SVMs project the data into a higher dimensional space, not lower. A mixed blob of dots on a plane can't be cleanly separated by a line into two colors, but if y

SVMs project the data into a higher dimensional space, not lower. A mixed blob of dots on a plane can't be cleanly separated by a line into two colors, but if you blow them out into a cube by some arbitrary projection, a plane will be able to separate them cleanly.