svm.LinearSVC¶

class
pai4sk.svm.
LinearSVC
(penalty='l2', loss='squared_hinge', dual=True, tol=0.0001, C=1.0, multi_class='ovr', fit_intercept=True, intercept_scaling=1, class_weight=None, verbose=0, random_state=None, max_iter=1000, use_gpu=True, device_ids=[], num_threads=1, return_training_history=None)¶ Linear Support Vector Classification.
Similar to SVC with parameter kernel=’linear’, but implemented in terms of liblinear rather than libsvm, so it has more flexibility in the choice of penalties and loss functions and should scale better to large numbers of samples.
This class supports both dense and sparse input and the multiclass support is handled according to a onevstherest scheme.
Read more in the User Guide.
For SnapML solver this supports both local and distributed(MPI) method of execution.
Parameters:  penalty (string, 'l1' or '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.  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.
 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=1e4)) – Tolerance for stopping criteria.
 C (float, optional (default=1.0)) – Penalty parameter C of the error term.
 multi_class (string, 'ovr' or 'crammer_singer' (default='ovr')) – Determines the multiclass strategy if y contains more than
two classes.
"ovr"
trains n_classes onevsrest classifiers, while"crammer_singer"
optimizes a joint objective over all classes. While crammer_singer is interesting from a theoretical perspective as it is consistent, it is seldom used in practice as it rarely leads to better accuracy and is more expensive to compute. If"crammer_singer"
is chosen, the options loss, penalty and dual will be ignored.  fit_intercept (boolean, optional (default=True)) – Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be already centered).
 intercept_scaling (float, optional (default=1)) – When self.fit_intercept is True, instance vector x becomes
[x, self.intercept_scaling]
, i.e. a “synthetic” feature with constant value equals to intercept_scaling is appended to the instance vector. The intercept becomes intercept_scaling * synthetic feature weight Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased.  class_weight ({dict, 'balanced'}, optional) – Set the parameter C of class i to
class_weight[i]*C
for SVC. If not given, all classes are supposed to have weight one. The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data asn_samples / (n_classes * np.bincount(y))
 verbose (int, (default=0)) – Enable verbose output. Note that this setting takes advantage of a perprocess runtime setting in liblinear that, if enabled, may not work properly in a multithreaded context.
 random_state (int, RandomState instance or None, optional (default=None)) – The seed of the pseudo random number generator to use when shuffling
the data for the dual coordinate descent (if
dual=True
). Whendual=False
the underlying implementation ofLinearSVC
is not random andrandom_state
has no effect on the results. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.  max_iter (int, (default=1000)) – The maximum number of iterations to be run.
 use_gpu (bool, default : True) – Flag for indicating the hardware platform used for training. If True, the training is performed using the GPU. If False, the training is performed using the CPU. The value of this parameter is subjected to changed based on the training data unless set explicitly. Applicable only for snapml solver
 device_ids (arraylike of int, default : []) – If use_gpu is True, it indicates the IDs of the GPUs used for training. For single GPU training, set device_ids to the GPU ID to be used for training, e.g., [0]. For multiGPU training, set device_ids to a list of GPU IDs to be used for training, e.g., [0, 1]. Applicable only for snapml solver
 num_threads (int, default : 1) – The number of threads used for running the training. The value of this parameter should be a multiple of 32 if the training is performed on GPU (use_gpu=True) (default value for GPU is 256). Applicable only for snapml solver
 return_training_history (str or None, default : None) – How much information about the training should be collected and returned by the fit function. By default no information is returned (None), but this parameter can be set to “summary”, to obtain summary statistics at the end of training, or “full” to obtain a complete set of statistics for the entire training procedure. Note, enabling either option will result in slower training. Applicable only for snapml solver
Variables:  coef (array, shape = [n_features] if n_classes == 2 else [n_classes, n_features]) –
Weights assigned to the features (coefficients in the primal problem). This is only available in the case of a linear kernel.
coef_
is a readonly property derived fromraw_coef_
that follows the internal memory layout of liblinear.  intercept (array, shape = [1] if n_classes == 2 else [n_classes]) – Constants in decision function.
 training_history (dict) – It returns a dictionary with the following keys : ‘epochs’, ‘t_elap_sec’, ‘train_obj’. If ‘return_training_history’ is set to “summary”, ‘epochs’ contains the total number of epochs performed, ‘t_elap_sec’ contains the total time for completing all of those epochs. If ‘return_training_history’ is set to “full”, ‘epochs’ indicates the number of epochs that have elapsed so far, and ‘t_elap_sec’ contains the time to do those epochs. ‘train_obj’ is the training loss. Applicable only for snapml solver.
 support (arraylike, shape (n_SV)) – indices of the support vectors.
 n_support (int) – Number of support vectors.
 n_iter (array, shape (n_classes,) or (1, )) – Actual number of iterations for all classes to reach the specified tolerance. If binary or multinomial, it returns only 1 element.
Examples
>>> from pai4sk.svm import LinearSVC >>> from pai4sk.datasets import make_classification >>> X, y = make_classification(n_features=4, random_state=0) >>> clf = LinearSVC(random_state=0, tol=1e5) >>> clf.fit(X, y) LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True, intercept_scaling=1, loss='squared_hinge', max_iter=1000, multi_class='ovr', penalty='l2', random_state=0, tol=1e05, verbose=0) >>> print(clf.coef_) [[0.085... 0.394... 0.498... 0.375...]] >>> print(clf.intercept_) [0.284...] >>> print(clf.predict([[0, 0, 0, 0]])) [1]
Notes
The underlying C implementation uses a random number generator to select features when fitting the model. It is thus not uncommon to have slightly different results for the same input data. If that happens, try with a smaller
tol
parameter.The underlying implementation, liblinear, uses a sparse internal representation for the data that will incur a memory copy.
Predict output may not match that of standalone liblinear in certain cases. See differences from liblinear in the narrative documentation.
References
LIBLINEAR: A Library for Large Linear Classification
See also
SVC
 Implementation of Support Vector Machine classifier using libsvm: the kernel can be nonlinear but its SMO algorithm does not scale to large number of samples as LinearSVC does. Furthermore SVC multiclass mode is implemented using one vs one scheme while LinearSVC uses one vs the rest. It is possible to implement one vs the rest with SVC by using the
pai4sk.multiclass.OneVsRestClassifier
wrapper. Finally SVC can fit dense data without memory copy if the input is Ccontiguous. Sparse data will still incur memory copy though. pai4sk.linear_model.SGDClassifier
 SGDClassifier can optimize the same cost function as LinearSVC by adjusting the penalty and loss parameters. In addition it requires less memory, allows incremental (online) learning, and implements various loss functions and regularization regimes.

decision_function
(X, num_threads=0)¶ Predicts confidence scores.
The confidence score of a sample is the signed distance of that sample to the decision boundary.
Parameters:  X (sparse matrix (csr_matrix) or dense matrix (ndarray)) – Dataset used for predicting distances to the decision boundary. For SnapML solver it also supports input of type SnapML data partition.
 num_threads (int, default : 0) – Number of threads used to run inference. By default inference runs with maximum number of available threads.
Returns: proba – Returns the distance to the decision boundary of the samples in X.
Return type: arraylike, shape = (n_samples,) or (n_sample, n_classes)

fit
(X, y, sample_weight=None)¶ Fit the model according to the given training data. :param X: Training vector, where n_samples in the number of samples and
n_features is the number of features. For SnapML solver it also supports input of types SnapML data partition and DeviceNDArray.Parameters:  y (arraylike, shape = [n_samples]) – Target vector relative to X
 sample_weight (arraylike, shape = [n_samples], optional) – Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight.
Returns: self
Return type:

predict
(X, num_threads=0)¶ Class predictions The returned class estimates. Parameters ——— X : sparse matrix (csr_matrix) or dense matrix (ndarray)
Dataset used for predicting class estimates. For SnapML solver it also supports input of type SnapML data partition. num_threads : int, default : 0
 Number of threads used to run inference. By default inference runs with maximum number of available threads.
 proba: arraylike, shape = (n_samples,)
 Returns the predicted class of the sample.
 penalty (string, 'l1' or 'l2' (default='l2')) – Specifies the norm used in the penalization. The ‘l2’
penalty is the standard used in SVC. The ‘l1’ leads to