Draft:Time series trajectory analysis

• Comment: Unreferenced. AI output. I've removed non-encyclopedic material. Further "#Possible Applications" reads oddly promotional and is also unrefferenced, and I also doubt its encyclopedic nature. We often have "Uses" or "Applications" sections with WP:RS, what we don't have is the promotional wording of research authors in articles. Bobby Cohn (talk) 16:15, 31 March 2025 (UTC)

• Comment: Article written like AI-generated. Rewrite. Jõsé^hola 07:47, 18 January 2025 (UTC)

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A time series trajectory analysis (TSTA) is a quantitative method used in land change science that quantifies and visualizes the trajectories of a binary variable during a time series. TSTA builds on existing land change analysis methods, particularly those developed by Robert Gil Pontius Jr and is presented as a method and analytic tool in Bilintoh, 2023. TSTA was first developed to better analyze trajectories in project data from Bahia, Brazil and Long Term Ecological Research sites in the United States (Figure 1). These projects received funding from NASA and the NSF, respectively.

Many existing methods of land change analysis focus on net change between two time points, while TSTA addresses the need in Geographic Information Science to capture the complexity of land change over multiple time points. By examining the land change of a time series over several time intervals, trends, and cyclical patterns can be identified. These patterns might be essential for understanding land degradation vegetation change or urban expansion

Methods

Time series trajectory analysis provides a method to analyze a series of Boolean images and classify each pixel as having one of eight possible trajectories. Taken together these trajectories can describe key insights into trends of persistence and absence of a variable in an area. These trajectories include gain, loss and alternation. If both gain and loss occur during the time period of study, this is alternation.

TSTA is able to compare among sites and across inconsistent time intervals by expressing results as an annual percentage of each site's unified size. A site's unified size is the union of where the category exists at any of the site's time points.

Key to the TSTA methods are visualizations of trajectory data. One visual output is a map showing the spatial distribution of different trajectories, as shown in Figure 1. Another, unique to TSTA, is stack bar plots, as shown in Figure 2. Stack bar plots show gain, loss, and stable trajectories, with or without alteration, over any degree of temporal resolution. Map e) in Figure 2 displays very different trajectories between the first and second intervals. This is an indicator of possible map errors/inconsistencies in data collection.

Comparison with existing land change analysis approaches

Trajectory Analysis is one of many methods to describe a time series. It is non-parametric and univariate. It can be used with unevenly spaced time series. While the examples presented here are related to Land Use Change, Trajectory Analysis can be used to describe any type of time series. The eight trajectories used in the analysis require a different number of time intervals in order to be produced:

With at least two time intervals, a component of Alternation can be described, and the trajectories of All Alternation Loss First and All Alternation Gain First can be described.

With at least three time intervals, Gain with Alternation and Loss with Alternation can be described. Thus, three time intervals or greater are needed in order to utilize all eight trajectories.

TSTA can be applied at different temporal resolutions and different spatial resolutions of a time series.

Trajectory Analysis can be used as a stepping-off point to deeper analysis. It is a package of trajectories and components that researchers can use for deeper understanding. It can be used to analyze different temporal or spatial resolutions of the same extent. A researcher may detect autocorrelation of the alternation trajectories for example, or an exponential trend in the gain trajectories.

Possible Applications

Trajectory Analysis was originally developed in the context of Remote sensing and Land Change Science. However, it can be used in a wide variety of applications involving a dataset with a binary variable of Presence of Absence.

Land Cover Change Detection: Helps to monitor changes in land cover over time. By analyzing the trajectories of specific land cover types, researchers can identify patterns of deforestation, urbanization and other land-use changes.

Politics: Trajectories of presence or absence of a political party's seats in a governing body.

Vegetation Dynamics: Monitoring the trajectories of vegetation derived from remote sensing data enables the assessment of ecosystem health, detecting disturbances, and understanding the impact of climate change of vegetation patterns.

Urban Growth and Expansion: Tracking trajectories of urban areas provides insights into urban growth and expansion. This is important for urban planning, resource management, and understanding the environmental consequences of rapid urbanization.

Natural disaster Assessment and Response: Can be used to understand patterns of severity and frequency in natural disasters such as floods, wildfires, and earthquakes. Monitoring the trajectory of changes before, during, and after a disaster helps in emergency response planning and post-disaster recovery efforts.

Medicine: Trajectories of presence or absence of cancerous tissue samples in a patient.

Land Management and Planning: Providing data-driven insights into the historical and current trends in land use. The information is valuable for making informed decisions about resource allocation, conservation efforts, and sustainable development.

R Package

Bilintoh has made available a package in the R programming language that can be adapted to perform time series trajectory analysis on any dataset of boolean images. It is available on GitHub.