## 2 Methods
### Statistical Modeling with Random Forests  
The segments (hereafter polygons) were used as the unit of analysis for the statistical model. Since land-cover change is a relatively rare event, we needed to stratify our sample to balance for our two classes, change and no change [52]. To achieve a balanced training sample we did two modeling iterations. To create the training data for the first iteration, we randomly selected ~500 polygons and manually searched for several hundred additional polygons that exhibited change-like differences in the imagery. While most of the change-like selected polygons were actual change (Figure 5A-E), we  
Figure 4: AAViewer. The AAViewer program displays three images and an attribution pane for rapidly classifying target polygons. In the figure, the upper left image is from 2006, the upper right image is from 2009, and the lower right image is the band-wise difference image. The ChangeClass box stays selected during review and movement between image sets is done with the “W” and “S” keys. The classification procedure requires 2 keystrokes, “S” to advance image sets and 1–9 to denote the change type.  
included some polygons that looked like change but were actually only different due to view angle or illumination angle (Figure 5F), which are common problems for OBIA with high resolution imagery [15].  
These initial polygons were labeled as either change-like, or not-change and used as the response in a Random Forest (RF) model [53, 76, 77, 78] implemented with the randomForest package in the R statistical environment [79, 80]. The predictor variables were derived from eCognition and ancillary  
Figure 5: Examples of typical changes included in the training data. Changes like (**A–C**) were labeled as development in the final maps. Changes like (**D**) were labeled forestry. (**E**) Natural changes most commonly are stream course changes, land-slides and fires. (**F**) False changes are due to events like tree lean and shifting shadow patterns.  
information derived from the land-cover modeling and topographic information (Table 1). Random Forests is a machine learning algorithm derived from Classification and Regression Trees (CART) [81, 82]. CART is a recursive partitioning algorithm that searches a parameter space for a variable value that splits a data set into two leaves with the minimum possible classification error. It continues to split the leaves of the tree until some stopping rule such as \"terminal leaf node variance dropping below some maximum value\" is reached. Random Forests performs multiple iterations of a CART-style algorithm. For each tree it subsamples both the data and the predictor variable set. The final classification is essentially a voting scheme where each classification tree makes a prediction for each analysis unit and the final class is the class with the most votes. A probability is generated by observing the proportion of votes for the winning class _versus_ the total number of trees. Because of this, interpreting RF results can be difficult if the analytical goal is to develop a mechanistic model for change. Relative importance is attributed to different variables depending on their cumulative contribution over the individual model runs.  
From the initial model output, we randomly selected 2500 polygons from each strata, where the strata were the non-change and change-like predictions from the first iteration. These 5000 total samples were reviewed with the AAViewer and labeled as actual change or no-change. They were then used in the second modeling iteration as the response to create the final model. Based on the RF voting scheme, a change polygon is any polygon that was predicted to be change in the majority of derived classification trees or rather had a change probability of \(\geq\)50%. This produces the base output map which will be called the RF50 map, denoting the predicted change polygons from the model with a 50% change probability threshold.