plot_perceptron: Display perceptron results for two-dimensional targets.
In jasmyace/rNeuralNetworkDesign: Learning Neural Networks by Programming in R

Description Usage Arguments Details Author(s) References See Also Examples

View source: R/plot_perceptron.R

Display perceptron results in two-dimensional space via two-dimensional targets. Decision boundaries, valid regions, and training data are included.

1	plot_perceptron(ans, xlo, xhi, ylo, yhi, repper = 100)

`ans`	A result originating from a call to package function `perceptron`.
`xlo`	The minimum value to display with respect to the x-axis.
`xhi`	The maximum value to display with respect to the x-axis.
`ylo`	The minimum value to display with respect to the y-axis.
`yhi`	The maximum value to display with respect to the y-axis.
`repper`	An integer giving the number of points to use to display linear decision boundaries. Resulting piecewise segments numbers `repper - 1`.

Function plot_perceptron assumes target vectors are two-dimensional, i.e., \mathbf{t} \in \mathbb{R}^2, so as to induce ease in depicting graphical results. Currently, the function assumes that no more than 26 distinct classes are to be included.

Output from function perceptron includes a final weights matrix \mathbf{W} and bias vector \mathbf{b}, each of which contributes to plotting final linear decision boundaries. Note that the i^{th} neuron corresponds to the i^{th} row of \mathbf{W}, say \mathbf{w}_i^T and bias vector \mathbf{b}, or b_i. From these, a linear decision boundary can be found.

To see this, let \mathbf{w}_i^T = [A_i \,\, B_i] and b_i = c_i, so that the i^{th} decision boundary has equation \mathbf{w}_i^T \begin{bmatrix} 1 \\ 1 \end{bmatrix} + b_i = 0, or A_i x_i + B_i y_i + c_i = 0. Simple rearrangement into the traditional line form of y = mx + b leads to y_i = -\frac{A_i}{B_i}x - \frac{c_i}{B}. Thus, the decision boundary of the i^{th} neuron has slope -\frac{A_i}{B_i} and y-intercept - \frac{c_i}{B}.

Function perceptron_plot uses these derived values of the slope and y-intercept to then draw linear decision boundaries. Colored regions always correspond to areas greater than the given line. In the case of a vertical line, the colored region subsumes +∞ if the weight row vector \mathbf{w}_i^T points towards -∞ along the y-axis, with the opposite true when \mathbf{w}_i^T points positively along the y-axis.

Jason Mitchell

Martin T. Hagan, Howard B. Demuth, Mark H. Beale and Orlando De Jesús. 2014. Neural Network Design (2nd. ed.). Martin Hagan, Stillwater, OK, USA.

perceptron

## Not run: 
p <- list(c(1, 1), c(1, 2), c(2, -1), c(2, 0), c(-1, 2), c(-2, 1), c(-1, -1), c(-2 ,-2))
t <- list(c(0, 0), c(0, 0), c(0, 1), c(0, 1), c(1, 0), c(1, 0), c(1, 1), c(1, 1))
verbose <- TRUE
W_0 <- matrix(c(1, 0, 0, 1), ncol = 2)
b_0 <- c(1, 1)
ans <- perceptron(p, t, verbose, W_0, b_0)

plot_perceptron(ans, -5, 5, -5, 5)
## End(Not run)