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# Copyright 2022 SPTK Working Group #
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import torch
from torch import nn
from ..misc.utils import check_size
[docs]
class PrincipalComponentAnalysis(nn.Module):
"""See `this page <https://sp-nitech.github.io/sptk/latest/main/pca.html>`_
for details.
Parameters
----------
order : int >= 0
Order of vector.
n_comp : int >= 1
Number of principal components, :math:`N`.
cov_type : ['sample', 'unbiased', 'correlation']
Type of covariance.
sort : ['ascending', 'descending']
Order of eigenvalues and eigenvectors.
"""
def __init__(self, order, n_comp, cov_type="sample", sort="descending"):
super().__init__()
assert 0 <= order
assert 1 <= n_comp <= order + 1
assert sort in ["ascending", "descending"]
self.order = order
self.n_comp = n_comp
self.cov_type = cov_type
self.sort = sort
if cov_type in (0, "sample"):
self.cov = lambda x: torch.cov(x, correction=0)
elif cov_type in (1, "unbiased"):
self.cov = lambda x: torch.cov(x, correction=1)
elif cov_type in (2, "correlation"):
self.cov = lambda x: torch.corrcoef(x)
else:
raise ValueError(f"cov_type {cov_type} is not supported.")
self.register_buffer("v", torch.eye(self.order + 1, self.n_comp))
self.register_buffer("m", torch.zeros(self.order + 1))
[docs]
def forward(self, x):
"""Perform PCA.
Parameters
----------
x : Tensor [shape=(..., M+1)]
Input vectors.
Returns
-------
e : Tensor [shape=(N,)]
Eigenvalues.
v : Tensor [shape=(M+1, N)]
Eigenvectors.
m : Tensor [shape=(M+1,)]
Mean vector.
Examples
--------
>>> x = diffsptk.nrand(10, 3)
>>> x.size()
torch.Size([10, 4])
>>> pca = diffsptk.PCA(3, 3)
>>> e, _, _ = pca(x)
>>> e
tensor([1.3465, 0.7497, 0.4447])
>>> y = pca.transform(x)
>>> y.size()
torch.Size([10, 3])
"""
check_size(x.size(-1), self.order + 1, "dimension of input")
x = x.reshape(-1, x.size(-1)).T
assert self.n_comp + 1 <= x.size(1), "Number of data samples is too small"
e, v = torch.linalg.eigh(self.cov(x))
e = e[-self.n_comp :]
v = v[:, -self.n_comp :]
if self.sort == "descending":
e = e.flip(-1)
v = v.flip(-1)
self.v[:] = v
self.m[:] = x.mean(1)
return e, self.v, self.m