Incremental enhanced α-expansion move for large data: a probability regularization perspective

Abstract

To deal with large data clustering tasks, an incremental version of exemplar-based clustering algorithm is proposed in this paper. The novel clustering algorithm, called Incremental Enhanced a-Expansion Move (IEEM), processes large data chunk by chunk. The work here includes two aspects. First, in terms of the maximum a posteriori principle, a unified target function is developed to unify two typical exemplar-based clustering algorithms, namely Affinity Propagation (AP) and Enhanced aExpansion Move (EEM). Secondly, with the proposed target function, the probability based regularization term is proposed and accordingly the proposed target function is extended to make IEEM have the ability to improve clustering performance of the entire dataset by leveraging the clustering result of previous chunks. Another outstanding characteristic of IEEM is that only by modifying the definitions of several variables used in EEM, the minimization procedure of EEM and its theoretical spirit can be easily kept in IEEM, and hence no more efforts are needed to develop a new optimization algorithm for IEEM. In contrast to AP, EEM and the existing incremental clustering algorithm IMMFC, our experimental results of synthetic and real-world datasets indicate the effectiveness of IEEM.

Fast Enhanced Exemplar-Based Clustering for Incomplete EEG Signals

“…(3) Generate the expansion order o on the potential exemplar list E new (4) Let t � 1; (5) for e ∈ o do (6) if e ∈ E then (7) compute R1 α , R1 by equations (15) and 16; (8) if R1 α > 0 then (9) for ∀x i ∈ X e , set E(x i ) � S(i) ; (10) end (11) else (12) compute R2 e , R2 α , R2 by equations (17)- (19) (13) if R2 α > R2 e then (14) for ∀x i ∈ X /e e,α , set E(x i ) � α (15) else (16) for ∀x i ∈ X e , set E(x i ) � S(i) (17) else (18) if R2 > 0 then (19) Accept the new exemplar α Computational and Mathematical Methods in Medicine compression stage, the time complexity of FEEC has been reduced, and the efficiency is improved as well. And FEEC has an equivalent computational time with FAP.…”

“…is the dataset among which the exemplar is l and s ∈ (E/l) represents other exemplars in E except for l. e EEM clustering model is a state-of-the-art achievement of exemplar-based clustering model and has been proved to be efficient and effective for numerous scenarios [16,17,30]. IEEM [30] is proposed to deal with link constraints by embedding a bound term in the target function.…”

“…IEEM [30] is proposed to deal with link constraints by embedding a bound term in the target function. For dynamic data stream, Bi and Wang [16] also proposed an incremental EEM version DSC which processes data chunk by chunk. However, for incomplete EEG signals, these methods would not recognize epilepsy well.…”

“…Here, we give the definitions of the three adopted performance indices ENERGY, NMI, and accuracy. Along with the description in [12,16,30,33,34], we call the result outputted by these involved models as cluster and the true labels as class.…”

“…(3) Moreover, this paper also considers the fact that the graph cuts [14] based optimization performs better than those loopy belief propagation (LBP) [15] based structure. So, the proposed FEEC algorithm optimizes the target model by the enhanced α-expansion move framework [16,17]. (4) Experimental results of both synthetic and realworld datasets indicate the promising efficiency of the proposed FEEC algorithm.…”