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//! # Support Vector Machines
//!
//! Support Vector Machines are a major branch of machine learning models and offer classification or
//! regression analysis of labeled datasets. They seek a discriminant, which separates the data in
//! an optimal way, e.g. have the fewest numbers of miss-classifications and maximizes the margin
//! between positive and negative classes. A support vector
//! contributes to the discriminant and is therefore important for the classification/regression
//! task. The balance between the number of support vectors and model performance can be controlled
//! with hyperparameters.
//!
//! More details can be found [here](https://en.wikipedia.org/wiki/Support_vector_machine)
//!
//! ## Available parameters in Classification and Regression
//!
//! For supervised classification tasks the C or Nu values are used to control this balance. In
//! [fit_c](SVClassify/fn.fit_c) the
//! C value controls the penalty given to missclassification and should be in the interval (0, inf). In
//! [fit_nu](SVClassify/fn.fit_nu.html) the Nu value controls the number of support vectors and should be in the interval (0, 1].
//!
//! For supervised classification with just one class of data a special classifier is available in
//! [fit_one_class](SVClassify/fn.fit_one_class.html). It also accepts a Nu value.
//!
//! For support vector regression two flavors are available. With
//! [fit_epsilon](SVRegress/fn.fit_epsilon.html) a regression task is learned while minimizing deviation
//! larger than epsilon. In [fit_nu](SVRegress/fn.fit_nu.html) the parameter epsilon is replaced with Nu
//! again and should be in the interval (0, 1]
//!
//! ## Kernel Methods
//! Normally the resulting discriminant is linear, but with [Kernel Methods](https://en.wikipedia.org/wiki/Kernel_method) non-linear relations between the input features
//! can be learned in order improve the performance of the model.
//!
//! For example to transform a dataset into a sparse RBF kernel with 10 non-zero distances you can
//! use `linfa_kernel`:
//! ```rust, ignore
//! use linfa_kernel::Kernel;
//! let train_kernel = Kernel::params()
//! .method(KernelMethod::Gaussian(30.0))
//! .transform(&train);
//! ```
//!
//! # The solver
//! This implementation uses Sequential Minimal Optimization, a widely used optimization tool for
//! convex problems. It selects in each optimization step two variables and updates the variables.
//! In each step it performs:
//!
//! 1. Find a variable, which violates the KKT conditions for the optimization problem
//! 2. Pick a second variables and crate a pair (a1, a2)
//! 3. Optimize the pair (a1, a2)
//!
//! After a couple of iterations the solution may be optimal.
//!
//! # Example
//! The wine quality data consists of 11 features, like "acid", "sugar", "sulfur dioxide", and
//! groups the quality into worst 3 to best 8. These are unified to good 8-7 and bad 3-6 to get a
//! binary classification task.
//!
//! With an RBF kernel and C-Support Vector Classification an
//! accuracy of 88.7% is reached within 79535 iterations and 316 support vectors. You can find the
//! example [here](https://github.com/rust-ml/linfa/blob/master/linfa-svm/examples/winequality.rs).
//! ```ignore
//! Fit SVM classifier with #1440 training points
//! Exited after 79535 iterations with obj = -46317.55802870996 and 316 support vectors
//!
//! classes | bad | good
//! bad | 133 | 9
//! good | 9 | 8
//!
//! accuracy 0.8867925, MCC 0.40720797
//! ```
use linfa::Float;
use ndarray::{ArrayBase, Data, Ix1};
use std::fmt;
use std::marker::PhantomData;
#[cfg(feature = "serde")]
use serde_crate::{Deserialize, Serialize};
mod classification;
pub mod error;
pub mod hyperparams;
mod permutable_kernel;
mod regression;
pub mod solver_smo;
pub use error::{Result, SvmError};
pub use hyperparams::{SvmParams, SvmValidParams};
use linfa_kernel::KernelMethod;
pub use solver_smo::{SeparatingHyperplane, SolverParams};
use std::ops::Mul;
/// Reason for stopping
///
/// SMO can either exit because a threshold is reached or the iterations are maxed out. To
/// differentiate between both this flag is passed with the solution.
#[cfg_attr(
feature = "serde",
derive(Serialize, Deserialize),
serde(crate = "serde_crate")
)]
#[derive(Debug, Clone, PartialEq, Eq, Hash)]
pub enum ExitReason {
ReachedThreshold,
ReachedIterations,
}
/// Fitted Support Vector Machines model
///
/// This is the result of the SMO optimizer and contains the support vectors, quality of solution
/// and optionally the linear hyperplane.
#[cfg_attr(
feature = "serde",
derive(Serialize, Deserialize),
serde(crate = "serde_crate")
)]
#[derive(Debug, Clone, PartialEq)]
pub struct Svm<F: Float, T> {
pub alpha: Vec<F>,
pub rho: F,
r: Option<F>,
exit_reason: ExitReason,
iterations: usize,
obj: F,
#[cfg_attr(
feature = "serde",
serde(bound(
serialize = "KernelMethod<F>: Serialize",
deserialize = "KernelMethod<F>: Deserialize<'de>"
))
)]
// the only thing I need the kernel for after the training is to
// compute the distances, but for that I only need the kernel method
// and not the whole inner matrix
kernel_method: KernelMethod<F>,
sep_hyperplane: SeparatingHyperplane<F>,
probability_coeffs: Option<(F, F)>,
phantom: PhantomData<T>,
}
impl<F: Float, T> Svm<F, T> {
/// Returns the number of support vectors
///
/// This function returns the number of support vectors which have an influence on the decision
/// outcome greater than zero.
pub fn nsupport(&self) -> usize {
self.alpha
.iter()
// around 1e-5 for f32 and 2e-14 for f64
.filter(|x| x.abs() > F::cast(100.) * F::epsilon())
.count()
}
pub(crate) fn with_phantom<S>(self) -> Svm<F, S> {
Svm {
alpha: self.alpha,
rho: self.rho,
r: self.r,
exit_reason: self.exit_reason,
obj: self.obj,
iterations: self.iterations,
sep_hyperplane: self.sep_hyperplane,
kernel_method: self.kernel_method,
probability_coeffs: self.probability_coeffs,
phantom: PhantomData,
}
}
/// Sums the inner product of `sample` and every one of the support vectors.
///
/// ## Parameters
///
/// * `sample`: the input sample
///
/// ## Returns
///
/// The sum of all inner products of `sample` and every one of the support vectors, scaled by their weight.
///
/// ## Panics
///
/// If the shape of `sample` is not compatible with the
/// shape of the support vectors
pub fn weighted_sum<D: Data<Elem = F>>(&self, sample: &ArrayBase<D, Ix1>) -> F {
match self.sep_hyperplane {
SeparatingHyperplane::Linear(ref x) => x.mul(sample).sum(),
SeparatingHyperplane::WeightedCombination(ref supp_vecs) => supp_vecs
.outer_iter()
.zip(
self.alpha
.iter()
.filter(|a| a.abs() > F::cast(100.) * F::epsilon()),
)
.map(|(x, a)| self.kernel_method.distance(x, sample.view()) * *a)
.sum(),
}
}
}
/// Display solution
///
/// In order to understand the solution of the SMO solver the objective, number of iterations and
/// required support vectors are printed here.
impl<'a, F: Float, T> fmt::Display for Svm<F, T> {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
match self.exit_reason {
ExitReason::ReachedThreshold => write!(
f,
"Exited after {} iterations with obj = {} and {} support vectors",
self.iterations,
self.obj,
self.nsupport()
),
ExitReason::ReachedIterations => write!(
f,
"Reached maximal iterations {} with obj = {} and {} support vectors",
self.iterations,
self.obj,
self.nsupport()
),
}
}
}
#[cfg(test)]
mod tests {
use crate::{Svm, SvmParams, SvmValidParams};
use linfa::prelude::*;
#[test]
fn autotraits() {
fn has_autotraits<T: Send + Sync + Sized + Unpin>() {}
has_autotraits::<Svm<f64, usize>>();
has_autotraits::<SvmParams<f64, usize>>();
has_autotraits::<SvmValidParams<f64, usize>>();
}
#[test]
fn test_iter_folding_for_classification() {
let mut dataset = linfa_datasets::winequality().map_targets(|x| *x > 6);
let params = Svm::<_, bool>::params()
.pos_neg_weights(7., 0.6)
.gaussian_kernel(80.0);
let avg_acc = dataset
.iter_fold(4, |training_set| params.fit(training_set).unwrap())
.map(|(model, valid)| {
model
.predict(valid.view())
.confusion_matrix(&valid)
.unwrap()
.accuracy()
})
.sum::<f32>()
/ 4_f32;
assert!(avg_acc >= 0.5)
}
/*#[test]
fn test_iter_folding_for_regression() {
let mut dataset: Dataset<f64, f64> = linfa_datasets::diabetes();
let params = Svm::params().linear_kernel().c_eps(100., 1.);
let _avg_r2 = dataset
.iter_fold(4, |training_set| params.fit(&training_set).unwrap())
.map(|(model, valid)| Array1::from(model.predict(valid.view())).r2(valid.targets()))
.sum::<f64>()
/ 4_f64;
}*/
}