@article {evenden_encoding_2021,
	title = {Encoding a {Categorical} {Independent} {Variable} for {Input} to {TerrSet}{\textquoteright}s {Multi}-{Layer} {Perceptron}},
	journal = {ISPRS International Journal of Geo-Information},
	volume = {10},
	number = {10},
	year = {2021},
	month = {oct},
	pages = {686},
	abstract = {The profession debates how to encode a categorical variable for input to machine learning algorithms, such as neural networks. A conventional approach is to convert a categorical variable into a collection of binary variables, which causes a burdensome number of correlated variables. TerrSet{\textquoteright}s Land Change Modeler proposes encoding a categorical variable onto the continuous closed interval from 0 to 1 based on each category{\textquoteright}s Population Evidence Likelihood (PEL) for input to the Multi-Layer Perceptron, which is a type of neural network. We designed examples to test the wisdom of these encodings. The results show that encoding a categorical variable based on each category{\textquoteright}s Sample Empirical Probability (SEP) produces results similar to binary encoding and superior to PEL encoding. The Multi-Layer Perceptron{\textquoteright}s sigmoidal smoothing function can cause PEL encoding to produce nonsensical results, while SEP encoding produces straightforward results. We reveal the encoding methods by illustrating how a dependent variable gains across an independent variable that has four categories. The results show that PEL can differ substantially from SEP in ways that have important implications for practical extrapolations. If users must encode a categorical variable for input to a neural network, then we recommend SEP encoding, because SEP efficiently produces outputs that make sense.},
	issn = {2220-9964},
	doi = {10.3390/ijgi10100686},
	url = {https://www.mdpi.com/2220-9964/10/10/686},
	author = {Evenden, Emily and Pontius Jr, Robert Gilmore}
}
@article {shafizadeh-moghadam_integrating_2021,
	title = {Integrating a {Forward} {Feature} {Selection} algorithm, {Random} {Forest}, and {Cellular} {Automata} to extrapolate urban growth in the {Tehran}-{Karaj} {Region} of {Iran}},
	journal = {Computers, Environment and Urban Systems},
	volume = {87},
	year = {2021},
	month = {may},
	pages = {101595},
	issn = {01989715},
	doi = {10.1016/j.compenvurbsys.2021.101595},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S0198971521000028},
	author = {Shafizadeh-Moghadam, Hossein and Minaei, Masoud and Pontius Jr, Robert Gilmore and Asghari, Ali and Dadashpoor, Hashem}
}
@article {liu_total_2021,
	title = {The {Total} {Operating} {Characteristic} from {Stratified} {Random} {Sampling} with an {Application} to {Flood} {Mapping}},
	journal = {Remote Sensing},
	volume = {13},
	number = {19},
	year = {2021},
	month = {sep},
	pages = {3922},
	abstract = {The Total Operating Characteristic (TOC) measures how the ranks of an index variable distinguish between presence and absence in a binary reference variable. Previous methods to generate the TOC required the reference data to derive from a census or a simple random sample. However, many researchers apply stratified random sampling to collect reference data because stratified random sampling is more efficient than simple random sampling for many applications. Our manuscript derives a new methodology that uses stratified random sampling to generate the TOC. An application to flood mapping illustrates how the TOC compares the abilities of three indices to diagnose water. The TOC shows visually and quantitatively each index{\textquoteright}s diagnostic ability relative to baselines. Results show that the Modified Normalized Difference Water Index has the greatest diagnostic ability, while the Normalized Difference Vegetation Index has diagnostic ability greater than the Normalized Difference Water Index at the threshold where the Diagnosed Presence equals the Abundance of water. Some researchers consider only one accuracy metric at only one threshold, whereas the TOC allows visualization of several metrics at all thresholds. The TOC gives more information and clearer interpretation compared to the popular Relative Operating Characteristic. Our software generates the TOC from a census, simple random sample, or stratified random sample. The TOC Curve Generator is free as an executable file at a website that our manuscript gives.},
	issn = {2072-4292},
	doi = {10.3390/rs13193922},
	url = {https://www.mdpi.com/2072-4292/13/19/3922},
	author = {Liu, Zhen and Pontius Jr, Robert Gilmore}
}
@article {xie_enhanced_2020,
	title = {Enhanced {Intensity} {Analysis} to {Quantify} {Categorical} {Change} and to {Identify} {Suspicious} {Land} {Transitions}: {A} {Case} {Study} of {Nanchang}, {China}},
	journal = {Remote Sensing},
	volume = {12},
	number = {20},
	year = {2020},
	pages = {3323},
	abstract = {Conventional methods to analyze a transition matrix do not offer in-depth signals concerning land changes. The land change community needs an effective approach to visualize both the size and intensity of land transitions while considering possible map errors. We propose a framework that integrates error analysis, intensity analysis, and difference components, and then uses the framework to analyze land change in Nanchang, the capital city of Jiangxi province, China. We used remotely sensed data for six categories at four time points: 1989, 2000, 2008, and 2016. We had a confusion matrix for only 2016, which estimated that the map of 2016 had a 12\% error, while the temporal difference during 2008{\textendash}2016 was 22\% of the spatial extent. Our tools revealed suspected errors at other years by analyzing the patterns of temporal difference. For example, the largest component of temporal difference was exchange, which could indicate map errors. Our framework identified categories that gained during one time interval then lost during the subsequent time interval, which raised the suspicion of map error. This proposed framework facilitated visualization of the size and intensity of land transitions while illustrating possible map errors that the profession routinely ignores.},
	issn = {2072-4292},
	doi = {10.3390/rs12203323},
	url = {https://www.mdpi.com/2072-4292/12/20/3323},
	author = {Xie, Zheyu and Pontius Jr, Robert Gilmore and Huang, Jinliang and Nitivattananon, Vilas}
}
