clustering approach is propose to iagnose neuromuscular isorers. This work proposes a clustering algorithm namely Neighbourhoo Distance Entropy Consistency (NDEC) to construct arbitrary shape clusters an

3 Receive: November 20, these clusters are passe to Support Vector Machine (SVM) an nearest neighbour classifiers. This work is reliable, however so many internal computations are carrie out to achieve better clusters. In [14], an improve version of DBSCAN algorithm, which is name as Different Densities- Base Spatial Clustering of Applications (DDBSCAN) is presente. The DDBSCAN algorithm calculates the cluster ensity with respect to epsilon an min_points. This is followe by the introuction of the ensity threshol, through which the ata points are inclue to or exclue from a cluster. Hence, the efficiency of the work epens on the effective choice of the threshol. A Simplifie Fingerprint Density-base Clustering Algorithm (SFDCA) is propose in [15] for clustering wi-fi fingerprints. This work presents a case stuy by collecting wi-fi fingerprints from smartphones an the fingerprints are clustere. In [16], a ensity base clustering algorithm base on ensity threshol is propose. Initially, this work fixes a raius threshol an is analyse. The ense clusters are forme by merging several partial clusters. The major rawback of this work is fixing the threshol by manual analysis. An extension of DBSCAN algorithm, which is name as Spatio- Temporal DBSCAN (STDBSCAN) is propose in [17]. The ST-DBSCAN algorithm clusters the ata by taking the spatial an temporal information into account. This work utilizes rough set to cluster ata an provies lower an upper approximation of the ata. The lower approximation enotes the ata points that must be a part of the cluster an the upper approximation inicates the cluster bounary that contains several ata points, which might fall into the cluster. This work goes through several conflicts while clustering the ata points. In [18], an unsupervise learning algorithm namely Density Base Self Organizing Incremental Neural Network (DenSOINN) is presente to cluster ata streams. This work is explaine as a self organizing network, which expans incrementally by placing suitable noes in a cluster an is achieve by Hebbian learning rule. By this way, DenSOINN constructs arbitrary shape clusters. Though the performance of this work is better, the computational complexity of this work is high, as so many complex algorithms are involve in the clustering process. In [19], a transfer learning algorithm that relies on fuzzy neighbourhoo ensity base clustering an resampling technique is propose. This algorithm clusters the ataset in various shapes. The rawback of this work is that the clustering results are not convincing. A feature selection base DBSCAN algorithm namely FS-DBSCAN is propose in [20]. The purpose of the algorithm is to hanle high imensional ata an the performance of this work is better. A real-time web base clustering application is propose in [21], which is meant for clustering hotspot ata being present in the peatlans by employing DBSCAN algorithm. This application clusters the hotspot ata an showcases the clustering outcomes with respect to hotspots, type of peat, epth of lan an so on. This work proposes a real-time clustering application an the clustering results are better. In [22], a novel ensity base clustering algorithm namely Probabilistic DBSCAN (PDBSCAN) is propose for uncertain ata. The PDBSCAN calculates the probability of the istance between two ifferent objects instea of the sampling process followe by the existing DBSCAN algorithm. Besies this, the probability of the core object an support egree are utilize to compute the threshol. The metho of threshol computation is complex, but the performance of this work is goo in terms of clustering. Motivate by the above works, this paper intens to propose a ensity base clustering algorithm which can choose the value of epsilon without human intervention. Besies this, as far as the similarity measure is concerne, DBSCAN s Eucliean istance is replace by Mahalanobis istance, owing to its insensitiveness to the shape of the cluster. The propose approach overthrows the hea ache of choosing the value for epsilon an improves the quality of service. The following section elaborates the propose approach. 3. Preliminaries This section gives the basic iea of the DBSCAN clustering algorithm an the important terminologies associate with it. 3.1 Terminologies The essences of DBSCAN algorithm are epsilon (ε) an minimum number of points (min_pts). The ε value enotes the maximum istance between two ata points an the min_pts enote the minimal number of points for builing a cluster. Let A be a ata point an the purpose of ε is explaine as follows. Epsilon (ε) : The ε value impacts over the ata point A by forming a circle aroun the point A, with ε as the raius. Here, A is consiere as the centroi of the circle. Epsilon neighbours ( ε N ) : ε_n enotes the ata points, which are enclose by the so

4 Receive: November 20, forme circle with respect to ata point A. The ata points enclose in the circle with respect to A are calle as the epsilon neighbours an is enote as ε N (A). Kins of points : The constituent ata points can be ifferentiate into three kins, which are core point, borer point an outlier point. A ata point A is classifie as core point, when the point A has many neighbouring points which are greater than the count of min_pts. A point A is state as borer point, when A has minimal neighbouring points. Finally, the outlier points o not come uner core or borer point. These points are usually consiere as noise. The core an borer points are enote as follows. core point ε N (A) min_pts (1) borer point ε N (A) min_pts (2) where ε N (A) is the carinality of ε N (A). Directly ensity reachability : A ata point A is consiere to be irectly ensity reachable to ata point B, when B is one of the points in ε N (A) an A is the core point. The ε N (B) are irectly ensity reachable from B an the borer points are irectly ensity reachable from its own epsilon neighbours that are core points. Density reachability : A ata point A is claime to be ensity reachable from the ata point B. Consier a set of interconnecte points A 1, A 2, A 3,, A n, such that A 1 A an A n B an A i 1 is irectly ensity reachable from p i. Density connecte : A ata point A is sai to be ensity connecte to a point B, if a point P is present an the points A, B are ensity reachable from P. Density base cluster : Consier a set of points, which is mentione as X. A ensity base cluster X is forme with atleast a core point an all other ata points are ensity reachable from the core point. Thus, the basic terminologies associate with DBSCAN algorithm are presente above an the traitional DBSCAN algorithm is presente below. DBSCAN Algorithm Input : ε, min pts, ataset; Output: Data clusters Begin Cluster = 0; for each point x If x is checke Check the next point; Compute neighbour points of x by passing region_query (x, ε); If ε N (x) < min pts Set x as outlier; Else Cluster=next cluster; Growcluster(x, ε N (x), cluster, ε, min pts ) Growcluster(x, ε N (x), cluster, ε, min pts ) Inclue x in cluster; For each point x in ε N (x) If p is not checke Set p as checke; Compute neighbour points of x by passing region_query (x, ε); If ε N (x) min pts ; A neighbour points of x an x ; If x is not a member of any cluster Inclue x in cluster; region_query (x, ε) return all the ata points that are insie the neighbourhoo of x; This original DBSCAN algorithm avois the nee of pre-etermining the count of clusters. DBSCAN can eal with noisy ata effectively an can fin clusters of irregular shape. However, this work cites two major rawbacks, which are as follows. Initially, it is quite har to set the initial parameter epsilon (ε). Taking this issue into account, the propose ensity base clustering algorithm intens to automate the choice of ε. Though the DBSCAN algorithm is claime to prouce arbitrary shape clusters, the employe similarity measure Eucliean istance is inee sensitive to the shape of the cluster. This issue is resolve by the propose approach by incorporating Mahalanobis istance in the place of Eucliean istance, as mahalanobis istance is insensitive to the shape of the cluster.

5 Receive: November 20, The following section presents the propose clustering algorithm. 4. Propose ensity base clustering algorithm The main goal of this algorithm is twofol. One is to automate the choice of ε an the secon one is to stuy the performances of ifferent similarity measures such as mahalanobis, manhattan, minkowski, which are compare with the Eucliean istance. Initially, this section presents the etails about the automate choice of ε. The traitional DBSCAN algorithm prompts the user to provie the value for ε an min_pts. The efficiency of the DBSCAN algorithm strongly relies on the choice of ε. The feasible value of ε prouces better clusters. Thus, preliminary knowlege about the ataset is necessary, such that the value of ε can be fixe. Yet, a novice user may not be able to select an optimal value of ε, which seriously impacts over the formation of clusters. Hence, the avice of a technical expert becomes necessary for the parameter fixation. However, it is not always possible to look for a technical expert. The secon issue is the emerits associate with Eucliean istance, which is the stanar similarity measure of DBSCAN algorithm. Though the computation of Eucliean istance is simple, it has certain rawbacks to be aresse. Eucliean istance is sensitive to the shape of the cluster an it coul not hanle the correlate ata items. All these issues are overthrown by mahalanobis istance, which is insensitive to the shape of the cluster an the correlate ata items are processe effectively. Besies this, the mahalanobis istance can fin the outliers effectively. The propose work proves its superiority by incluing the automate choice of ε an mahalanobis istance as the similarity measure. The propose clustering algorithm is as follows. Propose Algorithm for ε an min_pts computation Input : Dataset DS Output : ata clusters Begin For each ata point p i DS o Obtain the coorinates of p i Compute mahalanobis istance; Sort the istance outcome ( ist) in ascening orer; Fin the nearest neighbours nn of p i ; Count the nn for the top ranking ist; For each available ist n (p i ) o Count nn(p i ) as no; Store no(nn(ist j )) an (ist j ); Repeat the process for all ist n ; For all ist Compute avg(no(ist i )); Assign avg(no(ist i )) as min_pts; List ist n min_pts; Assign max (ist n ) as ε; En for En for En for En The above presente algorithm escribes the way to fin the values for ε an min_pts. The so foun values are passe as input to form the clusters. The clusters are forme with the compute ε an min_pts, which brings in simplicity an efficiency. Aitionally, the overhea associate with the choice of ε an min_pts are eliminate. As the choice of these parameters ecie the quality of clusters, it is better to choose optimal values for the parameters. Manual choice of ε an min_pts can be achieve by trial an error metho, which consumes more time an involves computational overhea. All these overheas are overcome by the propose approach, which fixes an optimal value for ε an min_pts, which is epenent on the nature of ataset. The propose algorithm can work for any kin of ataset, which wiens the applicability of the algorithm. There is no nee for proviing the values of ε an min_pts initially, as in traitional DBSCAN algorithm. Aitionally, the nee for passing the count of clusters as that of k-means algorithm is also eliminate. All these factors together make it simple to eal with cluster formation. This algorithm requires no prior knowlege with respect to clustering or its associate parameters, hence it is suitable for novice users an supports experts as well. As soon as the ataset is passe, the coorinates of all the points are obtaine an the mahalanobis istance is compute for all the ata points. By this way, the k-nearest neighbours of any particular ata point is obtaine. This is followe by sorting the compute istances in sorte orer (ascening). This way of istance sorting, helps in fining the least possible istance between the processe ata point an its neighbourhoo points. The next step is to count the number of nearest neighbours of a specific point with respect to all the compute istances. This is followe by computing the average of the count of neighbouring points of all istances being observe. This average value is set as the minimum

6 Receive: November 20, points. Now, the istance on which the neighbourhoo points equals or greater than the minimum points are liste. The maximum istance which encloses more number of points is chosen as the ε value. This process continues till all the ata points are inclue in a cluster. In case, if a point cannot come uner any cluster then those points are consiere as noise. The following section analyses the performance of the propose approach. 5. Results an iscussion The performance of the propose approach is teste with two ifferent atasets namely online retail an wholesale customer atasets, which are ownloae from [23, 24] respectively. The online retail ataset contains the transactional etails of a UK base online store. This ataset comprises eight ifferent attributes such as invoice number, stock coe, escription, quantity, invoice ate, unit price, customer ID an country. The wholesale customer ataset contains the annual expeniture etails of eight ifferent attributes such as fresh, milk, grocery, frozen, etergents&paper, elicatessen proucts, channel an region. Both these atasets contain about five hunre recors each. The experimental analysis is carrie out in a stan alone system with 4 GB RAM by utilizing MATLAB version 8.2. The performance of the propose approach is stuie in two ways. Initially, the propose approach is analyse by varying ifferent similarity measures such as Eucliean, Mahalanobis, Manhattan an Minkowski. Out of all these performance measures, mahalanobis istance performs better for the utilize atasets. Seconly, the performance of traitional DBSCAN algorithm is compare with the propose approach. The performance of the propose approach is analyse in terms of stanar performance metrics such as entropy, f-measure an purity. The efinitions of these performance metrics are provie below. F-measure : The greater the F-measure, the better is the clustering results. The maximal F-measure results in the correct mapping of ata points to the clusters. The F-measure of a particular cluster (cl) is compute by F(cl) = 2PrRc Pr+Rc (3) Pr(x, y) = C xy C y (4) Rc(x, y) = C xy C x (5) where Pr an Rc are the precision an recall rates respectively. C xy is the count of the entities of a particular category x in the cluster y. C x an C y are the total count of entities or points in class x an y respectively. Entropy : The entropy value etermines the homogeneity of the cluster. The homogeneity of the cluster is inversely proportional to the entropy value. The entropy value of a cluster is calculate by Ent(cl) = C cl C y y=1 (6) C Ent y where C y is the count of ata points in cluster y, C is the total count of ata points. Ent y is compute by the following Ent y = prb xy log (prb xy ) x (7) In the above equation, prb xy is the probability of ata point in cluster y to exist in category x. Hence, a better clustering algorithm shoul prove maximum F-measure an minimal entropy value. Purity : Purity of the cluster enotes the wholeness of a cluster. The purity of a cluster cl x whose size is sz x is measure by p(cl x ) = 1 max cl sz x (8) x In Eq. (8), max sz x is the count of ata points, which are the parts of a particular category in cl x an cl x are the total ata points in cluster that are allotte to the class. Suppose, if the purity of a cluster is 1, then all the ata points of the cluster belong to a single category. The greater the purity value, the better is the quality of the clusters. All these performance metrics are taken into account to assess the quality of the propose clustering algorithm. The performance of the propose approach is proven by the results. In Figs.1 an 2, the performance of the propose approach is teste by varying the similarity measure an the purity, F-measure an entropy are compute. On analysis, it is foun that Eucliean istance is the poor performer of all the similarity measures with the least F-measure, purity an the greatest entropy value. For the wholesale ataset, the entropy value being shown by Eucliean istance is The purity an F-measure of the Eucliean istance is 0.69 an 0.64 respectively. The purity, F-measure an entropy values shown by Eucliean istance for

7 Value Values Receive: November 20, Purity 0.1 F-Measure Entropy 0 Eucliean Manhattan Minkowski Mahalanobis Similarity measure Figure. 1 Performance analysis on wholesale ataset Purity 0.2 F-measure 0.1 Entropy 0 Eucliean Manhattan Minkowski Mahalanobis Similarity measure Figure. 2 Performance analysis on online retail ataset the online retail ataset are 0.9, 0.86 an 0.59 respectively. Minkowski is the secon poor performer that shows 0.83 an 0.76 as purity an F- measure respectively. The entropy value shown by minkowski istance is In case of online retail ataset, the minkowski istance proves 0.89, 0.88 an 0.51 as purity, F-measure an entropy respectively. The performance of minkowski an mahanttan istances is more or less the same. This is because, the minkowski istance is the generalization of Eucliean an manhattan istances. For the wholesale ataset, the manhattan istance shows 0.89, 0.81 an 0.44 as the purity, F- measure an entropy respectively. As far as the online retail ataset is consiere, the manhattan istance shows 0.91, 0.90 an 0.34 for purity, F- measure an entropy. The major rawback of manhattan istance is it consiers the mutual correlation of the ata points alone an oes not make ecision out of the ominance. However, manhattan istance is insensitive to noise an can hanle correlations between the ata points. Finally, mahalanobis istance shows the greatest F-measure an purity value an the least entropy value. The purity an the F-measure of the forme clusters for the wholesale ataset are 0.94 an 0.91 respectively. The entropy value being shown by mahalanobis istance is the The mahalanobis istance shows the best results even for the online retail

8 Values Receive: November 20, Figure. 3 Comparative analysis between DBSCAN an the propose approach ataset too. The purity an F-measure of the clusters are 0.95 an 0.93 respectively. The entropy value of the forme clusters is 0.26, which is the least. The reason for the better performance of mahalanobis istance is its ability to hanle scale, correlation issues an outliers. In Fig. 3, the performance of the DBSCAN algorithm propose in [8] is compare with the propose clustering algorithm. The performance ifference between the DBSCAN an propose approaches is obvious. The main reason for the poor performance of the DBSCAN algorithm is the incorporation of Eucliean istance, which oes not take the ata point correlation into account. Besies this, the effectiveness of the DBSCAN algorithm in [8] epens on the significant parameters such as ε an min_pts. These issues are aresse by the propose approach by incorporating mahalanobis istance, which can eal with scale an correlation issues. Aitionally, the outliers can be etecte easily. Apart from this, the propose approach eliminates the requirement of passing values for ε an min_pts manually. Instea, the optimal values for ε an min_pts are chosen by the algorithm itself. Thus, the propose approach is efficient an improves the quality of service as well. 6. Conclusion DBSCAN-ONLINE RETAIL PROPOSED-ONLINE RETAIL DBSCAN-WHOLESALE PROPOSED-WHOLESALE 0 Purity F-measure Entropy This paper introuces a ensity base clustering algorithm, which is base on traitional DBSCAN algorithm. The propose approach is observe to be superior to the traitional DBSCAN algorithm, owing to two soli reasons. Initially, the traitional DBSCAN algorithm requires the values for ε an Performance measures min_pts as input. As the efficiency of the clustering algorithm epens on the ε an min_pts values, it is necessary to choose the optimal values. However, this requires some prior knowlege about the ataset. This requirement is completely uproote by the propose approach, in which the values of ε an min_pts are chosen automatically, by analysing the ataset. However, the values of ε an min_pts varies with respect to the ataset. Seconly, mahalanobis istance is utilize as the istance measure in the place of Eucliean istance. This is because mahalanobis istance can eal with scale an correlation issues very well, which cannot be achieve by Eucliean istance. The performance of the propose approach is satisfactory in terms of purity, F-measure an entropy. However, the performance of the propose work is teste over static ataset. In future, this work is planne to be enhance by introucing a ynamic ataset. References [1] Z. Nafar an A. Golshani, Data Mining Methos for Protein Protein Interactions, In: Proc. of Canaian Conf. on Electrical an Computer Engineering, pp , [2] W. Yu, G. Qiang, an L. X. Li, A kernel aggregate clustering approach for mixe ata set an its application in customer segmentation, In: Proc. of International Conference on Management Science an Engineering, pp , [3] S. H. Cha, Comprehensive survey on istance/similarity measures between probability ensity functions, International

9 Receive: November 20, Journal of Mathematical Moels an Methos in Applie Sciences, Vol.1, No.4, pp , [4] C. Bahm, K. Haegler, N.S Maller, an C. Plant, CoCo: coing cost for parameter-free outlier etection, In: Proc. of the 15th ACM SIGKDD Conference on Knowlege Discovery an Data Mining, pp , [5] J. Han, J. Pei J, an M. Kamber, Data mining: concepts an techniques, Thir Eition, Elsevier, [6] E. Paquet, Exploring anthropometric ata through cluster analysis, Digital Human Moelling for Design an Engineering, Oaklan University, Michigan, [7] M. Ester, H.P. Kriegel, J. Saner, an X. Xu, A ensity-base algorithm for iscovering clusters in large spatial atabases with noise, In: Proc. of KDD, Vol. 96, No. 34, pp , [8] J. Lu an Q. Zhu, An Effective Algorithm Base on Density Clustering Framework, IEEE Access, Vol.5, pp , [9] K. Maheshwari an M. Singh, "Outlier etection using ivie-an-conquer strategy in ensity base clustering", In: Proc. of International Conference on Recent Avances an Innovations in Engineering, [10] M.F. Rahman, W. Liu, S.B. Suhaim, S. Thirumuruganathan, N. Zhang, an G. Das, "Density Base Clustering over Location Base Services", In: Proc. of International Conference on Data Engineering, [11] J. Hou, E. Xu, an H. Cui, "Density Base Dominant Sets Growing an Clustering", In: Proc. of European Moelling Symposium, [12] W. Li, X. Li, Y. Ye, Y. Li, an E.K. Wang, "A novel ensity peak base semi-supervise clustering algorithm", In: Proc. of International Conference on Machine Learning an Cybernetics, [13] T. Kamali an D. Stashuk, "A Density-Base Clustering Approach to Motor Unit Potential Characterizations to Support Diagnosis of Neuromuscular Disorers, IEEE Transactions on Neural Systems an Rehabilitation Engineering, Vol.25, No.7, pp , [14] M. F. Hassanin, M. Hassan, an A. Shoeb, "DDBSCAN: Different Densities-Base Spatial Clustering of Applications with Noise", In: Proc. of International Conference on Control, Instrumentation, Communication an Computational Technologies, [15] S. Lau, C. Toh an Y. Saleem, "Wi-Fi Fingerprint localisation using Density-base Clustering for public spaces: A case stuy in a shopping mall", In: Proc. of International Conference on Clou System an Big Data Engineering, [16] K. Zhang, L. Huang, an Y. Chai, "An algorithm to aaptive etermination of ensity threshol for ensity-base clustering", In: Proc. of Chinese Control Conference, [17] B. Chakraborty, K. Chakma, an A. Mukherjee, "A ensity-base clustering algorithm an experiments on stuent ataset with noises using Rough set theory", In: Proc. of IEEE International Conference on Engineering an Technology, Coimbatore, [18] B. Xu, F. Shen, an J. Zhao, "Density Base Self Organizing Incremental Neural Network for ata stream clustering", In: Proc. of International Joint Conference on Neural Networks, [19] Z. Liu, J. Yang, H. Liu, an W. Wang, "Transfer Learning by Fuzzy Neighbourhoo Density Base Clustering an Re-sampling", In: Proc. of International Conference on Computer Science an Applications, [20] A. Smiti an Z. Elouei, "Fuzzy ensity base clustering metho: Soft DBSCAN-GM", In: Proc. of International Conference on Intelligent Systems, [21] R. Hermawati an I. S. Sitanggang, "Web- Base Clustering Application Using Shiny Framework an DBSCAN Algorithm for Hotspots Data in Peatlan in Sumatra", Proceia Environmental Sciences, Vol.33, pp , [22] M.U. Yaseen, A. Anjum, O. Rana, an R. Hill, "Clou-base scalable object etection an classification in vieo streams", Future Generation Computer Systems, Vol.80, pp , [23] etail [24] e+customers