add SVM solver

Author: yixuan

NAMESPACE

@@ -1,4 +1,4 @@
 importFrom(Rcpp, evalCpp)
 useDynLib(rehline, .registration = TRUE)
 
-export(rehline, elastic_qr, elastic_huber)
+export(rehline, elastic_huber, elastic_qr, svm)

R/svm.R

@@ -0,0 +1,45 @@
+##' Solving Regularized Support Vector Machine
+##'
+##' @description
+##' This function solves the regularized support vector machine
+##' of the following form:
+##' \deqn{
+##' \min_{\beta}\ \frac{C}{n}\sum_{i=1}^n \max(1-y_i x_i^T\beta,0) +
+##' \frac{1}{2}\Vert\beta\Vert_2^2
+##' }
+##' where \eqn{\beta\in\mathbb{R}^d} is a length-\eqn{d} vector,
+##' \eqn{x_i\in\mathbb{R}^d} is the feature vector for the \eqn{i}-th observation,
+##' \eqn{y_i\in\{-1,1\}} is a binary label,
+##' and \eqn{C} is the cost parameter.
+##'
+##' @param x          The data matrix \eqn{X=(x_1,\ldots,x_n)^T} of size
+##'                   \eqn{n\times d}, representing \eqn{n} observations
+##'                   and \eqn{d} features.
+##' @param y          The length-\eqn{n} response vector.
+##' @param C          The cost parameter.
+##' @param max_iter   Maximum number of iterations.
+##' @param tol        Tolerance parameter for convergence test.
+##' @param shrink     Whether to use the shrinkage algorithm.
+##' @param verbose    Level of verbosity.
+##'
+##' @return A list of the following components:
+##' \item{beta}{Optimized value of the \eqn{\beta} vector.}
+##' \item{xi,Lambda,Gamma}{Values of dual variables.}
+##' \item{niter}{Number of iterations used.}
+##' \item{dual_objfns}{Dual objective function values during the optimization process.}
+##'
+##' @author Yixuan Qiu \url{https://statr.me}
+##'
+##'         Ben Dai \url{https://bendai.org}
+##'
+svm = function(x, y, C = 1, max_iter = 1000, tol = 1e-5, shrink = TRUE, verbose = 0)
+{
+    n = nrow(x)
+
+    Umat = -C / n * matrix(y, nrow = 1)
+    Vmat = matrix(C / n, 1, n)
+
+    res = rehline(x, Umat, Vmat, max_iter = max_iter,
+                  tol = tol, shrink = shrink, verbose = verbose)
+    res$beta
+}

test/test_svm.R

@@ -1,4 +1,5 @@
 library(rehline)
+library(LiblineaR)
 library(reticulate)
 
 py_config()
@@ -23,13 +24,21 @@ read_npz = function(npz_file)
 
 dat = read_npz("./dataset/sim/exp_svm.npz")
 X = dat[["X"]]
+y = dat[["y"]]
 U = dat[["U"]]
 V = dat[["V"]]
+C = 0.5
 
 print(dim(X))
 print(dim(U))
 print(dim(V))
 
+# LibLinear
+set.seed(123)
+y = matrix(y, ncol = 1)
+res = LiblineaR(X, y, type = 3, cost = C, epsilon = 1e-6, bias = 0, verbose = TRUE)
+print(as.numeric(res$W))
+
 # Algorithm with shrinking
 set.seed(123)
 res = rehline(X, U, V, max_iter = 1000, tol = 1e-6, verbose = 1)
@@ -43,6 +52,11 @@ set.seed(123)
 res = rehline(X, U, V, max_iter = 1000, tol = 1e-6, shrink = FALSE, verbose = 1)
 print(res$beta)
 
+# Directly call svm()
+set.seed(123)
+res = svm(X, y, C = C * nrow(X), max_iter = 1000, tol = 1e-6, verbose = 1)
+print(res$beta)
+
 # Add constraints
 set.seed(123)
 K = 5