Density peaks clustering (DPC) algorithm is a novel algorithm that efficiently deals with the complex structure of the data sets by finding the density peaks. It needs neither iterative process nor more parameters. The density–distance is utilized to find the density peaks in the DPC algorithm. But unfortunately, it will divide one cluster into multiple clusters if there are multiple density peaks in one cluster and ineffective when data sets have relatively higher dimensions. To overcome the first problem, we propose a FDPC algorithm based on a novel merging strategy motivated by support vector machine. First, the strategy utilizes the support vectors to calculate the feedback values between every two clusters after clustering based on the DPC. Then, it merges clusters to obtain accurate clustering results in a recursive way according to the feedback values. To address the second limitation, we introduce nonnegative matrix factorization into the FDPC to preprocess high-dimensional data sets before clustering. The experimental results on real-world data sets and artificial data sets demonstrate that our algorithm is robust and flexible and can recognize arbitrary shapes of the clusters effectively regardless of the space dimension and outperforms DPC.
This is a preview of subscription content, log in to check access
This work is supported by the Fundamental Research Funds for the Central Universities (No. 2017XKQY076)
Compliance with Ethical Standards
Conflict of interest:
All the authors declare that they have no conflict of interest.
Human and animal rights:
This article does not contain any studies with human or animal subjects performed by the any of the authors.
All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2008 (5). Additional informed consent was obtained from all patients for which identifying information is included in this article.
Bai L, Cheng X, Liang J et al (2017) Fast density clustering strategies based on the k-means algorithm. Pattern Recogn 71:375–386CrossRefGoogle Scholar
Birant D, Kut A (2007) ST-DBSCAN: an algorithm for clustering spatial-temporal data. Data Know Eng 60(1):208–221CrossRefGoogle Scholar
Gionis A, Mannila H, Tsaparas P (2007) Clustering aggregation. Acm Trans Know Discov Data 1(1):341–352Google Scholar
Gu B, Sheng V (2016) A Robust regularization path algorithm for \(\nu \)-support vector classification. IEEE Trans Neural Netw Learn Syst 1:1–8Google Scholar
Gu B, Sheng V, Wang Z et al (2015) Incremental learning for \(\nu \)-support vector regression. Neural Netw Off J Int Neural Netw Soc 67:140–150CrossRefGoogle Scholar
Jia H, Ding S, Du M (2015) Self-tuning p-spectral clustering based on shared nearest neighbors. Cognit Comput 7(5):1–11CrossRefGoogle Scholar
Kanungo T, Mount D, Netanyahu NS et al (2002) An efficient k-means clustering algorithm: analysis and implementation. IEEE Trans Pattern Anal Mach Intell 24(7):881–892CrossRefGoogle Scholar
Lee DD, Seung HS (2000) Algorithms for non-negative matrix factorization. In: International conference on neural information processing systems. MIT Press, pp 535–541Google Scholar
Lee D, Seung H (1999) Learning the parts of objects by non-negative matrix factorization. Nature 401(6755):788–791CrossRefMATHGoogle Scholar
Lee N, Tang R, Priebe C et al (2016) A model selection approach for clustering a multinomial sequence with non-negative factorization. IEEE Trans Pattern Anal Mach Intell 38(12):2345–2358CrossRefGoogle Scholar
Li C, Li L, Zhang J et al (2012) Highly efficient and exact method for parallelization of grid-based algorithms and its implementation in DelPhi. J Comput Chem 33(24):1960–1966CrossRefGoogle Scholar
Ma Y, Cheng G, Liu Z et al (2017) Fuzzy nodes recognition based on spectral clustering in complex networks. Phys A 465:792–797CrossRefGoogle Scholar
Mehmood R, Zhang G, Bie R et al (2016) Clustering by fast search and find of density peaks via heat diffusion. Neurocomputing 208(6191):210–217CrossRefGoogle Scholar
Morris K, Mcnicholas P (2016) Clustering, classification, discriminant analysis, and dimension reduction via generalized hyperbolic mixtures. Comput Stat Data Anal 97:133–150MathSciNetCrossRefGoogle Scholar
Papadimitriou CH, Steiglitz K (1982) Combinatorial optimization: algorithms and complexity. IEEE Trans Acoust Speech Signal Process 32(6):1258–1259MATHGoogle Scholar
Rodríguez A, Laio A (2014) Clustering by fast search and find of density peaks. Science 344(6191):1492–1496CrossRefGoogle Scholar
Ros F, Guillaume S (2016) DENDIS: a new density-based sampling for clustering algorithm. Expert Syst Appl 56:349–359CrossRefGoogle Scholar
Samaria F, Harter A (1994) Parameterisation of a stochastic model for human face identification. Proc Second IEEE Workshop Appl Comput Vis 1995:138–142Google Scholar
Sampat M, Wang Z, Gupta S et al (2009) Complex wavelet structural similarity: a new image similarity index. IEEE Trans Image Process 18(11):2385–2401MathSciNetCrossRefMATHGoogle Scholar
Trigeorgis G, Bousmalis K, Zafeiriou S et al (2017) A deep matrix factorization method for learning attribute representations. IEEE Trans Pattern Anal Mach Intell 39(3):417–429CrossRefGoogle Scholar