Support vector classifier with slack variables (soft margin)

MVSML (2022) eqs. (9.34)-(9.37) pp.354-355, dual (9.44)-(9.45) p.357. C is the box bound of (9.45); the realized slack total is reported as slack_sum. Delegates to the shared core mirror.

Usage

Svmsl(X, y, C, ...)

Arguments

X

Inputs, n by p.

y

Labels in {-1, +1}.

C

Box bound on the multipliers.

...

Passed to the dual solver.

Value

Named list; estimate is the margin.

References

MVSML (2022) eqs. (9.34)-(9.37), (9.44)-(9.45).

Examples

Svmsl(matrix(c(1, 2, 4, 5, 1, 2, 4, 3), ncol = 2), c(-1, -1, 1, 1), 1)
#> $beta
#> [1] 0.4000001 0.3999998
#> 
#> $beta0
#> [1] -2.333333
#> 
#> $norm_beta
#> [1] 0.5656854
#> 
#> $margin
#> [1] 1.767767
#> 
#> $zeta
#> [1] 0.0000000 0.2666667 0.1333335 0.1333332
#> 
#> $slack_sum
#> [1] 0.5333333
#> 
#> $n_violating
#> [1] 3
#> 
#> $n_misclassified
#> [1] 0
#> 
#> $alpha
#> [1] 0.000000e+00 1.000000e+00 5.999999e-01 1.316532e-07
#> 
#> $support_vectors
#> [1] 2 3
#> 
#> $objective
#> [1] 1.44
#> 
#> $estimate
#> [1] 1.767767
#> 
#> $method
#> [1] "SVM soft margin (MVSML 2022 eqs. 9.34-9.37)"
#>