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hyperplane
This term is primarily used in the fields of linear algebra, geometry, and machine learning. It describes a flat subspace that partitions a higher-dimensional space into two half-spaces. While a plane is a 2D object in 3D space, a hyperplane is the general version of this concept for any number of dimensions n, always having n-1 dimensions.
In the context of data science and support vector machines (SVMs), the hyperplane serves as the optimal decision boundary that separates different classes of data points. It is a technical term and is rarely used outside of mathematical or computational contexts.
Meanings
Examples
The algorithm seeks the optimal hyperplane to separate the two classes of data.
I wonder if this dataset can be linearly separated by a single hyperplane.
A hyperplane in three dimensional space is simply a flat plane.
We need to define the normal vector to determine the orientation of the hyperplane.
Can you explain how a hyperplane works in a ten dimensional space?
The distance from the point to the hyperplane is minimized during the training process.
The support vectors are the data points closest to the separating hyperplane.
It is impossible to visualize a hyperplane beyond three dimensions.