Python package for the GenSVM classifier

## Project description

This is the documentation of the Python package for the GenSVM classifier, introduced in GenSVM: A Generalized Multiclass Support Vector Machine by Gerrit J.J. van den Burg and Patrick J.F. Groenen.

The source code of this package is available on GitHub at: https://github.com/GjjvdBurg/PyGenSVM.

## Installation

**Before** GenSVM can be installed, a working NumPy installation is required.
Please see the installation instructions for NumPy, then install
GenSVM using the instructions below.

GenSVM can be easily installed through pip:

pip install gensvm

## Citing

If you use this package in your research please cite the paper, for instance using the following BibTeX entry:

@article{JMLR:v17:14-526, author = {Gerrit J.J. van den Burg and Patrick J.F. Groenen}, title = {{GenSVM}: A Generalized Multiclass Support Vector Machine}, journal = {Journal of Machine Learning Research}, year = {2016}, volume = {17}, number = {225}, pages = {1-42}, url = {http://jmlr.org/papers/v17/14-526.html} }

## Usage

The package contains two classes to fit the GenSVM model: GenSVM and GenSVMGridSearchCV. These classes respectively fit a single GenSVM model or fit a series of models for a parameter grid search. The interface to these classes is the same as that of classifiers in Scikit-Learn so users familiar with Scikit-Learn should have no trouble using this package. Below we will show some examples of using the GenSVM classifier and the GenSVMGridSearchCV class in practice.

In the examples we assume that we have loaded the iris dataset from Scikit-Learn as follows:

>>> from sklearn.datasets import load_iris >>> from sklearn.model_selection import train_test_split >>> from sklearn.preprocessing import maxabs_scale >>> X, y = load_iris(return_X_y=True) >>> X = maxabs_scale(X) >>> X_train, X_test, y_train, y_test = train_test_split(X, y)

Note that we scale the data using the maxabs_scale
function. This scales the columns of the data matrix to `[-1, 1]` without
breaking sparsity. Scaling the dataset can have a significant effect on the
computation time of GenSVM and is generally recommended for SVMs.

### Example 1: Fitting a single GenSVM model

Let’s start by fitting the most basic GenSVM model on the training data:

>>> from gensvm import GenSVM >>> clf = GenSVM() >>> clf.fit(X_train, y_train) GenSVM(coef=0.0, degree=2.0, epsilon=1e-06, gamma='auto', kappa=0.0, kernel='linear', kernel_eigen_cutoff=1e-08, lmd=1e-05, max_iter=100000000.0, p=1.0, random_state=None, verbose=0, weights='unit')

With the model fitted, we can predict the test dataset:

>>> y_pred = clf.predict(X_test)

Next, we can compute a score for the predictions. The GenSVM class has a
`score` method which computes the accuracy_score
for the predictions. In the GenSVM paper, the adjusted Rand index is often used
to compare performance. We illustrate both options below (your results may be
different depending on the exact train/test split):

>>> clf.score(X_test, y_test) 1.0 >>> from sklearn.metrics import adjusted_rand_score >>> adjusted_rand_score(clf.predict(X_test), y_test) 1.0

We can try this again by changing the model parameters, for instance we can
turn on verbosity and use the Euclidean norm in the GenSVM model by setting `p = 2`:

>>> clf2 = GenSVM(verbose=True, p=2) >>> clf2.fit(X_train, y_train) Starting main loop. Dataset: n = 112 m = 4 K = 3 Parameters: kappa = 0.000000 p = 2.000000 lambda = 0.0000100000000000 epsilon = 1e-06 iter = 0, L = 3.4499531579689533, Lbar = 7.3369415851139745, reldiff = 1.1266786095824437 ... Optimization finished, iter = 4046, loss = 0.0230726364692517, rel. diff. = 0.0000009998645783 Number of support vectors: 9 GenSVM(coef=0.0, degree=2.0, epsilon=1e-06, gamma='auto', kappa=0.0, kernel='linear', kernel_eigen_cutoff=1e-08, lmd=1e-05, max_iter=100000000.0, p=2, random_state=None, verbose=True, weights='unit')

For other parameters that can be tuned in the GenSVM model, see GenSVM.

### Example 2: Fitting a GenSVM model with a “warm start”

One of the key features of the GenSVM classifier is that training can be
accelerated by using so-called “warm-starts”. This way the optimization can be
started in a location that is closer to the final solution than a random
starting position would be. To support this, the `fit` method of the GenSVM
class has an optional `seed_V` parameter. We’ll illustrate how this can be
used below.

We start with relatively large value for the `epsilon` parameter in the
model. This is the stopping parameter that determines how long the
optimization continues (and therefore how exact the fit is).

>>> clf1 = GenSVM(epsilon=1e-3) >>> clf1.fit(X_train, y_train) ... >>> clf1.n_iter_ 163

The `n_iter_` attribute tells us how many iterations the model did. Now, we
can use the solution of this model to start the training for the next model:

>>> clf2 = GenSVM(epsilon=1e-8) >>> clf2.fit(X_train, y_train, seed_V=clf1.combined_coef_) ... >>> clf2.n_iter_ 3196

Compare this to a model with the same stopping parameter, but without the warm start:

>>> clf2.fit(X_train, y_train) ... >>> clf2.n_iter_ 3699

So we saved about 500 iterations! This effect will be especially significant with large datasets and when you try out many parameter configurations. Therefore this technique is built into the GenSVMGridSearchCV class that can be used to do a grid search of parameters.

### Example 3: Running a GenSVM grid search

Often when we’re fitting a machine learning model such as GenSVM, we have to try several parameter configurations to figure out which one performs best on our given dataset. This is usually combined with cross validation to avoid overfitting. To do this efficiently and to make use of warm starts, the GenSVMGridSearchCV class is available. This class works in the same way as the GridSearchCV class of Scikit-Learn, but uses the GenSVM C library for speed.

To do a grid search, we first have to define the parameters that we want to vary and what values we want to try:

>>> from gensvm import GenSVMGridSearchCV >>> param_grid = {'p': [1.0, 2.0], 'lmd': [1e-8, 1e-6, 1e-4, 1e-2, 1.0], 'kappa': [-0.9, 0.0] }

For the values that are not varied in the parameter grid, the default values
will be used. This means that if you want to change a specific value (such as
`epsilon` for instance), you can add this to the parameter grid as a
parameter with a single value to try (e.g. `'epsilon': [1e-8]`).

Running the grid search is now straightforward:

>>> gg = GenSVMGridSearchCV(param_grid) >>> gg.fit(X_train, y_train) GenSVMGridSearchCV(cv=None, iid=True, param_grid={'p': [1.0, 2.0], 'lmd': [1e-06, 0.0001, 0.01, 1.0], 'kappa': [-0.9, 0.0]}, refit=True, return_train_score=True, scoring=None, verbose=0)

Note that if we have set `refit=True` (the default), then we can use the
GenSVMGridSearchCV instance to predict or score using the best estimator
found in the grid search:

>>> y_pred = gg.predict(X_test) >>> gg.score(X_test, y_test) 1.0

A nice feature borrowed from Scikit-Learn is that the results from the grid
search can be represented as a `pandas` DataFrame:

>>> from pandas import DataFrame >>> df = DataFrame(gg.cv_results_)

This can make it easier to explore the results of the grid search.

## Known Limitations

The following are known limitations that are on the roadmap for a future release of the package. If you need any of these features, please vote on them on the linked GitHub issues (this can make us add them sooner!).

- Support for sparse matrices. NumPy supports sparse matrices, as does the GenSVM C library. Getting them to work together requires some time. In the meantime, if you really want to use sparse data with GenSVM (this can lead to significant speedups!), check out the GenSVM C library.
- Specification of instance weights. Currently the package
allows for two modes of instance weights:
`unit`weights where each instance gets weight 1 and`group`weights where instances get weights inversely proportional to the size of their class. In the future, we want to allow the user to specify a vector of weights as well. - Specification of class misclassification weights. Currently, incorrectly classification an object from class A to class C is as bad as incorrectly classifying an object from class B to class C. Depending on the application, this may not be the desired effect. Adding class misclassification weights can solve this issue.

## Questions and Issues

If you have any questions or encounter any issues with using this package, please ask them on GitHub.

## License

This package is licensed under the GNU General Public License version 3.

Copyright G.J.J. van den Burg, excluding the sections of the code that are explicitly marked to come from Scikit-Learn.

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