Visuzalizes the decision boundaries of multiple classification learners on some artificial data sets.

The visualization of decision boundaries helps to understand what the pros and cons of individual classification learners are. This posts demonstrates how to create such plots.

The three artificial data sets are generated by `task generators`

(implemented in mlr3):

```
library("mlr3")
N = 200
tasks = list(
tgen("xor")$generate(N),
tgen("moons")$generate(N),
tgen("circle")$generate(N)
)
```

Points are distributed on a 2-dimensional cube with corners \((\pm 1, \pm 1)\). Class is `"red"`

if \(x\) and \(y\) have the same sign, and `"black"`

otherwise.

```
plot(tgen("xor"))
```

Two circles with same center but different radii. Points in the smaller circle are `"black"`

, points only in the larger circle are `"red"`

.

```
plot(tgen("circle"))
```

Two interleaving half circles (“moons”).

```
plot(tgen("moons"))
```

We consider the following learners:

```
library("mlr3learners")
learners = list(
# k-nearest neighbours classifier
lrn("classif.kknn", id = "kkn", predict_type = "prob", k = 3),
# linear svm
lrn("classif.svm", id = "lin. svm", predict_type = "prob", kernel = "linear"),
# radial-basis function svm
lrn("classif.svm", id = "rbf svm", predict_type = "prob", kernel = "radial",
gamma = 2, cost = 1, type = "C-classification"),
# naive bayes
lrn("classif.naive_bayes", id = "naive bayes", predict_type = "prob"),
# single decision tree
lrn("classif.rpart", id = "tree", predict_type = "prob", cp = 0, maxdepth = 5),
# random forest
lrn("classif.ranger", id = "random forest", predict_type = "prob")
)
```

The hyperparameters are chosen in a way that the decision boundaries look “typical” for the respective classifier. Of course, with different hyperparameters, results may look very different.

To apply each learner on each task, we first build an exhaustive grid design of experiments with `benchmark_grid()`

and then pass it to `benchmark()`

to do the actual work. A simple holdout resampling is used here:

```
design = benchmark_grid(
tasks = tasks,
learners = learners,
resamplings = rsmp("holdout")
)
set.seed(123)
bmr = benchmark(design, store_models = TRUE)
```

A quick look into the performance values:

```
perf = bmr$aggregate(msr("classif.acc"))[, c("task_id", "learner_id", "classif.acc")]
knitr::kable(perf)
```

task_id | learner_id | classif.acc |
---|---|---|

xor_200 | kkn | 0.9253731 |

xor_200 | lin. svm | 0.5223881 |

xor_200 | rbf svm | 0.9701493 |

xor_200 | naive bayes | 0.5820896 |

xor_200 | tree | 0.8955224 |

xor_200 | random forest | 0.9552239 |

moons_200 | kkn | 0.9850746 |

moons_200 | lin. svm | 0.9104478 |

moons_200 | rbf svm | 0.9701493 |

moons_200 | naive bayes | 0.8955224 |

moons_200 | tree | 0.9104478 |

moons_200 | random forest | 0.9253731 |

circle_200 | kkn | 0.9104478 |

circle_200 | lin. svm | 0.4776119 |

circle_200 | rbf svm | 0.8805970 |

circle_200 | naive bayes | 0.8358209 |

circle_200 | tree | 0.8358209 |

circle_200 | random forest | 0.9402985 |

To generate the plots, we iterate over the individual `ResampleResult`

objects stored in the `BenchmarkResult`

, and in each iteration we store the plot of the learner prediction generated by the mlr3viz package.

```
library("mlr3viz")
n = bmr$n_resample_results
plots = vector("list", n)
for (i in seq_len(n)) {
rr = bmr$resample_result(i)
plots[[i]] = autoplot(rr, type = "prediction")
}
```

We now have a list of plots. Each one can be printed individually:

```
print(plots[[1]])
```

Note that only observations from the test data is plotted as points.

To get a nice annotated overview, we arranged all plots together in a single PDF file. The number in the upper right is the respective accuracy on the test set.

As you can see, the decision boundaries look very different. Some are linear, others are parallel to the axis, and yet others are highly non-linear. The boundaries are partly very smooth with a slow transition of probabilities, others are very abrupt. All these properties are important during model selection, and should be considered for your problem at hand.

For attribution, please cite this work as

Lang (2020, Aug. 14). mlr3gallery: Comparison of Decision Boundaries of Classification Learners. Retrieved from https://mlr3gallery.mlr-org.com/posts/2020-08-14-comparison-of-decision-boundaries/

BibTeX citation

@misc{lang2020comparison, author = {Lang, Michel}, title = {mlr3gallery: Comparison of Decision Boundaries of Classification Learners}, url = {https://mlr3gallery.mlr-org.com/posts/2020-08-14-comparison-of-decision-boundaries/}, year = {2020} }