Let $f$ be a Radial-Basis Function Network:$$f(X) = \sum_{i=1}^N a_i p( \lvert \lvert b_i X - c_i \lvert \lvert)$$From Artificial Intelligence for Human Beings, the following depicts $f$:In the concrete example of this diagram, it seems that $N = 3$ (i.e., there are $3$ RBFs).Question 1: How is it possible that there are multiple outputs on the right of this diagram coming from multiple summations? In particular, there are 3 summations producing 3 outputs. But shouldn't there just be 1 summation producing 1 output? Are the second and third summations coming from a different set of RBFs than the first summation?The textbook continues:Because multiple summations exist, you can see the development of a classification problem. The highest summation specifies the predicted class. A regression problem indicates that the model will output a single numeric value.Question 2: Here, does the highest summation refer to the very top Output 1 in the diagram? Or does it refer to the largest summation in the numerical sense?Question 3: Where in the equation for $f$ above is the $Bias$ (depicted in the diagram as $Bias (1)$) represented?
Understanding This Graphical Depiction of a Radial-Basis Function Network
neural networks