NORMA {NORMA} | R Documentation |
Computes general noise SVR based on NORMA optimization.
NORMA(x, y, f_0 = 0, beta_0 = 0, lambda = 0, rate = function(t) { 1
}, kernel = linear_kernel, cost_der = ILF_cost_der,
cost_name = "ILF_cost_der", gamma = 1, max_iterations = nrow(x),
stopping_threshold = 0, trace = TRUE, no_beta = TRUE,
fixed_epsilon = TRUE, ...)
x |
|
y |
|
f_0 |
initial hypothesis. |
beta_0 |
initial value for offset |
lambda |
NORMA optimization parameter |
rate |
learning rate for NORMA optimization. Must be a function with one argument. |
kernel |
kernel function to use. Must be a function with three arguments such as |
cost_der |
Loss function derivative to use. See also ILF_cost_der. Must be "ILF_cost_der" when ILF derivative is used. |
cost_name |
|
gamma |
gaussian kernel parameter |
max_iterations |
maximum number of NORMA iterations computed. |
stopping_threshold |
value indicating when to stop NORMA optimization. See also 'Details'. |
trace |
|
no_beta |
|
fixed_epsilon |
|
... |
additional arguments to be passed to the low level functions. |
Optimization will stop when the sum of the differences between all training predicted values of present
iteration versus values from previous iteration does not exceeds stopping_threshold
.
Returns a list
containing:
matrix
representing \alpha
parameters of NORMA optimization in each iteration, one per row.
numeric
representing \beta
parameter of NORMA optimization in each iteration.
Number of NORMA iterations performed.
Jesus Prada, jesus.prada@estudiante.uam.es
Link to the scientific paper
Kivinen J., Smola A. J., Williamson R.C.: Online learning with kernels. In: IEEE transactions on signal processing, vol. 52, pp. 2165-2176, IEEE (2004).
with theoretical background for NORMA optimization is provided below.
http://realm.sics.se/papers/KivSmoWil04(1).pdf
NORMA(x=matrix(rnorm(10),nrow=10,ncol=1,byrow=TRUE),y=rnorm(10),kernel=function(x,y,gamma=0){x%*%y},
cost_der=function(phi,sigma_cuad,mu){return((phi-mu)/sigma_cuad)},cost_name="example",
sigma_cuad=1,mu=0)