optimize_pos_above: Alternative algortihm for optimizing parameters

In COSNet: Cost Sensitive Network for node label prediction on graphs with highly unbalanced labelings

Description

Alternative algorithm to compute the two parameters: 'alpha', determining neurons activation values, and the neuron thresholds 'c'.

Usage

optimize_pos_above(pos_vect, neg_vect, training_labels, res)

Arguments

pos_vect	vector of abscissae of the points to be separated
neg_vect	vector of ordinates of the points to be separated
training_labels	1/-1 vector of the point labels
res	list containing the optimum angle (field alpha), neuron threshold (field c), maximum F-score (field Fscore) and positive halfplane (field pos_half) computed by the procedure corresponding to the choice 1) of function optimizep.

Details

Function to optimize the the parameters 'alpha' and 'c' when the function optimizep determines that the maximum F-score corresponds to the half-plane above the separation line. The algorithm works in three steps: 1) Selecting all the points which lie on the Y-axis. The aim is to choose a positive point which will be the center of the line bundle we consider in the next step. We sort the selected points by ordinate and for each positive point we compute the F-score of the almost vertical line (but with negative slope) crossing this point considering solely the selected points. Then we choose the point k which corresponds to the highest F-score. 2) The algorithm computes the slopes of the lines crossing the point k and each point not lying on the Y-axis. Then it searches the line, among those with negative slope, which maximizes the F-score criterion by sorting the computed lines according to their slopes in an increasing order. Consequently, the angle alpha relative to the optimum line is in the interval ]pi/2, pi[. 3) Compute the intercepts of the straight lines whose slope is tan(alpha) and crossing each available point. The optimum line is identified by scanning the computed lines according to their intercept in an increasing order. Let q be the intercept of the optimum line y = tan(alpha)z + q, then we set c = -cos(alpha)q. If there are no positive point with abscissa 0, the function returns the optimal parameters contained in input argument 'res' computed by the procedure corresponding to the choice 1) of function optimizep.

Value

list res with 3 components

res$alpha	value of the optimum angle alpha
res$c	value of the optimum threshold c
res$Fscore	value of the optimum F-score
res$pos_half	position of the positive half-plane (-1 below, 1 above the optimum straith line)

See Also

optimizep

Examples

library(bionetdata);
data(Yeast.STRING.data);
data(Yeast.STRING.FunCat);
n <- nrow(Yeast.STRING.data);
## removing dummy node 00
Yeast.STRING.FunCat <- Yeast.STRING.FunCat[,
                        -which(colnames(Yeast.STRING.FunCat) == "00")];
## selecting the class with index 1
class <- 1;
labels <- as.vector(Yeast.STRING.data[, class]);
names(labels) <- rownames(Yeast.STRING.FunCat);
labels <- as.vector(Yeast.STRING.FunCat[, class]);
names(labels) <- rownames(Yeast.STRING.FunCat);
## partitioning the data
folds <- find.division.strat(labels, 1:n, 3);
labels[labels <= 0] <- -1;
test.set <- folds[[1]];
training.set <- setdiff(1:n, test.set);
labels[test.set] <- 0;
points <- generate_points(Yeast.STRING.data, test.set, labels);
## setting values for the parameter
res <- list(alpha=pi/2, c=0, Fscore=0, pos_half=-1);
opt_parameters <- optimize_pos_above(points$pos_vect[training.set],
                    points$neg_vect[training.set], labels[training.set], res);
str(opt_parameters);

COSNet documentation built on Nov. 8, 2020, 8:12 p.m.