sksurv.svm.NaiveSurvivalSVM¶
-
class
sksurv.svm.
NaiveSurvivalSVM
(penalty='l2', loss='squared_hinge', dual=False, tol=0.0001, alpha=1.0, verbose=0, random_state=None, max_iter=1000)[source]¶ Naive version of linear Survival Support Vector Machine.
Uses regular linear support vector classifier (liblinear). A new set of samples is created by building the difference between any two feature vectors in the original data, thus this version requires O(n_samples^2) space.
See
sksurv.svm.HingeLossSurvivalSVM
for the kernel naive survival SVM.\[ \begin{align}\begin{aligned}\begin{split}\min_{\mathbf{w}}\quad \frac{1}{2} \lVert \mathbf{w} \rVert_2^2 + \gamma \sum_{i = 1}^n \xi_i \\ \text{subject to}\quad \mathbf{w}^\top \mathbf{x}_i - \mathbf{w}^\top \mathbf{x}_j \geq 1 - \xi_{ij},\quad \forall (i, j) \in \mathcal{P}, \\ \xi_i \geq 0,\quad \forall (i, j) \in \mathcal{P}.\end{split}\\\mathcal{P} = \{ (i, j) \mid y_i > y_j \land \delta_j = 1 \}_{i,j=1,\dots,n}.\end{aligned}\end{align} \]See 1, 2 for further description.
- Parameters
alpha (float, positive, default: 1.0) – Weight of penalizing the squared hinge loss in the objective function.
loss (string, 'hinge' or 'squared_hinge', default: 'squared_hinge') – Specifies the loss function. ‘hinge’ is the standard SVM loss (used e.g. by the SVC class) while ‘squared_hinge’ is the square of the hinge loss.
penalty ('l1' | 'l2', default: 'l2') – Specifies the norm used in the penalization. The ‘l2’ penalty is the standard used in SVC. The ‘l1’ leads to coef_ vectors that are sparse.
dual (bool, default: True) – Select the algorithm to either solve the dual or primal optimization problem. Prefer dual=False when n_samples > n_features.
tol (float, optional, default: 1e-4) – Tolerance for stopping criteria.
verbose (int, default: 0) – Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in liblinear that, if enabled, may not work properly in a multithreaded context.
random_state (int seed, RandomState instance, or None, default: None) – The seed of the pseudo random number generator to use when shuffling the data.
max_iter (int, default: 1000) – The maximum number of iterations to be run.
See also
sksurv.svm.FastSurvivalSVM
Alternative implementation with reduced time complexity for training.
References
- 1
Van Belle, V., Pelckmans, K., Suykens, J. A., & Van Huffel, S. Support Vector Machines for Survival Analysis. In Proc. of the 3rd Int. Conf. on Computational Intelligence in Medicine and Healthcare (CIMED). 1-8. 2007
- 2
Evers, L., Messow, C.M., “Sparse kernel methods for high-dimensional survival data”, Bioinformatics 24(14), 1632-8, 2008.
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__init__
(penalty='l2', loss='squared_hinge', dual=False, tol=0.0001, alpha=1.0, verbose=0, random_state=None, max_iter=1000)[source]¶ Initialize self. See help(type(self)) for accurate signature.
Methods
__init__
([penalty, loss, dual, tol, alpha, …])Initialize self.
fit
(X, y[, sample_weight])Build a survival support vector machine model from training data.
predict
(X)Rank samples according to survival times
score
(X, y)Returns the concordance index of the prediction.
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fit
(X, y, sample_weight=None)[source]¶ Build a survival support vector machine model from training data.
- Parameters
X (array-like, shape = (n_samples, n_features)) – Data matrix.
y (structured array, shape = (n_samples,)) – A structured array containing the binary event indicator as first field, and time of event or time of censoring as second field.
sample_weight (array-like, shape = (n_samples,), optional) – Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight.
- Returns
- Return type
self
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predict
(X)[source]¶ Rank samples according to survival times
Lower ranks indicate shorter survival, higher ranks longer survival.
- Parameters
X (array-like, shape = (n_samples, n_features,)) – The input samples.
- Returns
y – Predicted ranks.
- Return type
ndarray, shape = (n_samples,)
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score
(X, y)[source]¶ Returns the concordance index of the prediction.
- Parameters
X (array-like, shape = (n_samples, n_features)) – Test samples.
y (structured array, shape = (n_samples,)) – A structured array containing the binary event indicator as first field, and time of event or time of censoring as second field.
- Returns
cindex – Estimated concordance index.
- Return type
float