# Consensus Big Data Clustering for Bayesian Mixture Models
## 2 Related Work  
Cluster analysis has been utilised extensively in numerous disciplines to identify patterns and structures within data. [PERSON] et al. [6] applied cluster analysis to an actual mixed-type dataset and reported their findings. Meanwhile, [PERSON] et al. [7] provided a comprehensive survey of clustering algorithms, discussing the state-of-the-art machine learning applications, taxonomy, challenges, and future research prospects. [PERSON] et al. [8] conducted a survey of cluster analysis for gene expression data. Furthermore, [PERSON] et al. [9] proposed a locally weighted ensemble clustering method that assigns weights to individual partitions based on local information. These studies demonstrate the diversity of clustering methods and their applications, emphasizing the importance of choosing the appropriate method for specific datasets. Consensus clustering utilises \(W\) runs of a base model or learner (such as \(K\)-means clustering) and combines the \(W\) suggested partitions into a consensus matrix, where the \((i,j)\)-th entries reflect the percentage of model runs in which the \(i\)th and \(j\)th individuals co-cluster. This ratio indicates the degree of confidence in the co-clustering of any two elements. Moreover, ensembles may reduce computational execution time. This occurs because individual learners may be weaker (and hence consume less of the available data or stop before complete convergence), and the learners in the vast majority of ensemble techniques are independent of one another, enabling the use of a parallel environment for each of the faster model runs [10]. Bayesian clustering is a popular machine-learning technique for grouping data points into clusters based on their probability distributions. Hidden Markov models (HMM) [11] have been used to model the underlying probabilistic structure of data in Bayesian clustering. Accelerating hyperparameters via Bayesian optimizations can also help in building automated machine learning (AutoML) schemes [12], while such optimizations can also be applied in Tiny Machine Learning (TinyML) environments wherein devices can be trained to fulfil ML tasks [13]. Ensemble Bayesian Clustering [14] is a variation of Bayesian clustering that combines multiple models to produce more robust results, while cluster analysis [15] extends traditional clustering methods by considering the uncertainty in the data, which leads to more accurate results. Traditional clustering algorithms require a preset selection of the number of clusters \(K\), which can be challenging as it plagues many investigations, with researchers often depending on certain rules to choose a final model. Various selections of \(K\) are compared, for instance, using an evaluation metric for \(K\). Techniques for selecting \(K\) using the consensus matrix are offered in [16]; however, this implies that any uncertainty over \(K\) is not reflected in the final clustering, and each model run utilises the same, fixed number of clusters. An alternative clustering technique incorporates cluster analysis within a statistical framework [17], which implies that models may be formally compared and issues such as choosing \(K\) can be represented as a model-selection problem using relevant tools. In recent years, various clustering techniques have been developed to address the challenges associated with traditional clustering methods. Locally weighted ensemble clustering [9] leverages the advantages of ensemble clustering while accounting for the local structure of the data, leading to more accurate and robust results. Consensus clustering, a type of ensemble clustering, combines multiple runs of a base model into a consensus matrix to increase confidence in co-clustering [16]. Enhanced ensemble clustering via fast propagation of cluster-wise similarities [18; 19] improves the efficiency and effectiveness of clustering by propagating cluster-wise similarities more rapidly.