Vol.:(0123456789) Artifcial Intelligence Review https://doi.org/10.1007/s10462-020-09862-1 1 3 Consensus function based on cluster‑wise two level clustering Mohammad Reza Mahmoudi 1,2  · Hamidreza Akbarzadeh 3  · Hamid Parvin 4,5  · Samad Nejatian 6,7  · Vahideh Rezaie 7,8  · Hamid Alinejad‑Rokny 9,10,11 © Springer Nature B.V. 2020 Abstract The ensemble clustering tries to aggregate a number of basic clusterings with the aim of producing a more consistent, robust and well-performing consensus clustering result. The current paper wants to introduce an ensemble clustering method. The proposed method, called consensus function based on two level clustering (CFTLC), introduces a new con- sensus clustering where it makes a cluster clustering task through applying an average hierarchical clustering on a cluster–cluster similarity matrix obtained by an innovative similarity metric. By applying the average hierarchical clustering algorithm, a set of meta clusters has been attained. Considering each meta cluster as a consensus cluster in the con- sensus clustering output, it then assigns each data point to a meta cluster through defning an object-cluster similarity. Before doing anything, CFTLC converts the primary partitions into a binary cluster representation where the primary ensemble has been broken into a number of basic binary clusters (BC). CFTLC frst combines the basic BCs with the maxi- mum cluster–cluster similarity. This step is iterated as long as a predefned number of meta clusters are ready. At the subsequent step, it assigns each data point to exactly one meta cluster. The proposed method has been experimentally compared with the state of the art clustering algorithms in terms of accuracy and robustness. Keywords Consensus clustering · K-means · Similarity criterion · Machine learning · Data mining 1 Introduction In numerous applications, machine learning functions are extremely benefcial (Pattan- asri 2012; Yang and Yu 2017; Li et al. 2017; Deng et al. 2018; Chakraborty et al. 2017). In order to resolve numerous real world issues, straightforward machine learning mod- els are utilized. Moreover, understandable machine learning models are frail in facing * Hamid Parvin parvin@iust.ac.ir * Hamid Alinejad-Rokny h.alinejad@unsw.edu.au; h.alinejad@ieee.org Extended author information available on the last page of the article