Catgorising with Euclidean Distance

• If you have a bunch of items of different categories represented by vectors, you can categorise new items by saying the category of the known item that is nearest.
• A vector is just a position in a coordinate system.
• In a 2D system, this is just an x and a y coordinate.
• You judge distance using the pythagorean theorem (sqrt(square(x0-x1)+ square(y0-y1)).
• You can do this in any coordinate system.
• In three dimensions (sqrt(square(x0-x1)+ square(y0-y1)+square(z0-z1)).
• In 64 dimensions (sqrt(square(x0,0-x0,1)+ square(x1,0-x1,1)+....square(x63,0-x63,1)).
• How do you do the coursework with this?