A novel cluster center fast determination clustering algorithm

A Fast Granular-Ball-Based Density Peaks Clustering Algorithm for Large-Scale Data

Density peaks clustering algorithm (DP) has difficulty in clustering large-scale data, because it requires the distance matrix to compute the density and -distance for each object, which has time complexity. Granular ball (GB) is a coarse-grained representation of data. It is based on the fact that an object and its local neighbors have similar distribution and they have high possibility of belonging to the same class. It has been introduced into supervised learning by Xia et al. to improve the efficiency of supervised learning, such as support vector machine, -nearest neighbor classification, rough set, etc. Inspired by the idea of GB, we introduce it into unsupervised learning for the first time and propose a GB-based DP algorithm, called GB-DP. First, it generates GBs from the original data with an unsupervised partitioning method. Then, it defines the density of GBs, instead of the density of objects, according to the centers, radius, and distances between its members and centers, without setting any parameters. After that, it computes the distance between the centers of GBs as the distance between GBs and defines the -distance of GBs. Finally, it uses GBs' density and -distance to plot the decision graph, employs DP algorithm to cluster them, and expands the clustering result to the original data. Since there is no need to calculate the distance between any two objects and the number of GBs is far less than the scale of a data, it greatly reduces the running time of DP algorithm. By comparing with -means, ball -means, DP, DPC-KNN-PCA, FastDPeak, and DLORE-DP, GB-DP can get similar or even better clustering results in much less running time without setting any parameters. The source code is available at https://github.com/DongdongCheng/GB-DP.

Clustering Hidden Markov Models With Variational Bayesian Hierarchical EM

The hidden Markov model (HMM) is a broadly applied generative model for representing time-series data, and clustering HMMs attract increased interest from machine learning researchers. However, the number of clusters ( K ) and the number of hidden states ( S ) for cluster centers are still difficult to determine. In this article, we propose a novel HMM-based clustering algorithm, the variational Bayesian hierarchical EM algorithm, which clusters HMMs through their densities and priors and simultaneously learns posteriors for the novel HMM cluster centers that compactly represent the structure of each cluster. The numbers K and S are automatically determined in two ways. First, we place a prior on the pair (K,S) and approximate their posterior probabilities, from which the values with the maximum posterior are selected. Second, some clusters and states are pruned out implicitly when no data samples are assigned to them, thereby leading to automatic selection of the model complexity. Experiments on synthetic and real data demonstrate that our algorithm performs better than using model selection techniques with maximum likelihood estimation.

A Novel 2D Clustering Algorithm Based on Recursive Topological Data Structure

In the field of data science and data mining, the problem associated with clustering features and determining its optimum number is still under research consideration. This paper presents a new 2D clustering algorithm based on a mathematical topological theory that uses a pseudometric space and takes into account the local and global topological properties of the data to be clustered. Taking into account cluster symmetry property, from a metric and mathematical-topological point of view, the analysis was carried out only in the positive region, reducing the number of calculations in the clustering process. The new clustering theory is inspired by the thermodynamics principle of energy. Thus, both topologies are recursively taken into account. The proposed model is based on the interaction of particles defined through measuring homogeneous-energy criterion. Based on the energy concept, both general and local topologies are taken into account for clustering. The effect of the integration of a new element into the cluster on homogeneous-energy criterion is analyzed. If the new element does not alter the homogeneous-energy of a group, then it is added; otherwise, a new cluster is created. The mathematical-topological theory and the results of its application on public benchmark datasets are presented.

A Density-Peak-Based Clustering Method for Multiple Densities Dataset

Clustering methods in data mining are widely used to detect hotspots in many domains. They play an increasingly important role in the era of big data. As an advanced algorithm, the density peak clustering (DPC) algorithm is able to deal with arbitrary datasets, although it does not perform well when the dataset includes multiple densities. The parameter selection of cut-off distance dc is normally determined by users’ experience and could affect clustering result. In this study, a density-peak-based clustering method is proposed to detect clusters from datasets with multiple densities and shapes. Two improvements are made regarding the limitations of existing clustering methods. First, DPC finds it difficult to detect clusters in a dataset with multiple densities. Each cluster has a unique shape and the interior includes different densities. This method adopts a step by step merging approach to solve the problem. Second, high densities of points can automatically be selected without manual participation, which is more efficient than the existing methods, which require user-specified parameters. According to experimental results, the clustering method can be applied to various datasets and performs better than traditional methods and DPC.

PSO-CFDP: A Particle Swarm Optimization-Based Automatic Density Peaks Clustering Method for Cancer Subtyping

Cancer subtyping is of great importance for the prediction, diagnosis, and precise treatment of cancer patients. Many clustering methods have been proposed for cancer subtyping. In 2014, a clustering algorithm named Clustering by Fast Search and Find of Density Peaks (CFDP) was proposed and published in Science, which has been applied to cancer subtyping and achieved attractive results. However, CFDP requires to set two key parameters (cluster centers and cutoff distance) manually, while their optimal values are difficult to be determined. To overcome this limitation, an automatic clustering method named PSO-CFDP is proposed in this paper, in which cluster centers and cutoff distance are automatically determined by running an improved particle swarm optimization (PSO) algorithm multiple times. Experiments using PSO-CFDP, as well as LR-CFDP, STClu, CH-CCFDAC, and CFDP, were performed on four benchmark data-sets and two real cancer gene expression datasets. The results show that PSO-CFDP can determine cluster centers and cutoff distance automatically within controllable time/cost and, therefore, improve the accuracy of cancer subtyping.