a sparse gradient

USAGE SUMMARY

The phrase "a sparse gradient" is correct and usable in written English.
It can be used in contexts related to mathematics, machine learning, or optimization, where it describes a gradient that has many zero or near-zero values. Example: "In this optimization problem, we are dealing with a sparse gradient, which can lead to faster convergence."

✓ Grammatically correct

Science

News & Media

Wiki

Human-verified examples from authoritative sources

Exact Expressions

1 human-written examples

An example of this approach is Total Variation minimization, which can be used to accurately reconstruct objects that have a sparse gradient in a wide variety of applications [11, 12].

Advanced Structural and Chemical Imaging

Human-verified similar examples from authoritative sources

Similar Expressions

58 human-written examples

A well-known example of such methods is the Total Variation minimization, which promotes images with sparse gradient.

Advanced Structural and Chemical Imaging

For the cavity with a small portion of non-layered media, we propose a sparse preconditioned conjugate orthogonal conjugate gradient solver combined with the new preconditioner.

Journal of Computational Physics

Therefore, in this case, these two linear subsystems can be solved either exactly by a sparse Cholesky factorization or inexactly by conjugated gradient scheme.

Journal of Inequalities and Applications

These features lead to a particularly simple implementation using either a sparse direct solver or a matrix-free conjugate gradient solver.

Journal of Computational Physics

Blood oxygen level-dependent (BOLD) contrast-image volumes were acquired on a 1.5 T scanner (Siemens MAGNETOM Sonata) using gradient echo planar imaging in a sparse protocol (repetition time 12.5 seconds), in order to temporally separate the scanner noise and the experimental sounds [18], [19].

Plosone

Also, the gradient ∇f* of the target image can be passed through a sparse sieve [1].

EURASIP Journal on Advances in Signal Processing

A sparse classic.

The Guardian - Music

It's a sparse but intriguing catalog.

The New York Times - Tech

Together they evoke a sparse domestic interior.

The New York Times

First, a sparse representation (SR) mathematical model for sparse blade tip-timing signals is built.

Mechanical Systems and Signal Processing

Expert writing Tips

Best practice

When describing gradients in mathematical or computational contexts, use "a sparse gradient" to indicate that most of the gradient's components are zero or near-zero, which can be beneficial for optimization and efficiency.

Common error

Avoid using "a sparse gradient" when you actually mean a gradient with small magnitude values overall. Sparsity refers to the number of zero or near-zero components, not the size of the non-zero components.

Linguistic Context

The phrase "a sparse gradient" functions as a noun phrase, often serving as the subject or object in sentences related to mathematical optimization, machine learning, and image processing. Ludwig AI confirms its correctness and usability.

Expression frequency: Common

Frequent in

Science

65%

News & Media

20%

Wiki

15%

Less common in

Formal & Business

0%

Encyclopedias

0%

Reference

0%

Ludwig's WRAP-UP

In summary, the phrase "a sparse gradient" is a technically sound term prevalent in scientific and mathematical domains, denoting a gradient vector with numerous zero or near-zero components. As Ludwig AI confirms, the phrase is grammatically correct and frequently employed in research articles and technical documentation. Its usage is particularly relevant in discussions concerning optimization algorithms, machine learning models, and image processing techniques, where the sparsity property can significantly impact computational efficiency. Understanding the contexts of use helps avoid misinterpretations, ensuring precise communication in technical discourse. When in doubt, use alternatives like "a gradient with few elements" or "a thinly populated gradient".

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

a gradient with few elements

Focuses on the quantity of elements rather than the 'sparse' quality.

a thinly populated gradient

Replaces 'sparse' with 'thinly populated' emphasizing distribution.

a gradient of low density

Substitutes 'sparse' with 'low density', focusing on concentration.

a gradient lacking in data points

Highlights the lack of data which makes the gradient sparse.

a gradient with minimal values

Emphasizes the small magnitude of values within the gradient.

a gradient containing few non-zero values

Specifically points out the composition of the gradient with zero values.

a gradient having scattered data

Focuses on the scattered nature of the data points.

a gradient with infrequent changes

Highlights the lack of frequent changes within the gradient.

a scarcely populated gradient

Uses 'scarcely' to replace 'sparse', indicating a limited presence.

a gradient that is weakly defined

Describes the gradient as not being strongly or clearly defined.

FAQs

How is "a sparse gradient" used in mathematical contexts?

In mathematics, "a sparse gradient" describes a gradient vector where most of its elements are zero or close to zero. This property is exploited in optimization algorithms to improve computational efficiency, particularly in high-dimensional problems.

What's the difference between "a sparse gradient" and a dense gradient?

"A sparse gradient" has many zero or near-zero values, while a dense gradient has mostly non-zero values. Sparse gradients can lead to faster computations in certain algorithms, while dense gradients might be more informative in other contexts.

When would I use the term "a sparse gradient"?

Use "a sparse gradient" when discussing optimization, machine learning, or numerical methods where the gradient vector has a significant number of zero or near-zero components. This term is common in fields dealing with high-dimensional data or computationally intensive problems.

What are some alternative ways to describe gradients with few elements besides using "a sparse gradient"?

Depending on the context, you could use phrases like "a gradient with few elements", "a thinly populated gradient", or "a gradient of low density".