The Centroid Method

1. The Centroid:

   In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean (“average”) position of all the points in the shape.

   The definition extends to any object in n-dimensional space: its centroid is the mean position of all the points in all of the coordinate directions.

2. Procedure:

   Compute the mean (\(\mu_c\)) of all the vectors in class C and the mean (\(\mu_x\)) of all the vectors not in C.

3. Decision Function:

   \[f(x) = (\mu_c - \mu_x) \cdot \vec{x} - (\mu_c - \mu_x) \cdot \dfrac{\mu_c + \mu_x}{2}\]

4. Decision Boundary:

   The decision boundary is a Hyperplane that bisects the line segment with endpoints \(<\mu_c, \mu_x>\).