Last updated: 2020-09-16
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Probability filtering
Background
To predict the tree species for a pixel our random forest model calculates relative probabilities for that pixel to belong to each class. These probabilities sum up to 1. The tree species is predicted by choosing the class with highest probability. In areas where the model is quite sure probabilities will be high for one species and low for the others. In areas where the model is not fitted perfectly probabilities will be similar between species. The idea is to mask pixel predictions with low certainties and fill them with predictions of surrounding pixels in a later step.
Probability distributions
Most data which was classified correctly had high probability values, while incorrectly classified validation data has a much wider distribution but was mostly classified with probabilities around 0.5. Using a 4-class model without larch and douglas fir especially increased the probabilities of correctly classified validation pixels.
6-class
Prediction probability distributions (correct cs. incorrect), using 6-class model
4-class
Prediction probability distributions (correct cs. incorrect), using 4-class model
Question
Up until which classification probability is the chance of misclassification higher than the chance of correct classification?
Results
By model
Up until a probability value of 0.58 in the 6-class model, the chance of a pixel being misclassified is higher than the chance for correct classification. With higher probabilities we see a steep rise in correct classifications while incorrect classifications occur to a smaller fraction.
6-class
Cumulative proportion of correctly and incorrectly predicted validation data by prediction probability and corresponding threshold for equal shares (using 6-class model)
Using a probability threshold of 0.58 approximately 13.1% of the predictions are masked when using the 6-class model. About 6.6% of each correctly and incorrectly classified pixels will be masked.
4-class
Cumulative proportion of correctly and incorrectly predicted validation data by prediction probability and corresponding threshold for equal shares (using 4-class model)
Using a probability threshold of 0.534 approximately 3% of the predictions are masked when using the 4-class model. About 1.5% of each correctly and incorrectly classified pixels will be masked.
By region
Harz
Probability
Classification probability (maximum among species) calculated by the model
Classification
Tree species predictions from highest probabilities in the study area Harz
High probability
Tree species predictions with high probabilities (above threshold)
Low probability
Tree species predictions with low probabilities (below threshold)
Histogram
Histogram of predictions in the study area Harz, differentiated between low and high probabilities
Solling
Probability
Classification probability (maximum among species) calculated by the model
Classification
Tree species predictions from highest probabilities in the study area Solling
High probability
Tree species predictions with high probabilities (above threshold)
Low probability
Tree species predictions with low probabilities (below threshold)
Histogram
Histogram of predictions in the study area Solling, differentiated between low and high probabilities
Heide
Probability
Classification probability (maximum among species) calculated by the model
Classification
Tree species predictions from highest probabilities in the study area Heide
High probability
Tree species predictions with high probabilities (above threshold)
Low probability
Tree species predictions with low probabilities (below threshold)
Histogram
Histogram of predictions in the study area Heide, differentiated between low and high probabilities
By species
Beech
Cumulative proportion of validation data predicted correctly or incorrectly as beech (by prediction probability)
The species specific probability threshold for beech (below which more predictions are classified incorrectly and than correctly) is 0.524. Approximately 6.3% of the predictions classified as beech would be masked if we apply this threshold. About 3.1% of pixels classified correctly and 3.1% of pixels classified incorrectly as beech be masked.
Douglas fir
Cumulative proportion of validation data predicted correctly or incorrectly as douglas fir (by prediction probability)
The species specific probability threshold for douglas fir (below which more predictions are classified incorrectly and than correctly) is 0.624. Approximately % of the predictions classified as douglas fir would be masked if we apply this threshold. About % of pixels classified correctly and % of pixels classified incorrectly as douglas fir be masked.
Spruce
Cumulative proportion of validation data predicted correctly or incorrectly as spruce (by prediction probability)
The species specific probability threshold for spruce (below which more predictions are classified incorrectly and than correctly) is 0.702. Approximately % of the predictions classified as spruce would be masked if we apply this threshold. About % of pixels classified correctly and % of pixels classified incorrectly as spruce be masked.
Pine
Cumulative proportion of validation data predicted correctly or incorrectly as pine (by prediction probability)
The species specific probability threshold for pine (below which more predictions are classified incorrectly and than correctly) is 0.508. Approximately % of the predictions classified as pine would be masked if we apply this threshold. About % of pixels classified correctly and % of pixels classified incorrectly as pine be masked.
Larch
Cumulative proportion of validation data predicted correctly or incorrectly as larch (by prediction probability)
The species specific probability threshold for larch (below which more predictions are classified incorrectly and than correctly) is 0.604. Approximately % of the predictions classified as larch would be masked if we apply this threshold. About % of pixels classified correctly and % of pixels classified incorrectly as larch be masked.
Oak
Cumulative proportion of validation data predicted correctly or incorrectly as oak (by prediction probability)
The species specific probability threshold for oak (below which more predictions are classified incorrectly and than correctly) is 0.542. Approximately % of the predictions classified as oak would be masked if we apply this threshold. About % of pixels classified correctly and % of pixels classified incorrectly as oak be masked.
As we can see the probability threshold below which predictions are more likely to be misclassified than correctly classified also varies by species. However, the exact distribution of prediction probabilities and their classification result varies between random forest models which are created by stratified but randomized folding in our case. For a different random seed the species specific threshold might change to a certain degree.
R version 4.0.2 (2020-06-22)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 18362)
Matrix products: default
locale:
[1] LC_COLLATE=German_Germany.1252 LC_CTYPE=German_Germany.1252
[3] LC_MONETARY=German_Germany.1252 LC_NUMERIC=C
[5] LC_TIME=German_Germany.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] ggridges_0.5.2 rasterVis_0.48 latticeExtra_0.6-29
[4] lattice_0.20-41 ggplot2_3.3.2 randomForest_4.6-14
[7] groupdata2_1.3.0 tidyr_1.1.0 dplyr_1.0.0
[10] raster_3.3-13 rgdal_1.5-12 sp_1.4-2
[13] here_0.1 workflowr_1.6.2
loaded via a namespace (and not attached):
[1] zoo_1.8-8 tidyselect_1.1.0 xfun_0.15 reshape2_1.4.4
[5] purrr_0.3.4 colorspace_1.4-1 vctrs_0.3.2 generics_0.0.2
[9] htmltools_0.5.0 viridisLite_0.3.0 yaml_2.2.1 rlang_0.4.7
[13] hexbin_1.28.1 later_1.1.0.1 pillar_1.4.6 glue_1.4.1
[17] withr_2.2.0 RColorBrewer_1.1-2 plyr_1.8.6 jpeg_0.1-8.1
[21] lifecycle_0.2.0 stringr_1.4.0 munsell_0.5.0 gtable_0.3.0
[25] codetools_0.2-16 evaluate_0.14 labeling_0.3 knitr_1.29
[29] httpuv_1.5.4 parallel_4.0.2 highr_0.8 Rcpp_1.0.5
[33] checkmate_2.0.0 promises_1.1.1 backports_1.1.7 scales_1.1.1
[37] farver_2.0.3 fs_1.4.2 png_0.1-7 digest_0.6.25
[41] stringi_1.4.6 grid_4.0.2 rprojroot_1.3-2 tools_4.0.2
[45] magrittr_1.5 tibble_3.0.3 crayon_1.3.4 whisker_0.4
[49] pkgconfig_2.0.3 ellipsis_0.3.1 rmarkdown_2.3 rstudioapi_0.11
[53] R6_2.4.1 git2r_0.27.1 compiler_4.0.2