# chapter{Methodology}label{chap:met}section{Data angular distances at a given time threshold \$t_i

chapter{Methodology}label{chap:met}section{Data Analysis}Stationary or moving data in a trajectory are represented geographically on the map as a finite sequences:\$T = (x_1,t_1), (x_2,t_2), … , (x_n,t_n) \$Where, x = data points also known as flow vector.  with \$x_i extless x_{i+1},  \$ \$(i = 1,2, … , n-1)\$ and  t = time\$x \$ is represented in vector form because the object moves along in a trajectory and change in specific time threshold.All points, \$x_i  epsilon  mathbb{R}^2 \$ represents the approximated location of the object in 2-dimensional plane noted by latitude and longitude angular distances at a given time threshold \$t_i \$ When we analyse the structure of moving object in a trajectory, we get tremendous useful informations like existence of some interactions between bodies and properties of these interactions that can be very supportive in developing some new applications based on the analysis we discovered in the network and we can make some new prediction prior to our analysis such as predicting the next location of a moving object or destination for our moving object or traffic jams ahead, with help of the rate of accident to a particular location, predict what will happen in the coming years and help to take some pre-cautions (if it was found that more accidents happen at that particular location like Entertainment hall due to massive traffic in a particular month like end of December during the celebrations, more traffic police can be deployed to that particular location or take some other measures) etc..section{Software Analysis}subsection{Digital Globes}I used extbf{OpenStreetMap}, because it is open source, which means that the user has the ability to change the programming to their preferences and scale up or down with ease footnote{OpenStreetMap is extremely interactive} and reduces possible distortion and help discover the connections between places.   OpenStreetMap is a free editable mapping service that can be accessible from any device and the user can supply up-to-date information and it is possible to monitor the information in real-time.OpenStreetMap is a database that contains locations of continents, states, cities, roads, streets, building and is easily accessible by the user for further projectssubsection{Map Depiction} extbf{Python} is an object-oriented programming language with high-level built in data structures. It has dynamic typing and dynamic binding which makes it more useful for fast application development and for connecting existing components with each other.  Python is a programming language model that is simple and easy to learn and it has a set of open source libraries that are easily accessible by the user. There is no compilation step required in python which makes it’s edit and debugging test cycle faster and more productive. extbf{JavaScript} libraries were used also to depict the trajectories on web mapping application for visualizing and analyzing data set in the trajectory.I created a server in Python and then JavaScript code was used to visualize the trajectory data set and the JavaScript program was synchronized to the server to run in cycles and displayed on the map accordingly. To assess the visualization and performance, I used a set of  GPS trajectory dataset collected in Microsoft Research Asia, in Geolife project.I only used data set for two users collected according to their latitude and longitude as we wish to analyse these users with respect to the most visited location by these users to see the similarities and relationships, in order to make recommendations for the future use or to improve services provided in a given particular location with respect to our analysis.Then I visualized all these data set on the map synchronized to the server.In this project, each user’s data set is a directory containing a set of points representing a trajectory, and every point is represented by a vector of values as shown in the table below:egin{center}egin{longtable}{c c c}caption{Data set Unit Representation format.} label{tab:tabl} hline multicolumn{1}{|c|}{ extbf{Title}} & multicolumn{1}{c|}{ extbf{Units Representation}} hline endheadhlineendfoot Latitude  & decimal   Longitude & decimal  Date String & dd-mm-yy  Time String & hh:mm:ssend{longtable}end{center}