pca_lowrank

paddle.linalg. pca_lowrank ( x, q=None, center=True, niter=2, name=None ) [source]

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

Let \(X\) be the input matrix or a batch of input matrices, the output should satisfies:

\[X = U * diag(S) * V^{T}\]
Parameters

  • x (Tensor) – The input tensor. Its shape should be […, N, M], where … is zero or more batch dimensions. N and M can be arbitrary positive number. The data type of x should be float32 or float64.

  • q (int, optional) – a slightly overestimated rank of \(X\). Default value is \(q=min(6,N,M)\).

  • center (bool, optional) – if True, center the input tensor. Default value is True.

  • niter (int, optional) – number of iterations to perform. Default: 2.

  • name (str, optional) – Name for the operation. For more information, please refer to Name. Default: None.

Returns

  • Tensor U, is N x q matrix.

  • Tensor S, is a vector with length q.

  • Tensor V, is M x q matrix.

tuple (U, S, V): which is the nearly optimal approximation of a singular value decomposition of a centered matrix \(X\).

Examples

 >>> import paddle
 >>> paddle.seed(2023)

 >>> x = paddle.randn((5, 5), dtype='float64')
 >>> U, S, V = paddle.linalg.pca_lowrank(x)
 >>> print(U)
Tensor(shape=[5, 5], dtype=float64, place=Place(cpu), stop_gradient=True,
[[ 0.80131563,  0.11962647,  0.27667179, -0.25891214,  0.44721360],
 [-0.12642301,  0.69917551, -0.17899393,  0.51296394,  0.44721360],
 [ 0.08997135, -0.69821706, -0.20059228,  0.51396579,  0.44721360],
 [-0.23871837, -0.02815453, -0.59888153, -0.61932365,  0.44721360],
 [-0.52614559, -0.09243040,  0.70179595, -0.14869394,  0.44721360]])

 >>> print(S)
 Tensor(shape=[5], dtype=float64, place=Place(cpu), stop_gradient=True,
 [2.60101614, 2.40554940, 1.49768346, 0.19064830, 0.00000000])

 >>> print(V)
 Tensor(shape=[5, 5], dtype=float64, place=Place(cpu), stop_gradient=True,
 [[ 0.58339481, -0.17143771,  0.00522143,  0.57976310,  0.54231640],
  [ 0.22334335,  0.72963474, -0.30148399, -0.39388750,  0.41438019],
  [ 0.05416913,  0.34666487,  0.93549758,  0.00063507,  0.04162998],
  [-0.39519094,  0.53074980, -0.16687419,  0.71175586, -0.16638919],
  [-0.67131070, -0.19071018,  0.07795789, -0.04615811,  0.71046714]])