dimensionality
Học thuậtThân thiện
Definition
- Noun:
- The spatial property of having dimensions: The state or quality of possessing measurable spatial extent, such as length, width, and height. It refers to the number of coordinates needed to specify a point within a mathematical space or physical object.
- The number of independent parameters or coordinates required to define something: In mathematics, physics, and data science, it describes the number of variables, features, or axes needed to describe a system, object, or dataset.
Usage Examples
- Noun:
- The dimensionality of a line is one, while a plane has a dimensionality of two.
- Reducing the dimensionality of the dataset made the analysis much faster.
- All matter has dimensionality, meaning it occupies space.
Advanced Usage
- "High-dimensionality": Refers to a system or dataset with a large number of dimensions or variables.
- High-dimensionality data can be challenging to visualize and analyze.
- "Dimensionality reduction": A process in statistics and machine learning for reducing the number of random variables under consideration.
- Principal Component Analysis (PCA) is a common technique for dimensionality reduction.
Variants and Related Words
- Dimension (n): A measurable extent, such as length, width, or height. Also, an aspect or feature of a situation.
- We measured the dimensions of the room.
- Dimensional (adj): Relating to dimensions.
- The model shows a three-dimensional representation.
- Multidimensional (adj): Having or involving several dimensions or aspects.
- The problem requires a multidimensional approach.
Synonyms
- Spatial extent
- Number of dimensions
Related Phrases
- "Curse of dimensionality": A phrase in data science referring to various phenomena that arise when analyzing and organizing data in high-dimensional spaces.
- The algorithm's performance suffered due to the curse of dimensionality.
Noun
- the spatial property of having dimensions
- all matter has dimensionality