Fit and validate Support Vector Machine models
Usage
fit_svm(
data,
response,
predictors,
predictors_f = NULL,
fit_formula = NULL,
partition = NULL,
thr = NULL,
sigma = "automatic",
C = 1
)Arguments
- data
data.frame. Database with response (0,1) and predictors values.
- response
character. Column name with species absence-presence data (0,1).
- predictors
character. Vector with the column names of quantitative predictor variables (i.e. continuous variables). Usage predictors = c("aet", "cwd", "tmin")
- predictors_f
character. Vector with the column names of qualitative predictor variables (i.e. ordinal or nominal variables type). Usage predictors_f = c("landform")
- fit_formula
formula. A formula object with response and predictor variables (e.g. formula(pr_ab ~ aet + ppt_jja + pH + awc + depth + landform)). Note that the variables used here must be consistent with those used in response, predictors, and predictors_f arguments
- partition
character. Column name with training and validation partition groups. If partition = NULL, the model will be validated with the same data used for fitting.
- thr
character. Threshold used to get binary suitability values (i.e. 0,1) needed for threshold-dependent performance metrics. More than one threshold type can be used. It is necessary to provide a vector for this argument. The following threshold criteria are available:
lpt: The highest threshold at which there is no omission.
equal_sens_spec: Threshold at which the sensitivity and specificity are equal.
max_sens_spec: Threshold at which the sum of the sensitivity and specificity is the highest (aka threshold that maximizes the TSS).
max_jaccard: The threshold at which the Jaccard index is the highest.
max_sorensen: The threshold at which the Sorensen index is highest.
max_fpb: The threshold at which FPB (F-measure on presence-background data) is highest.
sensitivity: Threshold based on a specified sensitivity value. Usage thr = c('sensitivity', sens='0.6') or thr = c('sensitivity'). 'sens' refers to sensitivity value. If a sensitivity value is not specified, the default used is 0.9
If more than one threshold type is used they must be concatenated, e.g., thr=c('lpt', 'max_sens_spec', 'max_jaccard'), or thr=c('lpt', 'max_sens_spec', 'sensitivity', sens='0.8'), or thr=c('lpt', 'max_sens_spec', 'sensitivity'). Function will use all thresholds if no threshold is specified.
- sigma
numeric. Inverse kernel width for the Radial Basis kernel function "rbfdot". Default "automatic".
- C
numeric. Cost of constraints violation, the 'C'-constant of the regularization term in the Lagrange formulation. Default 1
Value
A list object with:
model: A "ksvm" class object from kernlab package. This object can be used for predicting.
predictors: A tibble with quantitative (c column names) and qualitative (f column names) variables use for modeling.
performance: Performance metric (see
sdm_eval). Threshold dependent metrics are calculated based on the threshold specified in the argument.performance_part: Performance metric for each replica and partition (see
sdm_eval).data_ens: Predicted suitability for each test partition based on the best model. This database is used in
fit_ensemble
Details
This function constructs 'C-svc' classification type and uses Radial Basis kernel "Gaussian" function (rbfdot). See details details in ksvm.
Examples
# Toy data: a small subset of 'abies' to keep this example fast
data("abies")
abies_toy <- abies[c(1:30, 701:730), ]
abies_toy <- part_random(
data = abies_toy,
pr_ab = "pr_ab",
method = c(method = "kfold", folds = 3)
)
svm_toy <- fit_svm(
data = abies_toy,
response = "pr_ab",
predictors = c("aet", "cwd", "tmin"),
partition = ".part",
thr = "max_sens_spec"
)
#> Formula used for model fitting:
#> pr_ab ~ aet + cwd + tmin
#> Replica number: 1/1
#> Partition number: 1/3
#> Partition number: 2/3
#> Partition number: 3/3
svm_toy$performance
#> # A tibble: 1 × 33
#> model threshold thr_value n_presences n_absences TPR_mean TPR_sd TNR_mean
#> <chr> <chr> <dbl> <int> <int> <dbl> <dbl> <dbl>
#> 1 svm max_sens_spec 0.700 30 30 0.8 0.265 0.833
#> # ℹ 25 more variables: TNR_sd <dbl>, W_TPR_TNR_mean <dbl>, W_TPR_TNR_sd <dbl>,
#> # SORENSEN_mean <dbl>, SORENSEN_sd <dbl>, JACCARD_mean <dbl>,
#> # JACCARD_sd <dbl>, FPB_mean <dbl>, FPB_sd <dbl>, OR_mean <dbl>, OR_sd <dbl>,
#> # TSS_mean <dbl>, TSS_sd <dbl>, KAPPA_mean <dbl>, KAPPA_sd <dbl>,
#> # MCC_mean <dbl>, MCC_sd <dbl>, AUC_mean <dbl>, AUC_sd <dbl>,
#> # BOYCE_mean <dbl>, BOYCE_sd <dbl>, CRPS_mean <dbl>, CRPS_sd <dbl>,
#> # IMAE_mean <dbl>, IMAE_sd <dbl>
# \donttest{
data("abies")
# Using k-fold partition method
abies2 <- part_random(
data = abies,
pr_ab = "pr_ab",
method = c(method = "kfold", folds = 5)
)
abies2
#> # A tibble: 1,400 × 14
#> id pr_ab x y aet cwd tmin ppt_djf ppt_jja pH awc
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 715 0 -95417. 314240. 323. 546. 1.24 62.7 17.8 5.77 0.108
#> 2 5680 0 98987. -159415. 448. 815. 9.43 130. 6.43 5.60 0.160
#> 3 7907 0 121474. -99463. 182. 271. -4.95 151. 11.2 0 0
#> 4 1850 0 -39976. -17456. 372. 946. 8.78 116. 2.70 6.41 0.0972
#> 5 1702 0 111372. -91404. 209. 399. -4.03 165. 9.27 0 0
#> 6 10036 0 -255715. 392229. 308. 535. 4.66 166. 16.5 5.70 0.0777
#> 7 12384 0 -311765. 380213. 568. 352. 4.38 480. 41.2 5.80 0.110
#> 8 6513 0 111360. -120229. 327. 633. 4.93 163. 8.91 1.18 0.0116
#> 9 9884 0 -284326. 442136. 377. 446. 3.99 296. 16.8 5.96 0.0900
#> 10 8651 0 137640. -110538. 215. 265. -4.62 180. 9.57 0 0
#> # ℹ 1,390 more rows
#> # ℹ 3 more variables: depth <dbl>, landform <fct>, .part <int>
svm_t1 <- fit_svm(
data = abies2,
response = "pr_ab",
predictors = c("aet", "ppt_jja", "pH", "awc", "depth"),
predictors_f = c("landform"),
partition = ".part",
thr = c("max_sens_spec", "equal_sens_spec", "max_sorensen"),
fit_formula = NULL
)
#> Formula used for model fitting:
#> pr_ab ~ aet + ppt_jja + pH + awc + depth + landform
#> Replica number: 1/1
#> Partition number: 1/5
#> Partition number: 2/5
#> Partition number: 3/5
#> Partition number: 4/5
#> Partition number: 5/5
names(svm_t1)
#> [1] "model" "predictors" "performance" "performance_part"
#> [5] "data_ens"
svm_t1$model
#> Support Vector Machine object of class "ksvm"
#>
#> SV type: C-svc (classification)
#> parameter : cost C = 1
#>
#> Gaussian Radial Basis kernel function.
#> Hyperparameter : sigma = 0.187560315237384
#>
#> Number of Support Vectors : 905
#>
#> Objective Function Value : -775.6347
#> Training error : 0.215714
#> Probability model included.
svm_t1$predictors
#> # A tibble: 1 × 6
#> c1 c2 c3 c4 c5 f
#> <chr> <chr> <chr> <chr> <chr> <chr>
#> 1 aet ppt_jja pH awc depth landform
svm_t1$performance
#> # A tibble: 3 × 33
#> model threshold thr_value n_presences n_absences TPR_mean TPR_sd TNR_mean
#> <chr> <chr> <dbl> <int> <int> <dbl> <dbl> <dbl>
#> 1 svm equal_sens_sp… 0.546 700 700 0.744 0.0366 0.744
#> 2 svm max_sens_spec 0.550 700 700 0.787 0.0926 0.736
#> 3 svm max_sorensen 0.307 700 700 0.881 0.0330 0.624
#> # ℹ 25 more variables: TNR_sd <dbl>, W_TPR_TNR_mean <dbl>, W_TPR_TNR_sd <dbl>,
#> # SORENSEN_mean <dbl>, SORENSEN_sd <dbl>, JACCARD_mean <dbl>,
#> # JACCARD_sd <dbl>, FPB_mean <dbl>, FPB_sd <dbl>, OR_mean <dbl>, OR_sd <dbl>,
#> # TSS_mean <dbl>, TSS_sd <dbl>, KAPPA_mean <dbl>, KAPPA_sd <dbl>,
#> # MCC_mean <dbl>, MCC_sd <dbl>, AUC_mean <dbl>, AUC_sd <dbl>,
#> # BOYCE_mean <dbl>, BOYCE_sd <dbl>, CRPS_mean <dbl>, CRPS_sd <dbl>,
#> # IMAE_mean <dbl>, IMAE_sd <dbl>
svm_t1$performance_part
#> # A tibble: 15 × 21
#> replica partition model threshold thr_value n_presences n_absences TPR
#> <chr> <chr> <chr> <chr> <dbl> <int> <int> <dbl>
#> 1 1 1 svm max_sorensen 0.467 140 140 0.907
#> 2 1 1 svm max_sens_spec 0.488 140 140 0.879
#> 3 1 1 svm equal_sens_sp… 0.559 140 140 0.771
#> 4 1 2 svm max_sorensen 0.365 140 140 0.907
#> 5 1 2 svm max_sens_spec 0.531 140 140 0.786
#> 6 1 2 svm equal_sens_sp… 0.539 140 140 0.779
#> 7 1 3 svm max_sorensen 0.291 140 140 0.893
#> 8 1 3 svm max_sens_spec 0.527 140 140 0.743
#> 9 1 3 svm equal_sens_sp… 0.523 140 140 0.743
#> 10 1 4 svm max_sorensen 0.369 140 140 0.871
#> 11 1 4 svm max_sens_spec 0.369 140 140 0.871
#> 12 1 4 svm equal_sens_sp… 0.576 140 140 0.686
#> 13 1 5 svm max_sorensen 0.395 140 140 0.829
#> 14 1 5 svm max_sens_spec 0.631 140 140 0.657
#> 15 1 5 svm equal_sens_sp… 0.503 140 140 0.743
#> # ℹ 13 more variables: TNR <dbl>, W_TPR_TNR <dbl>, SORENSEN <dbl>,
#> # JACCARD <dbl>, FPB <dbl>, OR <dbl>, TSS <dbl>, KAPPA <dbl>, MCC <dbl>,
#> # AUC <dbl>, BOYCE <dbl>, CRPS <dbl>, IMAE <dbl>
svm_t1$data_ens
#> # A tibble: 1,400 × 5
#> rnames replicates part pr_ab pred
#> <chr> <chr> <chr> <fct> <dbl>
#> 1 2 .part 1 0 0.138
#> 2 3 .part 1 0 0.146
#> 3 13 .part 1 0 0.526
#> 4 18 .part 1 0 0.0961
#> 5 21 .part 1 0 0.181
#> 6 24 .part 1 0 0.827
#> 7 29 .part 1 0 0.0584
#> 8 39 .part 1 0 0.838
#> 9 42 .part 1 0 0.191
#> 10 50 .part 1 0 0.0667
#> # ℹ 1,390 more rows
# Using bootstrap partition method and only with presence-absence
# and get performance for several method
abies2 <- part_random(
data = abies,
pr_ab = "pr_ab",
method = c(method = "boot", replicates = 10, proportion = 0.7)
)
abies2
#> # A tibble: 1,400 × 23
#> id pr_ab x y aet cwd tmin ppt_djf ppt_jja pH awc
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 715 0 -95417. 314240. 323. 546. 1.24 62.7 17.8 5.77 0.108
#> 2 5680 0 98987. -159415. 448. 815. 9.43 130. 6.43 5.60 0.160
#> 3 7907 0 121474. -99463. 182. 271. -4.95 151. 11.2 0 0
#> 4 1850 0 -39976. -17456. 372. 946. 8.78 116. 2.70 6.41 0.0972
#> 5 1702 0 111372. -91404. 209. 399. -4.03 165. 9.27 0 0
#> 6 10036 0 -255715. 392229. 308. 535. 4.66 166. 16.5 5.70 0.0777
#> 7 12384 0 -311765. 380213. 568. 352. 4.38 480. 41.2 5.80 0.110
#> 8 6513 0 111360. -120229. 327. 633. 4.93 163. 8.91 1.18 0.0116
#> 9 9884 0 -284326. 442136. 377. 446. 3.99 296. 16.8 5.96 0.0900
#> 10 8651 0 137640. -110538. 215. 265. -4.62 180. 9.57 0 0
#> # ℹ 1,390 more rows
#> # ℹ 12 more variables: depth <dbl>, landform <fct>, .part1 <chr>, .part2 <chr>,
#> # .part3 <chr>, .part4 <chr>, .part5 <chr>, .part6 <chr>, .part7 <chr>,
#> # .part8 <chr>, .part9 <chr>, .part10 <chr>
svm_t2 <- fit_svm(
data = abies2,
response = "pr_ab",
predictors = c("aet", "ppt_jja", "pH", "awc", "depth"),
predictors_f = c("landform"),
partition = ".part",
thr = c("max_sens_spec", "equal_sens_spec", "max_sorensen"),
fit_formula = NULL
)
#> Formula used for model fitting:
#> pr_ab ~ aet + ppt_jja + pH + awc + depth + landform
#> Replica number: 1/10
#> Partition number: 1/1
#> Replica number: 2/10
#> Partition number: 1/1
#> Replica number: 3/10
#> Partition number: 1/1
#> Replica number: 4/10
#> Partition number: 1/1
#> Replica number: 5/10
#> Partition number: 1/1
#> Replica number: 6/10
#> Partition number: 1/1
#> Replica number: 7/10
#> Partition number: 1/1
#> Replica number: 8/10
#> Partition number: 1/1
#> Replica number: 9/10
#> Partition number: 1/1
#> Replica number: 10/10
#> Partition number: 1/1
#> line search fails -1.347888 0.1516195 1.093732e-05 -5.313894e-06 -6.990186e-08 3.298222e-08 -9.398032e-13
svm_t2
#> $model
#> Support Vector Machine object of class "ksvm"
#>
#> SV type: C-svc (classification)
#> parameter : cost C = 1
#>
#> Gaussian Radial Basis kernel function.
#> Hyperparameter : sigma = 0.19552750209237
#>
#> Number of Support Vectors : 904
#>
#> Objective Function Value : -771.0377
#> Training error : 0.213571
#> Probability model included.
#>
#> $predictors
#> # A tibble: 1 × 6
#> c1 c2 c3 c4 c5 f
#> <chr> <chr> <chr> <chr> <chr> <chr>
#> 1 aet ppt_jja pH awc depth landform
#>
#> $performance
#> # A tibble: 3 × 33
#> model threshold thr_value n_presences n_absences TPR_mean TPR_sd TNR_mean
#> <chr> <chr> <dbl> <int> <int> <dbl> <dbl> <dbl>
#> 1 svm equal_sens_sp… 0.537 700 700 0.770 0.0243 0.770
#> 2 svm max_sens_spec 0.563 700 700 0.803 0.0639 0.769
#> 3 svm max_sorensen 0.305 700 700 0.898 0.0409 0.654
#> # ℹ 25 more variables: TNR_sd <dbl>, W_TPR_TNR_mean <dbl>, W_TPR_TNR_sd <dbl>,
#> # SORENSEN_mean <dbl>, SORENSEN_sd <dbl>, JACCARD_mean <dbl>,
#> # JACCARD_sd <dbl>, FPB_mean <dbl>, FPB_sd <dbl>, OR_mean <dbl>, OR_sd <dbl>,
#> # TSS_mean <dbl>, TSS_sd <dbl>, KAPPA_mean <dbl>, KAPPA_sd <dbl>,
#> # MCC_mean <dbl>, MCC_sd <dbl>, AUC_mean <dbl>, AUC_sd <dbl>,
#> # BOYCE_mean <dbl>, BOYCE_sd <dbl>, CRPS_mean <dbl>, CRPS_sd <dbl>,
#> # IMAE_mean <dbl>, IMAE_sd <dbl>
#>
#> $performance_part
#> # A tibble: 30 × 21
#> replica partition model threshold thr_value n_presences n_absences TPR
#> <chr> <chr> <chr> <chr> <dbl> <int> <int> <dbl>
#> 1 1 1 svm max_sorensen 0.410 210 210 0.867
#> 2 1 1 svm max_sens_spec 0.475 210 210 0.829
#> 3 1 1 svm equal_sens_sp… 0.541 210 210 0.776
#> 4 2 1 svm max_sorensen 0.454 210 210 0.886
#> 5 2 1 svm max_sens_spec 0.558 210 210 0.795
#> 6 2 1 svm equal_sens_sp… 0.536 210 210 0.810
#> 7 3 1 svm max_sorensen 0.372 210 210 0.924
#> 8 3 1 svm max_sens_spec 0.442 210 210 0.862
#> 9 3 1 svm equal_sens_sp… 0.545 210 210 0.781
#> 10 4 1 svm max_sorensen 0.411 210 210 0.857
#> # ℹ 20 more rows
#> # ℹ 13 more variables: TNR <dbl>, W_TPR_TNR <dbl>, SORENSEN <dbl>,
#> # JACCARD <dbl>, FPB <dbl>, OR <dbl>, TSS <dbl>, KAPPA <dbl>, MCC <dbl>,
#> # AUC <dbl>, BOYCE <dbl>, CRPS <dbl>, IMAE <dbl>
#>
#> $data_ens
#> # A tibble: 4,200 × 5
#> rnames replicates part pr_ab pred
#> <chr> <chr> <chr> <fct> <dbl>
#> 1 2 .part1 1 0 0.109
#> 2 5 .part1 1 0 0.217
#> 3 8 .part1 1 0 0.428
#> 4 10 .part1 1 0 0.252
#> 5 11 .part1 1 0 0.278
#> 6 12 .part1 1 0 0.348
#> 7 13 .part1 1 0 0.366
#> 8 17 .part1 1 0 0.572
#> 9 20 .part1 1 0 0.193
#> 10 23 .part1 1 0 0.267
#> # ℹ 4,190 more rows
#>
# }