#!/usr/bin/env python3
# coding: utf-8
"""
Created on July 10 2019
Authors:
Nathan De Lara <nathan.delara@telecom-paris.fr>
"""
from abc import ABC
from typing import Union
import numpy as np
from scipy import sparse
from scipy.sparse.linalg import svds
from sknetwork.base import Algorithm
class SVDSolver(Algorithm, ABC):
"""Generic class for SVD-solvers.
Attributes
----------
singular_vectors_left_: np.ndarray
Two-dimensional array, each column is a left singular vector of the input.
singular_vectors_right_: np.ndarray
Two-dimensional array, each column is a right singular vector of the input.
singular_values_: np.ndarray
Singular values.
"""
def __init__(self):
self.singular_vectors_left_ = None
self.singular_vectors_right_ = None
self.singular_values_ = None
[docs]class LanczosSVD(SVDSolver):
"""SVD solver using Lanczos method on :math:`AA^T` or :math:`A^TA`.
Parameters
----------
n_iter : int
Maximum number of Arnoldi update iterations allowed.
Default = 10 * nb or rows or columns.
tol : float
Relative accuracy for eigenvalues (stopping criterion).
Default = 0 (machine precision).
Attributes
----------
singular_vectors_left_: np.ndarray
Two-dimensional array, each column is a left singular vector of the input.
singular_vectors_right_: np.ndarray
Two-dimensional array, each column is a right singular vector of the input.
singular_values_: np.ndarray
Singular values.
See Also
--------
scipy.sparse.linalg.svds
"""
def __init__(self, n_iter: int = None, tol: float = 0.):
super(LanczosSVD, self).__init__()
self.n_iter = n_iter
self.tol = tol
[docs] def fit(self, matrix: Union[sparse.csr_matrix, sparse.linalg.LinearOperator], n_components: int,
init_vector: np.ndarray = None):
"""Perform singular value decomposition on input matrix.
Parameters
----------
matrix :
Matrix to decompose.
n_components : int
Number of singular values to compute
init_vector : np.ndarray
Starting vector for iteration.
Default = random.
Returns
-------
self: :class:`SVDSolver`
"""
u, s, vt = svds(matrix.astype(float), n_components, v0=init_vector)
# order the singular values by decreasing order
index = np.argsort(-s)
self.singular_vectors_left_ = u[:, index]
self.singular_vectors_right_ = vt.T[:, index]
self.singular_values_ = s[index]
return self