torchbox.ml package

Submodules

torchbox.ml.reduction_pca module

torchbox.ml.reduction_pca.pca(x, sdim=- 2, fdim=- 1, npcs='all', eigbkd='svd')

Principal Component Analysis (pca) on raw data

Parameters

  • x (Tensor) – the input data

  • sdim (int, optional) – the dimension index of sample, by default -2

  • fdim (int, optional) – the dimension index of feature, by default -1

  • npcs (int or str, optional) – the number of components, by default 'all'

  • eigbkd (str, optional) – the backend of eigen decomposition, 'svd' (default) or 'eig'

Returns

U, S, K (if npcs is integer)

Return type

tensor

Examples

_images/MNISTPCA_ORIG.png _images/MNISTPCA_K90.png

The results shown in the above figure can be obtained by the following codes.

rootdir, dataset = '/mnt/d/DataSets/oi/dgi/mnist/official/', 'test'
x, _ = tb.read_mnist(rootdir=rootdir, dataset=dataset, fmt='ubyte')
print(x.shape)
N, M2, _ = x.shape
x = x.to(th.float32)
pcr = 0.9

u, s = tb.pca(x, sdim=0, fdim=(1, 2), eigbkd='svd')
k = tb.pcapc(s, pcr=pcr)
print(u.shape, s.shape, k)
u = u[..., :k]
y = x.reshape(N, -1) @ u  # N-k
z = y @ u.T.conj()
# z[z<0] = 0
z = z.reshape(N, M2, M2)
print(tb.nmse(x, z, dim=(1, 2)))
xp = th.nn.functional.pad(x[:35], (1, 1, 1, 1, 0, 0), 'constant', 255)
zp = th.nn.functional.pad(z[:35], (1, 1, 1, 1, 0, 0), 'constant', 255)
plt = tb.imshow(tb.patch2tensor(xp, (5*(M2+2), 7*(M2+2)), dim=(1, 2)), titles=['Orignal'])
plt = tb.imshow(tb.patch2tensor(zp, (5*(M2+2), 7*(M2+2)), dim=(1, 2)), titles=['Reconstructed with %d PCs(%.2f%%)' % (k, 100*k/u.shape[0])])
plt.show()

u, s = tb.pca(x.reshape(N, -1), sdim=0, fdim=1, npcs=2, eigbkd='svd')
print(u.shape, s.shape)
y = x.reshape(N, -1) @ u  # N-k
z = y @ u.T.conj()
z = z.reshape(N, M2, M2)
print(tb.nmse(x, z, dim=(1, 2)))
torchbox.ml.reduction_pca.pcapc(s, pcr=0.9)

get principal component according to the ratio of variance

Parameters

  • s (Tensor) – eigenvalues

  • pcr (float, optional) – the ratio of variance, by default 0.9

torchbox.ml.reduction_pca.pcat(x, sdim=- 2, fdim=- 1, isnorm=True, eigbkd='svd')

gets Principal Component Analysis transformation

Parameters

  • x (Tensor) – the input data

  • sdim (int, optional) – the dimension index of sample, by default -2

  • fdim (int or tuple, optional) – the dimension index of feature, by default -1

  • isnorm (bool, optional) – whether to normalize covariance matric with the number of samples, by default True

  • eigbkd (str, optional) – the backend of eigen decomposition, 'svd' (default) or 'eig'

Returns

the PCA transformation matrix, the eigenvalues

Return type

tensor

Module contents