torch.pca_lowrank — PyTorch 2.7 documentation (original) (raw)

torch.pca_lowrank(A, q=None, center=True, niter=2)[source][source]¶

Performs linear Principal Component Analysis (PCA) on a low-rank matrix, batches of such matrices, or sparse matrix.

This function returns a namedtuple (U, S, V) which is the nearly optimal approximation of a singular value decomposition of a centered matrix AA such that A≈Udiag⁡(S)VHA \approx U \operatorname{diag}(S) V^{\text{H}}

Note

The relation of (U, S, V) to PCA is as follows:

• AA is a data matrix with m samples andn features
• the VV columns represent the principal directions
• S∗∗2/(m−1)S ** 2 / (m - 1) contains the eigenvalues ofATA/(m−1)A^T A / (m - 1) which is the covariance ofA when center=True is provided.
• matmul(A, V[:, :k]) projects data to the first k principal components

Note

Different from the standard SVD, the size of returned matrices depend on the specified rank and q values as follows:

• UU is m x q matrix
• SS is q-vector
• VV is n x q matrix

Note

To obtain repeatable results, reset the seed for the pseudorandom number generator

Parameters

• A (Tensor) – the input tensor of size (∗,m,n)(*, m, n)
• q (int, optional) – a slightly overestimated rank ofAA. By default, q = min(6, m, n).
• center (bool, optional) – if True, center the input tensor, otherwise, assume that the input is centered.
• niter (int, optional) – the number of subspace iterations to conduct; niter must be a nonnegative integer, and defaults to 2.

Return type

tuple[torch.Tensor, torch.Tensor, torch.Tensor]

References:

• Nathan Halko, Per-Gunnar Martinsson, and Joel Tropp, Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions, arXiv:0909.4061 [math.NA; math.PR], 2009 (available at arXiv <http://arxiv.org/abs/0909.4061>_).