# Source code for qiskit_machine_learning.algorithms.classifiers.pegasos_qsvc

```
# This code is part of Qiskit.
#
# (C) Copyright IBM 2022.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""Pegasos Quantum Support Vector Classifier."""
from __future__ import annotations
import logging
from datetime import datetime
from typing import Dict
import numpy as np
from qiskit.utils import algorithm_globals
from sklearn.base import ClassifierMixin
from ...algorithms.serializable_model import SerializableModelMixin
from ...exceptions import QiskitMachineLearningError
from ...kernels import BaseKernel, FidelityQuantumKernel
logger = logging.getLogger(__name__)
[docs]class PegasosQSVC(ClassifierMixin, SerializableModelMixin):
r"""
Implements Pegasos Quantum Support Vector Classifier algorithm. The algorithm has been
developed in [1] and includes methods ``fit``, ``predict`` and ``decision_function`` following
the signatures
of `sklearn.svm.SVC <https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html>`_.
This implementation is adapted to work with quantum kernels.
**Example**
.. code-block:: python
quantum_kernel = FidelityQuantumKernel()
pegasos_qsvc = PegasosQSVC(quantum_kernel=quantum_kernel)
pegasos_qsvc.fit(sample_train, label_train)
pegasos_qsvc.predict(sample_test)
**References**
[1]: Shalev-Shwartz et al., Pegasos: Primal Estimated sub-GrAdient SOlver for SVM.
`Pegasos for SVM <https://home.ttic.edu/~nati/Publications/PegasosMPB.pdf>`_
"""
FITTED = 0
UNFITTED = 1
# pylint: disable=invalid-name
def __init__(
self,
quantum_kernel: BaseKernel | None = None,
C: float = 1.0,
num_steps: int = 1000,
precomputed: bool = False,
seed: int | None = None,
) -> None:
"""
Args:
quantum_kernel: a quantum kernel to be used for classification. Has to be ``None`` when
a precomputed kernel is used.
C: Positive regularization parameter. The strength of the regularization is inversely
proportional to C. Smaller ``C`` induce smaller weights which generally helps
preventing overfitting. However, due to the nature of this algorithm, some of the
computation steps become trivial for larger ``C``. Thus, larger ``C`` improve
the performance of the algorithm drastically. If the data is linearly separable
in feature space, ``C`` should be chosen to be large. If the separation is not
perfect, ``C`` should be chosen smaller to prevent overfitting.
num_steps: number of steps in the Pegasos algorithm. There is no early stopping
criterion. The algorithm iterates over all steps.
precomputed: a boolean flag indicating whether a precomputed kernel is used. Set it to
``True`` in case of precomputed kernel.
seed: a seed for the random number generator
Raises:
ValueError:
- if ``quantum_kernel`` is passed and ``precomputed`` is set to ``True``. To use
a precomputed kernel, ``quantum_kernel`` has to be of the ``None`` type.
TypeError:
- if ``quantum_kernel`` neither instance of
:class:`~qiskit_machine_learning.kernels.BaseKernel` nor ``None``.
"""
if precomputed:
if quantum_kernel is not None:
raise ValueError("'quantum_kernel' has to be None to use a precomputed kernel")
else:
if quantum_kernel is None:
quantum_kernel = FidelityQuantumKernel()
self._quantum_kernel = quantum_kernel
self._precomputed = precomputed
self._num_steps = num_steps
if seed is not None:
algorithm_globals.random_seed = seed
if C > 0:
self.C = C
else:
raise ValueError(f"C has to be a positive number, found {C}.")
# these are the parameters being fit and are needed for prediction
self._alphas: Dict[int, int] | None = None
self._x_train: np.ndarray | None = None
self._n_samples: int | None = None
self._y_train: np.ndarray | None = None
self._label_map: Dict[int, int] | None = None
self._label_pos: int | None = None
self._label_neg: int | None = None
# added to all kernel values to include an implicit bias to the hyperplane
self._kernel_offset = 1
# for compatibility with the base SVC class. Set as unfitted.
self.fit_status_ = PegasosQSVC.UNFITTED
# pylint: disable=invalid-name
[docs] def fit(
self, X: np.ndarray, y: np.ndarray, sample_weight: np.ndarray | None = None
) -> "PegasosQSVC":
"""Fit the model according to the given training data.
Args:
X: Train features. For a callable kernel (an instance of
:class:`~qiskit_machine_learning.kernels.BaseKernel`) the shape
should be ``(n_samples, n_features)``, for a precomputed kernel the shape should be
``(n_samples, n_samples)``.
y: shape (n_samples), train labels . Must not contain more than two unique labels.
sample_weight: this parameter is not supported, passing a value raises an error.
Returns:
``self``, Fitted estimator.
Raises:
ValueError:
- X and/or y have the wrong shape.
- X and y have incompatible dimensions.
- y includes more than two unique labels.
- Pre-computed kernel matrix has the wrong shape and/or dimension.
NotImplementedError:
- when a sample_weight which is not None is passed.
"""
# check whether the data have the right format
if np.ndim(X) != 2:
raise ValueError("X has to be a 2D array")
if np.ndim(y) != 1:
raise ValueError("y has to be a 1D array")
if len(np.unique(y)) != 2:
raise ValueError("Only binary classification is supported")
if X.shape[0] != y.shape[0]:
raise ValueError("'X' and 'y' have to contain the same number of samples")
if self._precomputed and X.shape[0] != X.shape[1]:
raise ValueError(
"For a precomputed kernel, X should be in shape (n_samples, n_samples)"
)
if sample_weight is not None:
raise NotImplementedError(
"Parameter 'sample_weight' is not supported. All samples have to be weighed equally"
)
# reset the fit state
self.fit_status_ = PegasosQSVC.UNFITTED
# the algorithm works with labels in {+1, -1}
self._label_pos = np.unique(y)[0]
self._label_neg = np.unique(y)[1]
self._label_map = {self._label_pos: +1, self._label_neg: -1}
# the training data are later needed for prediction
self._x_train = X
self._y_train = y
self._n_samples = X.shape[0]
# empty dictionary to represent sparse array
self._alphas = {}
t_0 = datetime.now()
# training loop
for step in range(1, self._num_steps + 1):
# for every step, a random index (determining a random datum) is fixed
i = algorithm_globals.random.integers(0, len(y))
value = self._compute_weighted_kernel_sum(i, X, training=True)
if (self._label_map[y[i]] * self.C / step) * value < 1:
# only way for a component of alpha to become non zero
self._alphas[i] = self._alphas.get(i, 0) + 1
self.fit_status_ = PegasosQSVC.FITTED
logger.debug("fit completed after %s", str(datetime.now() - t_0)[:-7])
return self
# pylint: disable=invalid-name
[docs] def predict(self, X: np.ndarray) -> np.ndarray:
"""
Perform classification on samples in X.
Args:
X: Features. For a callable kernel (an instance of
:class:`~qiskit_machine_learning.kernels.BaseKernel`) the shape
should be ``(m_samples, n_features)``, for a precomputed kernel the shape should be
``(m_samples, n_samples)``. Where ``m`` denotes the set to be predicted and ``n`` the
size of the training set. In that case, the kernel values in X have to be calculated
with respect to the elements of the set to be predicted and the training set.
Returns:
An array of the shape (n_samples), the predicted class labels for samples in X.
Raises:
QiskitMachineLearningError:
- predict is called before the model has been fit.
ValueError:
- Pre-computed kernel matrix has the wrong shape and/or dimension.
"""
t_0 = datetime.now()
values = self.decision_function(X)
y = np.array([self._label_pos if val > 0 else self._label_neg for val in values])
logger.debug("prediction completed after %s", str(datetime.now() - t_0)[:-7])
return y
[docs] def decision_function(self, X: np.ndarray) -> np.ndarray:
"""
Evaluate the decision function for the samples in X.
Args:
X: Features. For a callable kernel (an instance of
:class:`~qiskit_machine_learning.kernels.BaseKernel`) the shape
should be ``(m_samples, n_features)``, for a precomputed kernel the shape should be
``(m_samples, n_samples)``. Where ``m`` denotes the set to be predicted and ``n`` the
size of the training set. In that case, the kernel values in X have to be calculated
with respect to the elements of the set to be predicted and the training set.
Returns:
An array of the shape (n_samples), the decision function of the sample.
Raises:
QiskitMachineLearningError:
- the method is called before the model has been fit.
ValueError:
- Pre-computed kernel matrix has the wrong shape and/or dimension.
"""
if self.fit_status_ == PegasosQSVC.UNFITTED:
raise QiskitMachineLearningError("The PegasosQSVC has to be fit first")
if np.ndim(X) != 2:
raise ValueError("X has to be a 2D array")
if self._precomputed and self._n_samples != X.shape[1]:
raise ValueError(
"For a precomputed kernel, X should be in shape (m_samples, n_samples)"
)
values = np.zeros(X.shape[0])
for i in range(X.shape[0]):
values[i] = self._compute_weighted_kernel_sum(i, X, training=False)
return values
def _compute_weighted_kernel_sum(self, index: int, X: np.ndarray, training: bool) -> float:
"""Helper function to compute the weighted sum over support vectors used for both training
and prediction with the Pegasos algorithm.
Args:
index: fixed index distinguishing some datum
X: Features
training: flag indicating whether the loop is used within training or prediction
Returns:
Weighted sum of kernel evaluations employed in the Pegasos algorithm
"""
# non-zero indices corresponding to the support vectors
support_indices = list(self._alphas.keys())
# for training
if training:
# support vectors
x_supp = X[support_indices]
# for prediction
else:
x_supp = self._x_train[support_indices]
if not self._precomputed:
# evaluate kernel function only for the fixed datum and the support vectors
kernel = self._quantum_kernel.evaluate(X[index], x_supp) + self._kernel_offset
else:
kernel = X[index, support_indices]
# map the training labels of the support vectors to {-1,1}
y = np.array(list(map(self._label_map.get, self._y_train[support_indices])))
# weights for the support vectors
alphas = np.array(list(self._alphas.values()))
# this value corresponds to a sum of kernel values weighted by their labels and alphas
value = np.sum(alphas * y * kernel)
return value
@property
def quantum_kernel(self) -> BaseKernel:
"""Returns quantum kernel"""
return self._quantum_kernel
@quantum_kernel.setter
def quantum_kernel(self, quantum_kernel: BaseKernel):
"""
Sets quantum kernel. If previously a precomputed kernel was set, it is reset to ``False``.
"""
self._quantum_kernel = quantum_kernel
# quantum kernel is set, so we assume the kernel is not precomputed
self._precomputed = False
# reset training status
self._reset_state()
@property
def num_steps(self) -> int:
"""Returns number of steps in the Pegasos algorithm."""
return self._num_steps
@num_steps.setter
def num_steps(self, num_steps: int):
"""Sets the number of steps to be used in the Pegasos algorithm."""
self._num_steps = num_steps
# reset training status
self._reset_state()
@property
def precomputed(self) -> bool:
"""Returns a boolean flag indicating whether a precomputed kernel is used."""
return self._precomputed
@precomputed.setter
def precomputed(self, precomputed: bool):
"""Sets the pre-computed kernel flag. If ``True`` is passed then the previous kernel is
cleared. If ``False`` is passed then a new instance of
:class:`~qiskit_machine_learning.kernels.FidelityQuantumKernel` is created."""
self._precomputed = precomputed
if precomputed:
# remove the kernel, a precomputed will
self._quantum_kernel = None
else:
# re-create a new default quantum kernel
self._quantum_kernel = FidelityQuantumKernel()
# reset training status
self._reset_state()
def _reset_state(self):
"""Resets internal data structures used in training."""
self.fit_status_ = PegasosQSVC.UNFITTED
self._alphas = None
self._x_train = None
self._n_samples = None
self._y_train = None
self._label_map = None
self._label_pos = None
self._label_neg = None
```