def _calc(self, data, ret_obj):
"""
Calculate SVD (wrap numpy SVD).
"""
try:
if self.rng is None:
self._U, self._s, self._Vh = _svd(data, full_matrices=False)
else:
self._U, self._s, self._Vh = _svd(data[..., self.rng],
full_matrices=False)
except:
return False
else:
return True
def _calc(self, data, ret_obj):
"""
Calculate SVD (wrap numpy SVD).
"""
try:
if self.rng is None:
self._U, self._s, self._Vh = _svd(data, full_matrices=False)
else:
self._U, self._s, self._Vh = _svd(data[..., self.rng],
full_matrices=False)
except:
return False
else:
return True
def pca(D, n_components=None):
"""
Principal component analysis
Parameters
----------
D : ndarray [n_sample, n_features]
Data
n_components : int
Number of components to calculate (using scipy.sparse.linalg.svds). If
None use numpy.linalg.svd
Returns
-------
Tuple with 3 items: Scores (T), Loadings (W), eigenvalues (singular values-squared)
"""
Dcenter = D - D.mean(axis=0, keepdims=True)
if n_components is None:
W, s2, Wt = _svd(_np.dot(Dcenter.T, Dcenter),
full_matrices=False)
# Note: s2 contains trivial values.
# Ex) Let D n x d matrix (n >= d),
# s2 is n-length vector,
# though the mathematical rank of the metrics is at most d
else:
if n_components == Dcenter.shape[0]:
n_components -= 1
W, s2, Wt = _svds(_np.dot(Dcenter.T, Dcenter), k=n_components)
# svds does not sort by variance; thus, manually sorting from biggest to
# smallest variance
sort_vec = _np.flipud(_np.argsort(s2))
W = W[:, sort_vec]
Wt = Wt[sort_vec, :]
s2 = s2[sort_vec]
# FIXME: T.var(axis=0) is not equal to s2 values.
# SVD decomposes A into U * S * V^T
# It is thought that U == Wt is false.
T = _np.dot(D, W)
# Note: T.mean(axis=0) is almost zeros
return T, W, s2
def svd(X):
return _svd(X, full_matrices=False)