# A Novel K-Means Clustering Algorithm with a Noise Algorithm for Capturing Urban Hotspots
## 1 Introduction
Clustering analysis algorithms can be divided into partition methods, hierarchical methods, density-based methods, grid-based methods, and model-based methods. Among them, K-means clustering is the simplest, most used, and computationally efficient clustering algorithm, but it faces three major problems for any given dataset. As such, it is very difficult to find the appropriate number of clusters, optimize clustering centers, and capture global clustering results. For the past several decades, many researchers have proposed some new ideas and methods. An improved K-means algorithm based on density (canopy K-means) has been proposed to solve the problem of determining the most suitable number of clusters and the best initial seeds [30]. An evolutionary K-means (EKM) method, based on combining K-means and a genetic algorithm, has been proposed to select parameters automatically through the evolution of partitions for solving the initiation problem of K-means [31]. The K-means++ algorithm has been proposed to quickly capture a better clustering center to find the sensitivity of the clustering process for the clustering center [32]. Fuzzy C-means (FCM) has been proposed to solve the problem of clustering edge data attribution [33; 34; 35; 36]. An intelligent optimization algorithm with a K-means algorithm has been proposed to effectively solve the global optimization of clustering and the sensitivity of clustering center effectively [37; 38]. In addition, some researchers have also proposed some improved methods for K-means algorithms and new application scenarios. For example, the depth representation extracted by depth learning technology has been proposed to improve the clustering performance of K-means clustering [39]. A competing cluster center approach has been proposed to maximize the benefits of cluster centers [40]. [PERSON] and [PERSON] [41] proposed a novel sharing-based niche genetic algorithm with an initial population based on hybrid K-means clustering in order to obtain the best chromosome and perform K-means clustering. [PERSON] et al. [42] proposed a framework to differentiate between these two types of methods with the following procedure. These K-means clustering algorithms have adequately realized clustering and have obtained clustering results in actual engineering applications; however, some shortcomings still exist, such as a low processing efficiency, difficulty in determining the number of clusters, sensitively initializing the cluster center, and so on. In order to solve these problems, a novel K-means clustering algorithm based on a noise algorithm, namely, a noise K-means clustering algorithm, is developed here in order to improve the processing efficiency of automatic clustering and avoid both excessive manual configuration of parameter uncertainty and clustering results falling into local optimums in this paper. The noise algorithm is employed to randomly enhance the attribution of data points and output the results of clustering by adding noise judgment in order to automatically obtain the number of clusters for the given data and initialize the center cluster. Four unsupervised evaluation indexes of DB, PBM, SC, and SSE, and the nonparametric Wilcoxon statistical analysis method are employed to evaluate and analyze the clustering results and verify the distribution states and differences. Finally, five taxi GPS datasets, including Beijing, Chongqing, San Francisco, Rome and Aracaju, are selected to test and verify the effectiveness of the proposed noise K-means clustering algorithm in comparison with fuzzy C-means, K-means, and K-means plus approaches. The innovations and main contributions of this paper are described as follows. * A novel noise K-means clustering algorithm based on a noise algorithm is developed to capture urban hotspots. * The noise algorithm is employed to randomly enhance the attribution of data points and output results of clustering by adding noise judgment to automatically obtain the number of clusters and initialize the center cluster.