Implementation:Scikit learn Scikit learn BenchPlotRandomizedSVD

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Machine Learning, Benchmarking
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for benchmarking randomized SVD power iteration strategies provided by scikit-learn.

Description

This benchmark script evaluates the effect of increasing the number of power iterations in randomized SVD on both approximation quality and running time. It tests several normalization policies (none, LU, QR, auto) and compares them against fbpca if installed. The quality of approximation is measured by the spectral norm discrepancy between the original and reconstructed matrices. The benchmarks test on various synthetic and real datasets.

Usage

Use this benchmark to determine the optimal number of power iterations and normalization policy for randomized SVD, especially for noisy matrices characterized by slow spectral decay.

Code Reference

Source Location

• Repository: scikit-learn
• File: benchmarks/bench_plot_randomized_svd.py

Signature

# Key function benchmarked
from sklearn.utils.extmath import randomized_svd

# Comparison algorithms:
# randomized_svd(..., power_iteration_normalizer='none')
# randomized_svd(..., power_iteration_normalizer='LU')
# randomized_svd(..., power_iteration_normalizer='QR')
# randomized_svd(..., power_iteration_normalizer='auto')
# fbpca.pca() (if installed)

Import

from sklearn.utils.extmath import randomized_svd

I/O Contract

Inputs

Name	Type	Required	Description
M	ndarray	Yes	Input matrix for SVD decomposition
n_components	int	Yes	Number of singular values/vectors to extract
n_iter	int	No	Number of power iterations (default varies)
power_iteration_normalizer	str	No	Normalization policy: 'none', 'LU', 'QR', or 'auto'

Outputs

Name	Type	Description
Plots	matplotlib figures	Time vs norm plots, n_iter vs norm plots, comparison plots
Console output	text	Timing and accuracy metrics for each configuration

Usage Examples

Basic Usage

import numpy as np
from sklearn.utils.extmath import randomized_svd

# Generate a low-rank matrix
rng = np.random.RandomState(42)
A = rng.randn(1000, 100)
U, S, Vt = randomized_svd(A, n_components=10, n_iter=5,
                            power_iteration_normalizer='QR',
                            random_state=42)
print("Singular values:", S[:5])

Related Pages

• Principle:Scikit_learn_Scikit_learn_Dimensionality_Reduction