maximum variance

USAGE SUMMARY

The phrase "maximum variance" is correct and usable in written English.
It can be used in various contexts, but it is commonly used in statistics or data analysis to describe the spread or range of data points. Example: The results of the survey showed a maximum variance in opinions on climate change, with some participants strongly supporting immediate action while others believed it was not a pressing issue.

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

In this case, the maximum variance criterion should be used.

Renewables: Wind, Water, and Solar

The new axes lie along the directions of maximum variance.

Applied Water Science

However, the maximum variance would be as large as 78.21, which is noticeably larger than the maximum variance from simple kriging.

Environmental Systems Research

To do so, PCA considers the maximum variance in the dataset, whereas MAD considers maximum autocorrelation, since it takes into account the maximum variance of the difference images.

Open Geospatial Data, Software and Standards

We also identify which stage within the protocol is associated with maximum variance.

Journal of Proteomics

It minimizes the maximum variance of the predicted value of the regression model.

Neurocomputing

The maximum variance criterion discussed above is used by Minasny et al. (2007).

Renewables: Wind, Water, and Solar

Hence, there is no guarantee that the directions of maximum variance enhance class separabilities.

Open Geospatial Data, Software and Standards

The solution with the maximum variance reduction is the optimal solution.

Earth, Planets and Space

It retains maximum variance of multidimensional data whilst reducing their dimensionality.

Chemistry Central Journal

The first principal component is associated with the axis that captures the maximum variance.

Cognitive Research: Principles and Implications

Expert writing Tips

Best practice

When describing statistical analyses, clearly define the variables for which you are calculating the "maximum variance" to ensure clarity and avoid ambiguity.

Common error

Avoid interchanging "variance" with standard deviation. While related, variance is the square of the standard deviation and represents the average squared distance from the mean, not the typical distance itself.

Linguistic Context

The phrase "maximum variance" functions as a noun phrase, often used as a criterion or objective in statistical and machine learning contexts. Ludwig shows it is frequently employed to describe the goal of capturing the most significant variation in a dataset.

Expression frequency: Very common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

In summary, the phrase "maximum variance" is grammatically sound and exceptionally common in scientific and statistical discourse. As highlighted by Ludwig, it describes the state of greatest variability in a dataset and is central to methods like PCA. To use it effectively, define the variables clearly and avoid confusion with related concepts like standard deviation. Remember, Ludwig AI affirms its correct usage, predominantly within formal, scientific contexts.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

maximum data dispersion

This alternative replaces "variance" with "data dispersion" maintaining the same meaning.

highest variability

This alternative focuses on the concept of variability, emphasizing its peak level.

peak data dispersion

This alternative emphasizes the dispersion of data, pinpointing the highest point.

greatest data spread

This alternative replaces "variance" with the more general term "spread", indicating the extent of data distribution.

largest statistical variation

This option specifies the context as "statistical", and uses "variation" instead of "variance".

maximal data scattering

This phrase utilizes 'scattering' instead of 'variance', emphasizing the spread of data points.

topmost degree of dispersion

This alternative uses a more descriptive and elaborate way to refer to the dispersion.

extreme data fluctuation

This alternative highlights the concept of data fluctuation reaching an extreme point.

highest point of divergence

This alternative emphasizes the divergence of data reaching an extreme point.

ultimate degree of diversity

This alternative focuses on diversity as the extreme level of spread.

FAQs

How is "maximum variance" used in data analysis?

In data analysis, "maximum variance" is often used to identify the principal components of a dataset, aiming to capture the most significant variations within the data. Techniques like Principal Component Analysis (PCA) use this concept to reduce dimensionality while retaining essential information.

What is the difference between "maximum variance" and "average variance"?

"Maximum variance" refers to the highest level of dispersion within a dataset, indicating the greatest degree of variability. "Average variance", on the other hand, represents the typical or expected amount of variation across the entire dataset.

In what fields is the concept of "maximum variance" most relevant?

The concept of "maximum variance" is particularly relevant in fields such as statistics, data science, machine learning, and signal processing, where understanding and modeling data variability is crucial for analysis and prediction.

What are some statistical methods that utilize "maximum variance"?

Principal Component Analysis (PCA), Maximum Variance Unfolding (MVU), and Variance Inflation Factor (VIF) calculations all utilize the concept of "maximum variance". These methods aim to identify, maximize, or mitigate the effects of high variability in data.