# A Novel K-Means Clustering Algorithm with a Noise Algorithm for Capturing Urban Hotspots
## 1 Introduction  
Modern cities have become important engines and hubs to drive social development. A city represents the most concentrated residence of people and the gathering place of social resources. Both work and life are inseparable from urban support. In recent years, there has been a \"big city disease\", of which the most prominent phenomenon is urban congestion, which has become a nearly unavoidable problem for almost every large-scale city. Consequently, from the perspective of informatization and intelligence, people have successively used information technology to put forward digital cities and smart cities from the strategic level and have formulated construction schemes to meet the development needs of different cities, hoping to solve the challenges faced in the process of urban development and alleviating urban congestion. In particular, the application of the new generation of cloud computing, big data, the Internet of Things, and artificial intelligencetechnology has made urban operation more intelligent and has gradually become a reality, making rail transit and urban transportation more predictable and widely applied; however, a city is a densely populated area with a high concentration of both living and vehicle operation. The growth of the world's civil vehicle sales from 2010 to 2020 is shown in Figure 1.  
Moreover, population flow is directly related to time, and urban congestion is still an important challenge for every city. The application of big data has served as a basic strategic digital resource in smart cities. Many researchers have analyzed the trajectory GPS data of transportation vehicles in order to mine the hidden information behind the data to reflect the urban operation status and define temporal and spatial change rules [1], in addition to use in traffic congestion status analysis [2; 3; 4; 5; 6; 7], crowd movement distribution [8; 9; 10], traffic travel recommendation [11; 12], and road planning [13; 14], urban hotspot discovery [15; 16; 17; 18], and so on. Such research results are directly applied to the construction of a smart city to elucidate more reasonable urban road planning and a more reasonable dispersion of vehicle flow and human flow. Such research methods usually use machine learning algorithms (such as cluster analysis and feature learning) to capture the vehicle trajectory patterns, including the origins and destinations (OD) [19; 20; 21], stops and moves (SM) [22; 23], and moving objects (MO) [24; 25] from the GPS data. [PERSON] et al. [26] proposed a midlatitude Klobuchar correction model to correct the Klobuchar model for midlatitude users. [PERSON] et al. [27] proposed a data-based methodology to estimate the traffic congestion of road segments between bus stops in order to improve the travel time reliability and quality of public transport services. [PERSON] et al. [28] proposed a specific and accurate definition of traffic congestion to quantify the level of traffic congestion and constructed an image-based traffic congestion estimation framework based on a convolutional neural network. [PERSON] and [PERSON] [29] proposed a Bayesian network based on speed- and volume-related measures and a probabilistic congestion estimation approach. These models have been used to explain and discover urban operation states, crowd migration hotspots, and other urban operations. Figure 1: The growth of the world’s civil vehicle Sales from 2010 to 2020. In order to learn the valuable information hidden behind the location data, a clustering learning algorithm is a common and simple method that is used in many studies. Cluster analysis, also known as group analysis, is not only a statistical analysis method to study a classification problem (sample or index), but is also an important algorithm for data mining. Cluster analysis is composed of several patterns. Usually, a pattern is a vector of measurement or a point in multi-dimensional space. Cluster analysis is based on similarity. Patterns in a cluster have more similarity than patterns that are not in the same cluster.