Skip to main content
Log in

On cluster validity indices with its application to interleaved radar pulse separation through fuzzy-based representation

  • Original Paper
  • Published:
Evolving Systems Aims and scope Submit manuscript

Abstract

The present research describes an approach to radar pulse separation through a set of state-of-the-art cluster validity indices in association with fuzzy-based representation. Detection of a number of radars during the separation process is an important applicable issue, which needs to be investigated more in both real and academic environments. It is obvious that the fuzzy-based clustering approach may be known as one of the intelligent solutions regarding the interleaved radar pulse separation. In a word, the study considers the optimal number of clusters on the basis of the cluster validity indices that are useful to determine the radars. To consider the performance of the proposed approach, the whole of cluster validity indices are simulated though a series of experiments in some applicable scenarios in the area of interleaved radar pulse separation. The outcomes indicate that W-index is known as a suitable candidate to guarantee the better performance with high accuracy, while the fuzzy c-means technique is realized. In fact, a purposeful integration of the fuzzy c-means in association with W-index aims us to separate the interleaved radar pulse trains, efficiently. Subsequently, the effectiveness of the approach performance is verified by demonstrating its accuracy to be resulted as 96.71 %, while 10 % of additional pulse and 2 % of noise are included.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Arbelaitz O, Gurrutxaga I, Muguerza J, Pérez JM, Perona I (2013) An extensive comparative study of cluster validity indices. Pattern Recogn 46(1):243–256

    Article  Google Scholar 

  • Başkır MB, Türkşen IB (2013) Enhanced fuzzy-based clustering algorithm and cluster validity index for human perception. Expert Syst Appl 40(3):929–937

    Article  Google Scholar 

  • Cheng H, Tang B, Du J, Chen X (2009) Single channel pulse train radar signal separation using algebraic method. IET International Radar Conference, pp 1–4

  • Dai S, Lei W, Cheng Y, Wang D (2014) Clustering of DOA data in radar pulse based on SOFM and CDBW. J Electron 31(2):107–114 (Springer Publisher)

    Google Scholar 

  • De Carvalho FAT, Tenróio CP, Cavalcanti NL Jr (2006) Partitional fuzzy clustering methods based on adaptive quadratic distances. Fuzzy Sets Syst 157:2833–2857

    Article  MathSciNet  MATH  Google Scholar 

  • Fazel Zarandi MH, Faraji MR, Karbasian M (2010) An exponential cluster validity Index for fuzzy clustering with crisp and fuzzy data. Trans Sharif Univ Technol 17(2):95–110

    Google Scholar 

  • Filev D, Angelov P (2007) Algorithms for Real-Time Clustering and Generation of Rules from Data. In: Advances in Fuzzy Clustering and its Applications. Wiley, Chichester, pp 353–370

  • Hantscher S, Diskus CG (2009) Pulse-based radar imaging using a genetic optimization approach for echo separation. IEEE Sens J 9(3):271–276

    Article  Google Scholar 

  • Kauppi J-P, Martikainen K, Ruotsalainen U (2010) Hierarchical classification of dynamically varying radar pulse repetition interval modulation patterns. Neural Netw 23(10):1226–1237

    Article  Google Scholar 

  • Kim D-W, Lee KH, Lee D (2004) On cluster validity index for estimation of the optimal number of fuzzy clusters. Pattern Recogn 37(10):2009–2025

    Article  Google Scholar 

  • Kulkarni PA, Mulay P (2013) Evolve systems using incremental clustering approach. Evol Syst 4(2):71–85 (Springer Publisher)

    Article  Google Scholar 

  • Maulik U, Bandyopadhyay S (2002) Performance evaluation of some clustering algorithms and validity indices. IEEE Trans Pattern Anal Mach Intell 24:1650–1654

    Article  Google Scholar 

  • Motlagh O, Jamaludin Z, Tang SH, Khaksar W (2015) An agile FCM for real-time modeling of dynamic and real-life systems. Evol Syst 6(3):153–165

    Article  Google Scholar 

  • Pan X, Wang W, Feng D, Fu Q, Wang G (2013) Repeat jamming against LFM radars based on pulse separation. J Natl Univ Def Technol 35(3):119–125

    Google Scholar 

  • Shieh H-L (2014) Robust validity index for a modified subtractive clustering algorithm. Appl Soft Comput 22:47–59

    Article  Google Scholar 

  • Wang W, Zhang Y (2007) On fuzzy cluster validity indices. Fuzzy Sets Syst 158:2095–2117

    Article  MathSciNet  MATH  Google Scholar 

  • Wu K-L, Yang M-S (2005) A cluster validity index for fuzzy clustering. Sci Pattern Recogn Lett 26:1275–1291

    Article  Google Scholar 

  • Zhang Y, Wang W, Zhang X, Li Y (2008) A cluster validity index for fuzzy clustering. Inf Sci 178(4):1205–1218

    Article  MATH  Google Scholar 

  • Zhang D, Ji M, Yang J, Zhang Y, Xie F (2014) A novel cluster validity index for fuzzy clustering based on bipartite modularity. Fuzzy Sets Syst 253:122–137

    Article  MathSciNet  Google Scholar 

  • Zhang W, Li K, Jiang W (2015) Micro-motion frequency estimation of radar targets with complicated translations. AEU—Int J Electron Commun 69(6):903–914

    Article  Google Scholar 

  • Zhao Q, Fränti P (2014) WB-index: a sum-of-squares based index for cluster validity. Data Knowl Eng 92:77–89

    Article  Google Scholar 

Download references

Acknowledgments

The corresponding Author would like to appreciate respected Editor-in-Chiefs and also respected Associate Editor of ‘Evolving Systems’, Springer Publisher for giving the opportunity to improve the research. Moreover, the impressive, desirable, constructive and technical comments of the whole of respected potential anonymous reviewers in all the rounds of processing are greatly appreciated. Afterwards, Dr. Mazinan is highly grateful to the Islamic Azad University (IAU), South Tehran Brach, Tehran, Iran in support of the present research, which is carried out under contract with the Research Department of the IAU, South Tehran Brach. And also he appreciates Mrs. Maryam Aghaei Sarchali, Miss Mohadeseh Mazinan and finally Mr. Mohammad Mazinan for their sufficient supports in the process of paper investigation and organization.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. H. Mazinan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mazinan, A.H. On cluster validity indices with its application to interleaved radar pulse separation through fuzzy-based representation. Evolving Systems 7, 243–254 (2016). https://doi.org/10.1007/s12530-015-9136-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12530-015-9136-2

Keywords

Navigation