Hyperplane in machine learning

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space. If a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hyperplanes are the 1-dimensional lines.

In machine learning we can consider it as decision boundaries that help classify the data points. Data points falling on either side of the hyperplane can be attributed to different classes.

For example, let’s assume a line to be our one-dimensional Euclidean space (i.e. let’s say our datasets lie on a line). Now pick a point on the line, this point divides the line into two parts. The line has 1 dimension, while the point has 0 dimensions. So a point is a hyperplane of the line.

For two dimensions we can see that the separating line (1D) is a hyperplane. 

Similarly, for three dimensions a plane with two dimensions divides the 3d space into two parts and thus act as a hyperplane. Thus, for a space of n dimensions we have a hyperplane of n-1 dimensions separating it into two parts.