tropsvm {Rtropical}

Tropical Support Vector Machines

Description

Fit a discriminative two-class classifier via linear programming defined by the tropical hyperplane which maximizes the minimum tropical distance from data points to itself in order to separate the data points into sectors (half-spaces) in the tropical projective torus.

Usage

tropsvm(x, y, auto.assignment = FALSE, assignment = NULL, ind = 1)

Arguments

x

a data matrix, of dimension nobs x nvars; each row is an observation vector.

y

a response vector with one label for each row/component of x.

auto.assignment

a logical value indicating if to provide an assignment manually. If FALSE, an input is required, otherwise the function automatically finds a good assignment.(default: FALSE)

assignment

a numeric vector of length 4 indicating the sectors of tropical hyperplane that the data will be assigned to. The first and third elements in the assignment are the coordinates of an observed point in data matrix x believed from the first category where the maximum and second maximum of the vector addition between the fitted optimal tropical hyperplane and the point itself are achieved. The meanings for the second and the fourth element in the assignment are the same but for the points in the second category. Namely, the first and second values in the assignment are the indices of sectors where the two point clouds are assigned. Not needed when auto.assignment = TRUE. (default: NULL)

ind

a numeric value or a numeric vector ranging from 1 to 70 indicating which classification method to be used. There are 70 different classification methods. Details of a given method can be retrieved by summary. The different classification methods are proposed to resolve the issue when points fall on the intersections of sectors. Users can have personal choices if better knowledge is assumed. (default: 1)

Value

An object with S3 class tropsvm containing the fitted model, including:

apex

The negative apex of the fitted optimal tropical hyperplane.

assignment

The user-input or auto-found assignment.

index

The user-input classification method.

levels

The name of each category, consistent with categories in y.

See Also

predict, coef and the cv.tropsvm function.

Examples

# data generation
library(Rfast)
e <- 100
n <- 10
N <- 100
s <- 10
x <- rbind(
  rmvnorm(n, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
  rmvnorm(n, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
y <- as.factor(c(rep(1, n), rep(2, n)))
newx <- rbind(
  rmvnorm(N, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
  rmvnorm(N, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
newy <- as.factor(rep(c(1, 2), each = N))

# train the tropical svm
tropsvm_fit <- tropsvm(x, y, auto.assignment = TRUE, ind = 1)

coef(tropsvm_fit)

# test with new data
pred <- predict(tropsvm_fit, newx)

# check with accuracy
table(pred, newy)

# compute testing accuracy
sum(pred == newy) / length(newy)