# Measuring the Effect of the C Hyperparameter for SVM Classifiers: Examples using Scikit-Learn

Last updated:- SVM tries to find planes to separate Positive from Negative points
- SVM can also find other surfaces via Kernel methods
- Noisy points
- Soft-margin vs hard-margin SVM
- The C parameter
- Examples: Generating synthetic datasets for the examples
- Examples: Choice of C for SVM Linear Kernel
- Examples: Choice of C for SVM, Polynomial Kernel
- Examples: Choice of C for SVM, RBF Kernel

TL;DR:Use a lower setting for`C`

(e.g. 0.001) if your training data is very noisy. For polynomial and RBF kernels, this makes alotof difference. Not so much for linear kernels.

View all code on this jupyter notebook

## SVM tries to find planes to separate Positive from Negative points

*The solid line in the middle represents the best possible line for separating positive from negative samples.*

The circled points are the support vectors.

Source: Sklearn Guide on SVMs

The circled points are the support vectors.

Source: Sklearn Guide on SVMs

## SVM can also find other surfaces via Kernel methods

*Kernels (transformation functions) can be used to transform*

the points such that hyperplanes can be found even for points that are not

linearly separable

Source: Wikipedia Article on Kernel Methods

the points such that hyperplanes can be found even for points that are not

linearly separable

Source: Wikipedia Article on Kernel Methods

## Noisy points

Real-life data is noisy, so a robust SVM classifier must be able to ignore noisy, outlier points to discover a generalizable plane.

*A separating plane that ignores some (probably noisy) points.*

Source: Learn OpenCV

Source: Learn OpenCV

## Soft-margin vs hard-margin SVM

Hard-margin SVM | Soft-Margin SVM |
---|---|

Try to find a hyperplane that best separates positive from negative points, such that no point is misclassified. |
Try to find a hyperplane that best separates positive from negative points, but allows for some points to be misclassified, in which case the objective function is punished proportionally to degree of misclassification |

By default, most packages like scikit-learn implement a *soft-margin* SVM.

This means that a separating hyperplane that separates positive from negative points will still be considered *even if* some points are misclassified.

## The C parameter

The lower the

Cparameters, thesofterthe margin

The `C`

parameter controls how much you want to punish your model for each misclassified point for a given curve:

Large values of C | Small Values of C |
---|---|

Large effect of noisy points. A plane with very few misclassifications will be given precedence. |
Low effect of noisy points. Planes that separate the points well will be found, even if there are some misclassifications |

In other words, `C`

is a **regularization parameter** for SVMs.

## Examples: Generating synthetic datasets for the examples

More information on creating synthetic datasets here: Scikit-Learn examples: Making Dummy Datasets

For all the following examples, a **noisy** classification problem was created as follows:

We generated a dummy

**training**dataset setting`flip_y`

to 0.35, which means that in this dataset, 35% of the targets are*flipped*, i.e. a 1 where a 0 should be and a 0 where there should be a 1We generated a dummy

**test**dataset with the same settings as the training dataset, except for the noise parameter (`flip_y`

). There is no noise in the test dataset because we want to ascertain how much a model*trained*on noisy data performs with respect to the choice of C.

```
np.random.seed(222)
# train dataset
X, y = make_classification(
n_samples=10000,
n_features=10,
n_informative=10,
n_redundant=0,
weights=[0.3,0.7],
class_sep=0.7,
flip_y=0.35) # the default value for flip_y is 0.01, or 1%
X_train, _ , y_train, _ = train_test_split(X, y, test_size=0.25)
np.random.seed(222)
# test dataset
X, y = make_classification(
n_samples=10000,
n_features=10,
n_informative=10,
n_redundant=0,
weights=[0.3,0.7],
class_sep=0.7,
flip_y=0.0)
_, X_test , _ , y_test = train_test_split(X, y, test_size=0.25)
```

## Examples: Choice of C for SVM Linear Kernel

For a linear kernel, the choice of `C`

does not seem to affect performance very much:

*For a linear kernel, varying the C parameter doesn't make much difference*

even though we are using a highly noisy dataset.

View the full code here: linear-kernel

even though we are using a highly noisy dataset.

View the full code here: linear-kernel

## Examples: Choice of C for SVM, Polynomial Kernel

For polynomial kernels, the choice of C does affect the out-of-sample performance, but the optimal value for C may not necessarily be the lowest one.

*For a polynomial kernel with degree 3, there's a clear pattern of lower*

performances with higher values of C, but the best value for out-of-sample

score was not achieved at the minimum C, but with C=0.01.

View the full code here: polynomial kernel, degree=3

performances with higher values of C, but the best value for out-of-sample

score was not achieved at the minimum C, but with C=0.01.

View the full code here: polynomial kernel, degree=3

*Again, for a polynomial kernel with degree 5, the optimal value for out-of-sample score*

was not achieved at the minimum C, but with C=1.0.

View the full code here: polynomial kernel, degree=5

was not achieved at the minimum C, but with C=1.0.

View the full code here: polynomial kernel, degree=5

## Examples: Choice of C for SVM, RBF Kernel

For an SVM model with the RBF kernel, it is once more easy to see that lower values of the C parameter allow the classifier to learn better under noisy data.

*Difference in performance for a SVM trained*

using the RBF kernel, with varying choice of C.

View the full code here: RBF kernel

using the RBF kernel, with varying choice of C.

View the full code here: RBF kernel