A convex combination is a linear combination of data points (which can be vectors or scalars) where all coefficients are positive and sum up to 1. It is called a convex combination since all possible convex combinations (given the base vectors) will be part of a convex hull with the given datapoints as the vertices. A special case is with only two data points, where the value of the new point (formed by the convex combination) will lie on a straight line between the two points.