如何在 python 中使用 scikit-tensor

Question

如何在python中使用scikit-tensor？

我想用 parafac 分解来分解张量。输入是：张量数据 - 分解秩输出是：因子矩阵

Answer 1

这段代码： parafac_base 函数获取 X 张量和 return 3 个因子矩阵

import operator, logging
import numpy as np
def ribs(loadings):
  '''
  Convert a list of n loading matrices [A_{fi}, B_{fj}, C_{fk}, ...] into ribs
  [A_{fi11...}, B_{f1j1...}, C_{f11k...}, ...]. These ribs can be multiplied
  with numpy broadcasting to fill a tensor with data.
  '''
  loadings = [np.atleast_2d(l) for l in loadings]
  nfactors = loadings[0].shape[0]
  assert np.alltrue([l.ndim == 2 and l.shape[0] == nfactors for l in loadings])
  ribs = []
  for mi in range(len(loadings)):
    shape = [nfactors] + [-1 if fi == mi else 1 for fi in range(len(loadings))]
    ribs.append(loadings[mi].reshape(shape))
  return ribs

def para_compose(ribs):
  return np.sum(reduce(operator.mul, ribs), axis=0)

def parafac_base(x, nfactors, max_iter):
  '''
  PARAFAC is a multi-way tensor decomposition method. Given a tensor X, and a
  number of factors nfactors, PARAFAC decomposes the X in n factors for each
  dimension in X using alternating least squares:

  X_{ijk} = \sum_{f} a_{fi} b_{fj} c_{fk} + e_{ijk}

  PARAFAC can be seen as a generalization of PCA to higher order arrays [1].
  Return a ([a, b, c, ...], mse)

  [1] Rasmus Bro. PARAFAC. Tutorial and applications. Chemometrics and
  Intelligent Laboratory Systems, 38(2):149-171, 1997.
  '''
  log = logging.getLogger('psychic.parafac')
  loadings = [np.random.rand(nfactors, n) for n in x.shape]

  last_mse = np.inf
  for i in range(max_iter):
    # 1) forward (predict x)
    xhat = para_compose(ribs(loadings))

    # 2) stopping?
    mse = np.mean((xhat - x) ** 2)
    if last_mse - mse < 1e-10 or mse < 1e-20:
      break
    last_mse = mse

    for mode in range(len(loadings)):
      log.debug('iter: %d, dir: %d' % (i, mode))
      # a) Re-compose using other factors
      Z = ribs([l for li, l in enumerate(loadings) if li != mode])
      Z = reduce(operator.mul, Z)

      # b) Isolate mode
      Z = Z.reshape(nfactors, -1).T # Z = [long x fact]
      Y = np.rollaxis(x, mode)
      Y = Y.reshape(Y.shape[0], -1).T # Y = [mode x long]

      # c) least squares estimation: x = np.lstsq(Z, Y) -> Z x = Y
      new_fact, _, _, _ = np.linalg.lstsq(Z, Y)
      loadings[mode] = new_fact
  if not i < max_iter - 1:
    log.warning('parafac did not converge in %d iterations (mse=%.2g)' %
      (max_iter, mse))
  return loadings, mse

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