CUR Decomposition

Dimensionality reduction using CUR decomposition ($A\approx CUR$)

Parameters

• A : numpy.array, default=None, n x m dataset matrix (n: number of features, m: number of instances)
• n_components : int, default=2, Desired dimensionality of output data
• sampling : str, default='random', Sampling method for column and row selection
• n_iter : int, default=5, Number of iterations for CUR approximations

Attributes

• C : numpy.array, Matrix containing selected columns of A
• Cpinv : numpy.array, Pseudo inverse of C
• R : numpy.array, Matrix containing selected rows of A
• Rpinv : numpy.array, Pseudo inverse of R
• U : numpy.array, U = Cpinv @ A @ Rpinv
• colidx : list, List of selected column indices for constructing C
• rowidx : list, List of selected row indices for constructing R

Example

import numpy as np
import curd
from sklearn.datasets import load_wine

n_components = 10
A = load_wine().data.T

cur = curd.CURdecomposition(A=A, n_components=n_components)
cur_error = np.linalg.norm(A - cur.C @ cur.Cpinv @ A)
print(f"[CUR] reconstruction error: {cur_error:.4f}")

# Output
[CUR] reconstruction error: 6.5836