The k-means algorithm is generally the most known and used clustering method. There are various extensions of k-means to be proposed in the literature. Although it is an unsupervised learning to clustering in pattern recognition and machine learning, the k-means algorithm and its extensions are always influenced by initializations with a necessary number of clusters a priori. That is, the k-means algorithm is not exactly an unsupervised clustering method. In this paper, we construct an unsupervised learning schema for the k-means algorithm so that it is free of initializations without parameter selection and can also simultaneously find an optimal number of clusters. That is, we propose a novel unsupervised k-means (U-k-means) clustering algorithm with automatically finding an optimal number of clusters without giving any initialization and parameter selection. The computational complexity of the proposed U-k-means clustering algorithm is also analyzed. Comparisons between the proposed U-k-means and other existing methods are made. Experimental results and comparisons actually demonstrate these good aspects of the proposed U-k-means clustering algorithm.

The k-means clustering algorithm is the oldest and most known method in cluster analysis. It has been widely studied with various extensions and applied in a variety of substantive areas. Since internet, social network, and big data grow rapidly, multi-view data become more important. For analyzing multi-view data, various multi-view k-means clustering algorithms have been studied. However, most of multi-view k-means clustering algorithms in the literature cannot give feature reduction during clustering procedures. In general, there often exist irrelevant feature components in multi-view data sets that may cause bad performance for these clustering algorithms. There also exists high feature dimension in multi-view data sets so it is necessary to consider reducing its dimension for clustering algorithms. In this paper, a learning mechanism for the multi-view k-means algorithm to automatically compute individual feature weight is constructed. It can reduce these irrelevant feature components in each view. A new multi-view k-means objective function is firstly proposed for constructing the learning mechanism for feature weights in multi-view clustering. A schema for eliminating irrelevant feature(s) with small weight(s) is then considered for feature reduction. Therefore, a new type of multi-view k-means, called a feature-reduction multi-view k-means (FRMVK), is proposed. The computational complexity of FRMVK is also analyzed. Numerical and real data sets are used to compare FRMVK with other feature-weighted multi-view k-means algorithms. Experimental results and comparisons actually demonstrate the effectiveness and usefulness of the proposed FRMVK clustering algorithm.

The k-means algorithm with its extensions is the most used clustering method in the literature. But, the k-means and its various extensions are generally affected by initializations with a given number of clusters. On the other hand, most of k-means always treat data points with equal importance for feature components. There are several feature-weighted k-means proposed in literature, but, these feature-weighted k-means do not give a feature reduction behavior. In this paper, based on several entropy-regularized terms we can construct a novel k-means clustering algorithm, called Entropy-k-means, such that it can be free of initializations without a given number of clusters, and also has a feature reduction behavior. That is, the proposed Entropy-k-means algorithm can eliminate irrelevant features with feature reduction under free of initializations with automatically finding an optimal number of clusters. Comparisons between the proposed Entropy-k-means and other methods are made. Experimental results and comparisons actually demonstrate these good aspects of the proposed Entropy-k-means with its effectiveness and usefulness in practice.

The increasing effect of Internet of Things (IoT) unlocks the massive volume of the availability of Big Data in many fields. Generally, these Big Data may be in a non-independently and identically distributed fashion (non-IID). In this paper, we have contributions in such a way enable multi-view k-means (MVKM) clustering to maintain the privacy of each database by allowing MVKM to be operated on the local principle of clients' multi-view data. This work integrates the exponential distance to transform the weighted Euclidean distance on MVKM so that it can make full use of development in federated learning via the MVKM clustering algorithm. The proposed algorithm, called a federated MVKM (Fed-MVKM), can provide a whole new level adding a lot of new ideas to produce a much better output. The proposed Fed-MVKM is highly suitable for clustering large data sets. To demonstrate its efficient and applicable, we implement a synthetic and six real multi-view data sets and then perform Federated Peter-Clark in Huang et al. [1] for causal inference setting to split the data instances over multiple clients, efficiently. The results show that shared-models based local cluster centers with data-driven in the federated environment can generate a satisfying final pattern of one multi-view data that simultaneously improve the clustering performance of (non-federated) MVKM clustering algorithms.

The rapid development in information technology makes it easier to collect vast numbers of data through the cloud, internet and other sources of information. Multiview clustering is a significant way for clustering multiview data that may come from multiple ways. The fuzzy c-means (FCM) algorithm for clustering (single-view) datasets was extended to process multiview datasets in the literature, called the multiview FCM (MV-FCM). However, most of the MV-FCM clustering algorithms and their extensions in the literature need prior information about the number of clusters and are also highly influenced by initializations. In this paper, we propose a novel MV-FCM clustering algorithm with an unsupervised learning framework, called the unsupervised MV-FCM (U-MV-FCM), such that it can search an optimal number of clusters during the iteration process of the algorithm without giving the number of clusters a priori. It is also free of initializations and parameter selection. We then use three synthetic and six benchmark datasets to make comparisons between the proposed U-MV-FCM and other existing algorithms and to highlight its practical implications. The experimental results show that our proposed U-MV-FCM algorithm is superior and more useful for clustering multiview datasets.

Multi-view (MV) data are increasingly collected from various fields, like IoT. The surge in MV data demands clustering algorithms capable of handling heterogeneous features and high dimensionality. Existing feature-weighted MV k-means (MVKM) algorithms often neglect effective dimensionality reduction such that their scalability and interpretability are limited. To address this, we propose a novel procedure for clustering MV data, namely a globally collaborative MVKM (G-CoMVKM) clustering algorithm. The proposed G-CoMVKM integrates a collaborative transfer learning framework with entropy-regularized feature-view reduction, enabling dynamic elimination of uninformative components. This method achieves clustering by balancing local view importance and global consensus, without relying on matrix reconstruction. We design a feature-view reduction by embedding transferred learning processes across view components by using penalty terms and entropy to simultaneously reduce these unimportant feature-view components. Experiments on synthetic and real-world datasets demonstrate that G-CoMVKM consistently outperforms these existing MVKM clustering algorithms in clustering accuracy, performance, and dimensionality reduction, affirming its robustness and efficiency.