The dot product of two vectors a and b (sometimes called the inner product, or, since its result is a scalar, the scalar product) is denoted by a ∙ b, and is defined as: a ⋅ b = ‖ a ‖ ‖ b ‖ cos ⁡ θ , {\displaystyle \mathbf {a} \cdot \mathbf {b} =\left\|\mathbf {a} \right\|\left\|\mathbf {b} \right\|\cos \theta ,} where θ is the measure of the angle between a and b (see trigonometric function for an explanation of cosine). Geometrically, this means that a and b are drawn with a common start point, and then the length of a is multiplied with the length of the component of b that points in the same direction as a. The dot product can also be defined as the sum of the products of the components of each vector as a ⋅ b = a 1 b 1 + a 2 b 2 + a 3 b 3 . {\displaystyle \mathbf {a} \cdot \mathbf {b} =a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}.}

Transformation to binary[edit] This section discusses strategies for reducing the problem of multiclass classification to multiple binary classification problems. It can be categorized into one vs rest and one vs one. The techniques developed based on reducing the multi-class problem into multiple binary problems can also be called problem transformation techniques.