239c00428f
* uncomment test * Add random test for logistic regression * linting * Bump version * Add test for logistic regression * linting * initial commit * final * final-clean * Bump to 0.4.0 * Fix linter * cleanup * Update CHANDELOG with breaking changes * Update CHANDELOG date * Add functional methods to DenseMatrix implementation * linting * add type declaration in test * Fix Wasm tests failing * linting * fix tests * linting * Add type annotations on BBDTree constructor * fix clippy * fix clippy * fix tests * bump version * run fmt. fix changelog --------- Co-authored-by: Edmund Cape <edmund@Edmunds-MacBook-Pro.local>
1119 lines
36 KiB
Rust
1119 lines
36 KiB
Rust
//! # Support Vector Classifier.
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//!
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//! Support Vector Classifier (SVC) is a binary classifier that uses an optimal hyperplane to separate the points in the input variable space by their class.
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//!
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//! During training, SVC chooses a Maximal-Margin hyperplane that can separate all training instances with the largest margin.
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//! The margin is calculated as the perpendicular distance from the boundary to only the closest points. Hence, only these points are relevant in defining
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//! the hyperplane and in the construction of the classifier. These points are called the support vectors.
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//!
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//! While SVC selects a hyperplane with the largest margin it allows some points in the training data to violate the separating boundary.
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//! The parameter `C` > 0 gives you control over how SVC will handle violating points. The bigger the value of this parameter the more we penalize the algorithm
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//! for incorrectly classified points. In other words, setting this parameter to a small value will result in a classifier that allows for a big number
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//! of misclassified samples. Mathematically, SVC optimization problem can be defined as:
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//!
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//! \\[\underset{w, \zeta}{minimize} \space \space \frac{1}{2} \lVert \vec{w} \rVert^2 + C\sum_{i=1}^m \zeta_i \\]
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//!
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//! subject to:
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//!
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//! \\[y_i(\langle\vec{w}, \vec{x}_i \rangle + b) \geq 1 - \zeta_i \\]
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//! \\[\zeta_i \geq 0 for \space any \space i = 1, ... , m\\]
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//!
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//! Where \\( m \\) is a number of training samples, \\( y_i \\) is a label value (either 1 or -1) and \\(\langle\vec{w}, \vec{x}_i \rangle + b\\) is a decision boundary.
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//!
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//! To solve this optimization problem, `smartcore` uses an [approximate SVM solver](https://leon.bottou.org/projects/lasvm).
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//! The optimizer reaches accuracies similar to that of a real SVM after performing two passes through the training examples. You can choose the number of passes
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//! through the data that the algorithm takes by changing the `epoch` parameter of the classifier.
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//!
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//! Example:
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//!
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//! ```
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//! use smartcore::linalg::basic::matrix::DenseMatrix;
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//! use smartcore::svm::Kernels;
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//! use smartcore::svm::svc::{SVC, SVCParameters};
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//!
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//! // Iris dataset
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//! let x = DenseMatrix::from_2d_array(&[
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//! &[5.1, 3.5, 1.4, 0.2],
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//! &[4.9, 3.0, 1.4, 0.2],
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//! &[4.7, 3.2, 1.3, 0.2],
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//! &[4.6, 3.1, 1.5, 0.2],
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//! &[5.0, 3.6, 1.4, 0.2],
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//! &[5.4, 3.9, 1.7, 0.4],
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//! &[4.6, 3.4, 1.4, 0.3],
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//! &[5.0, 3.4, 1.5, 0.2],
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//! &[4.4, 2.9, 1.4, 0.2],
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//! &[4.9, 3.1, 1.5, 0.1],
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//! &[7.0, 3.2, 4.7, 1.4],
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//! &[6.4, 3.2, 4.5, 1.5],
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//! &[6.9, 3.1, 4.9, 1.5],
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//! &[5.5, 2.3, 4.0, 1.3],
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//! &[6.5, 2.8, 4.6, 1.5],
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//! &[5.7, 2.8, 4.5, 1.3],
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//! &[6.3, 3.3, 4.7, 1.6],
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//! &[4.9, 2.4, 3.3, 1.0],
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//! &[6.6, 2.9, 4.6, 1.3],
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//! &[5.2, 2.7, 3.9, 1.4],
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//! ]).unwrap();
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//! let y = vec![ -1, -1, -1, -1, -1, -1, -1, -1,
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//! 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1];
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//!
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//! let knl = Kernels::linear();
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//! let params = &SVCParameters::default().with_c(200.0).with_kernel(knl);
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//! let svc = SVC::fit(&x, &y, params).unwrap();
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//!
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//! let y_hat = svc.predict(&x).unwrap();
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//! ```
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//!
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//! ## References:
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//!
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//! * ["Support Vector Machines", Kowalczyk A., 2017](https://www.svm-tutorial.com/2017/10/support-vector-machines-succinctly-released/)
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//! * ["Fast Kernel Classifiers with Online and Active Learning", Bordes A., Ertekin S., Weston J., Bottou L., 2005](https://www.jmlr.org/papers/volume6/bordes05a/bordes05a.pdf)
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//!
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//! <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
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//! <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
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use std::collections::{HashMap, HashSet};
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use std::fmt::Debug;
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use std::marker::PhantomData;
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use num::Bounded;
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use rand::seq::SliceRandom;
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#[cfg(feature = "serde")]
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use serde::{Deserialize, Serialize};
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use crate::api::{PredictorBorrow, SupervisedEstimatorBorrow};
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use crate::error::{Failed, FailedError};
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use crate::linalg::basic::arrays::{Array1, Array2, MutArray};
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use crate::numbers::basenum::Number;
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use crate::numbers::realnum::RealNumber;
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use crate::rand_custom::get_rng_impl;
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use crate::svm::Kernel;
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#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
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#[derive(Debug)]
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/// SVC Parameters
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pub struct SVCParameters<TX: Number + RealNumber, TY: Number + Ord, X: Array2<TX>, Y: Array1<TY>> {
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/// Number of epochs.
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pub epoch: usize,
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/// Regularization parameter.
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pub c: TX,
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/// Tolerance for stopping criterion.
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pub tol: TX,
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/// The kernel function.
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#[cfg_attr(
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all(feature = "serde", target_arch = "wasm32"),
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serde(skip_serializing, skip_deserializing)
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)]
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pub kernel: Option<Box<dyn Kernel>>,
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/// Unused parameter.
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m: PhantomData<(X, Y, TY)>,
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/// Controls the pseudo random number generation for shuffling the data for probability estimates
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seed: Option<u64>,
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}
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#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
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#[derive(Debug)]
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#[cfg_attr(
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feature = "serde",
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serde(bound(
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serialize = "TX: Serialize, TY: Serialize, X: Serialize, Y: Serialize",
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deserialize = "TX: Deserialize<'de>, TY: Deserialize<'de>, X: Deserialize<'de>, Y: Deserialize<'de>",
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))
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)]
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/// Support Vector Classifier
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pub struct SVC<'a, TX: Number + RealNumber, TY: Number + Ord, X: Array2<TX>, Y: Array1<TY>> {
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classes: Option<Vec<TY>>,
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instances: Option<Vec<Vec<TX>>>,
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#[cfg_attr(feature = "serde", serde(skip))]
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parameters: Option<&'a SVCParameters<TX, TY, X, Y>>,
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w: Option<Vec<TX>>,
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b: Option<TX>,
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phantomdata: PhantomData<(X, Y)>,
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}
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#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
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#[derive(Debug)]
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struct SupportVector<TX: Number + RealNumber> {
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index: usize,
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x: Vec<TX>,
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alpha: f64,
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grad: f64,
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cmin: f64,
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cmax: f64,
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k: f64,
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}
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struct Cache<TX: Number + RealNumber, TY: Number + Ord, X: Array2<TX>, Y: Array1<TY>> {
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data: HashMap<(usize, usize), f64>,
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phantom: PhantomData<(X, Y, TY, TX)>,
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}
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struct Optimizer<'a, TX: Number + RealNumber, TY: Number + Ord, X: Array2<TX>, Y: Array1<TY>> {
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x: &'a X,
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y: &'a Y,
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parameters: &'a SVCParameters<TX, TY, X, Y>,
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svmin: usize,
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svmax: usize,
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gmin: TX,
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gmax: TX,
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tau: TX,
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sv: Vec<SupportVector<TX>>,
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recalculate_minmax_grad: bool,
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}
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impl<TX: Number + RealNumber, TY: Number + Ord, X: Array2<TX>, Y: Array1<TY>>
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SVCParameters<TX, TY, X, Y>
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{
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/// Number of epochs.
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pub fn with_epoch(mut self, epoch: usize) -> Self {
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self.epoch = epoch;
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self
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}
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/// Regularization parameter.
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pub fn with_c(mut self, c: TX) -> Self {
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self.c = c;
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self
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}
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/// Tolerance for stopping criterion.
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pub fn with_tol(mut self, tol: TX) -> Self {
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self.tol = tol;
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self
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}
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/// The kernel function.
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pub fn with_kernel<K: Kernel + 'static>(mut self, kernel: K) -> Self {
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self.kernel = Some(Box::new(kernel));
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self
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}
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/// Seed for the pseudo random number generator.
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pub fn with_seed(mut self, seed: Option<u64>) -> Self {
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self.seed = seed;
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self
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}
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}
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impl<TX: Number + RealNumber, TY: Number + Ord, X: Array2<TX>, Y: Array1<TY>> Default
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for SVCParameters<TX, TY, X, Y>
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{
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fn default() -> Self {
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SVCParameters {
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epoch: 2,
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c: TX::one(),
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tol: TX::from_f64(1e-3).unwrap(),
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kernel: Option::None,
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m: PhantomData,
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seed: Option::None,
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}
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}
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}
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impl<'a, TX: Number + RealNumber, TY: Number + Ord, X: Array2<TX>, Y: Array1<TY>>
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SupervisedEstimatorBorrow<'a, X, Y, SVCParameters<TX, TY, X, Y>> for SVC<'a, TX, TY, X, Y>
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{
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fn new() -> Self {
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Self {
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classes: Option::None,
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instances: Option::None,
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parameters: Option::None,
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w: Option::None,
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b: Option::None,
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phantomdata: PhantomData,
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}
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}
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fn fit(
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x: &'a X,
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y: &'a Y,
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parameters: &'a SVCParameters<TX, TY, X, Y>,
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) -> Result<Self, Failed> {
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SVC::fit(x, y, parameters)
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}
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}
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impl<'a, TX: Number + RealNumber, TY: Number + Ord, X: Array2<TX>, Y: Array1<TY>>
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PredictorBorrow<'a, X, TX> for SVC<'a, TX, TY, X, Y>
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{
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fn predict(&self, x: &'a X) -> Result<Vec<TX>, Failed> {
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Ok(self.predict(x).unwrap())
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}
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}
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impl<'a, TX: Number + RealNumber, TY: Number + Ord, X: Array2<TX> + 'a, Y: Array1<TY> + 'a>
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SVC<'a, TX, TY, X, Y>
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{
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/// Fits SVC to your data.
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/// * `x` - _NxM_ matrix with _N_ observations and _M_ features in each observation.
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/// * `y` - class labels
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/// * `parameters` - optional parameters, use `Default::default()` to set parameters to default values.
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pub fn fit(
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x: &'a X,
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y: &'a Y,
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parameters: &'a SVCParameters<TX, TY, X, Y>,
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) -> Result<SVC<'a, TX, TY, X, Y>, Failed> {
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let (n, _) = x.shape();
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if parameters.kernel.is_none() {
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return Err(Failed::because(
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FailedError::ParametersError,
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"kernel should be defined at this point, please use `with_kernel()`",
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));
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}
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if n != y.shape() {
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return Err(Failed::fit(
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"Number of rows of X doesn\'t match number of rows of Y",
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));
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}
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let classes = y.unique();
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if classes.len() != 2 {
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return Err(Failed::fit(&format!(
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"Incorrect number of classes: {}",
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classes.len()
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)));
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}
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// Make sure class labels are either 1 or -1
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for e in y.iterator(0) {
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let y_v = e.to_i32().unwrap();
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if y_v != -1 && y_v != 1 {
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return Err(Failed::because(
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FailedError::ParametersError,
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"Class labels must be 1 or -1",
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));
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}
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}
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let optimizer: Optimizer<'_, TX, TY, X, Y> = Optimizer::new(x, y, parameters);
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let (support_vectors, weight, b) = optimizer.optimize();
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Ok(SVC::<'a> {
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classes: Some(classes),
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instances: Some(support_vectors),
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parameters: Some(parameters),
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w: Some(weight),
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b: Some(b),
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phantomdata: PhantomData,
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})
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}
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/// Predicts estimated class labels from `x`
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/// * `x` - _KxM_ data where _K_ is number of observations and _M_ is number of features.
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pub fn predict(&self, x: &'a X) -> Result<Vec<TX>, Failed> {
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let mut y_hat: Vec<TX> = self.decision_function(x)?;
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for i in 0..y_hat.len() {
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let cls_idx = match *y_hat.get(i).unwrap() > TX::zero() {
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false => TX::from(self.classes.as_ref().unwrap()[0]).unwrap(),
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true => TX::from(self.classes.as_ref().unwrap()[1]).unwrap(),
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};
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y_hat.set(i, cls_idx);
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}
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Ok(y_hat)
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}
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/// Evaluates the decision function for the rows in `x`
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/// * `x` - _KxM_ data where _K_ is number of observations and _M_ is number of features.
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pub fn decision_function(&self, x: &'a X) -> Result<Vec<TX>, Failed> {
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let (n, _) = x.shape();
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let mut y_hat: Vec<TX> = Array1::zeros(n);
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let mut row = Vec::with_capacity(n);
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for i in 0..n {
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row.clear();
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row.extend(x.get_row(i).iterator(0).copied());
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let row_pred: TX = self.predict_for_row(&row);
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y_hat.set(i, row_pred);
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}
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Ok(y_hat)
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}
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fn predict_for_row(&self, x: &[TX]) -> TX {
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let mut f = self.b.unwrap();
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let xi: Vec<_> = x.iter().map(|e| e.to_f64().unwrap()).collect();
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for i in 0..self.instances.as_ref().unwrap().len() {
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let xj: Vec<_> = self.instances.as_ref().unwrap()[i]
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.iter()
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.map(|e| e.to_f64().unwrap())
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.collect();
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f += self.w.as_ref().unwrap()[i]
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* TX::from(
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self.parameters
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|
.as_ref()
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.unwrap()
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.kernel
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|
.as_ref()
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|
.unwrap()
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.apply(&xi, &xj)
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.unwrap(),
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)
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.unwrap();
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}
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|
|
|
f
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}
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}
|
|
|
|
impl<'a, TX: Number + RealNumber, TY: Number + Ord, X: Array2<TX>, Y: Array1<TY>> PartialEq
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for SVC<'a, TX, TY, X, Y>
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|
{
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|
fn eq(&self, other: &Self) -> bool {
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|
if (self.b.unwrap().sub(other.b.unwrap())).abs() > TX::epsilon() * TX::two()
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|| self.w.as_ref().unwrap().len() != other.w.as_ref().unwrap().len()
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|| self.instances.as_ref().unwrap().len() != other.instances.as_ref().unwrap().len()
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|
{
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|
false
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|
} else {
|
|
if !self
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|
.w
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|
.as_ref()
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|
.unwrap()
|
|
.approximate_eq(other.w.as_ref().unwrap(), TX::epsilon())
|
|
{
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|
return false;
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|
}
|
|
for i in 0..self.w.as_ref().unwrap().len() {
|
|
if (self.w.as_ref().unwrap()[i].sub(other.w.as_ref().unwrap()[i])).abs()
|
|
> TX::epsilon()
|
|
{
|
|
return false;
|
|
}
|
|
}
|
|
for i in 0..self.instances.as_ref().unwrap().len() {
|
|
if !(self.instances.as_ref().unwrap()[i] == other.instances.as_ref().unwrap()[i]) {
|
|
return false;
|
|
}
|
|
}
|
|
true
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|
}
|
|
}
|
|
}
|
|
|
|
impl<TX: Number + RealNumber> SupportVector<TX> {
|
|
fn new(i: usize, x: Vec<TX>, y: TX, g: f64, c: f64, k_v: f64) -> SupportVector<TX> {
|
|
let (cmin, cmax) = if y > TX::zero() {
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|
(0f64, c)
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|
} else {
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|
(-c, 0f64)
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|
};
|
|
SupportVector {
|
|
index: i,
|
|
x,
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|
grad: g,
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|
k: k_v,
|
|
alpha: 0f64,
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|
cmin,
|
|
cmax,
|
|
}
|
|
}
|
|
}
|
|
|
|
impl<TX: Number + RealNumber, TY: Number + Ord, X: Array2<TX>, Y: Array1<TY>> Cache<TX, TY, X, Y> {
|
|
fn new() -> Cache<TX, TY, X, Y> {
|
|
Cache {
|
|
data: HashMap::new(),
|
|
phantom: PhantomData,
|
|
}
|
|
}
|
|
|
|
fn get(&mut self, i: &SupportVector<TX>, j: &SupportVector<TX>, or_insert: f64) -> f64 {
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|
let idx_i = i.index;
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|
let idx_j = j.index;
|
|
#[allow(clippy::or_fun_call)]
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|
let entry = self.data.entry((idx_i, idx_j)).or_insert(or_insert);
|
|
*entry
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|
}
|
|
|
|
fn insert(&mut self, key: (usize, usize), value: f64) {
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|
self.data.insert(key, value);
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|
}
|
|
|
|
fn drop(&mut self, idxs_to_drop: HashSet<usize>) {
|
|
self.data.retain(|k, _| !idxs_to_drop.contains(&k.0));
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|
}
|
|
}
|
|
|
|
impl<'a, TX: Number + RealNumber, TY: Number + Ord, X: Array2<TX>, Y: Array1<TY>>
|
|
Optimizer<'a, TX, TY, X, Y>
|
|
{
|
|
fn new(
|
|
x: &'a X,
|
|
y: &'a Y,
|
|
parameters: &'a SVCParameters<TX, TY, X, Y>,
|
|
) -> Optimizer<'a, TX, TY, X, Y> {
|
|
let (n, _) = x.shape();
|
|
|
|
Optimizer {
|
|
x,
|
|
y,
|
|
parameters,
|
|
svmin: 0,
|
|
svmax: 0,
|
|
gmin: <TX as Bounded>::max_value(),
|
|
gmax: <TX as Bounded>::min_value(),
|
|
tau: TX::from_f64(1e-12).unwrap(),
|
|
sv: Vec::with_capacity(n),
|
|
recalculate_minmax_grad: true,
|
|
}
|
|
}
|
|
|
|
fn optimize(mut self) -> (Vec<Vec<TX>>, Vec<TX>, TX) {
|
|
let (n, _) = self.x.shape();
|
|
|
|
let mut cache: Cache<TX, TY, X, Y> = Cache::new();
|
|
|
|
self.initialize(&mut cache);
|
|
|
|
let tol = self.parameters.tol;
|
|
let good_enough = TX::from_i32(1000).unwrap();
|
|
|
|
let mut x = Vec::with_capacity(n);
|
|
for _ in 0..self.parameters.epoch {
|
|
for i in self.permutate(n) {
|
|
x.clear();
|
|
x.extend(self.x.get_row(i).iterator(0).take(n).copied());
|
|
self.process(i, &x, *self.y.get(i), &mut cache);
|
|
loop {
|
|
self.reprocess(tol, &mut cache);
|
|
self.find_min_max_gradient();
|
|
if self.gmax - self.gmin < good_enough {
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
self.finish(&mut cache);
|
|
|
|
let mut support_vectors: Vec<Vec<TX>> = Vec::new();
|
|
let mut w: Vec<TX> = Vec::new();
|
|
|
|
let b = (self.gmax + self.gmin) / TX::two();
|
|
|
|
for v in self.sv {
|
|
support_vectors.push(v.x);
|
|
w.push(TX::from(v.alpha).unwrap());
|
|
}
|
|
|
|
(support_vectors, w, b)
|
|
}
|
|
|
|
fn initialize(&mut self, cache: &mut Cache<TX, TY, X, Y>) {
|
|
let (n, _) = self.x.shape();
|
|
let few = 5;
|
|
let mut cp = 0;
|
|
let mut cn = 0;
|
|
|
|
let mut x = Vec::with_capacity(n);
|
|
for i in self.permutate(n) {
|
|
x.clear();
|
|
x.extend(self.x.get_row(i).iterator(0).take(n).copied());
|
|
if *self.y.get(i) == TY::one() && cp < few {
|
|
if self.process(i, &x, *self.y.get(i), cache) {
|
|
cp += 1;
|
|
}
|
|
} else if *self.y.get(i) == TY::from(-1).unwrap()
|
|
&& cn < few
|
|
&& self.process(i, &x, *self.y.get(i), cache)
|
|
{
|
|
cn += 1;
|
|
}
|
|
|
|
if cp >= few && cn >= few {
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
fn process(&mut self, i: usize, x: &[TX], y: TY, cache: &mut Cache<TX, TY, X, Y>) -> bool {
|
|
for j in 0..self.sv.len() {
|
|
if self.sv[j].index == i {
|
|
return true;
|
|
}
|
|
}
|
|
|
|
let mut g: f64 = y.to_f64().unwrap();
|
|
|
|
let mut cache_values: Vec<((usize, usize), TX)> = Vec::new();
|
|
|
|
for v in self.sv.iter() {
|
|
let xi: Vec<_> = v.x.iter().map(|e| e.to_f64().unwrap()).collect();
|
|
let xj: Vec<_> = x.iter().map(|e| e.to_f64().unwrap()).collect();
|
|
let k = self
|
|
.parameters
|
|
.kernel
|
|
.as_ref()
|
|
.unwrap()
|
|
.apply(&xi, &xj)
|
|
.unwrap();
|
|
cache_values.push(((i, v.index), TX::from(k).unwrap()));
|
|
g -= v.alpha * k;
|
|
}
|
|
|
|
self.find_min_max_gradient();
|
|
|
|
if self.gmin < self.gmax
|
|
&& ((y > TY::zero() && g < self.gmin.to_f64().unwrap())
|
|
|| (y < TY::zero() && g > self.gmax.to_f64().unwrap()))
|
|
{
|
|
return false;
|
|
}
|
|
|
|
for v in cache_values {
|
|
cache.insert(v.0, v.1.to_f64().unwrap());
|
|
}
|
|
|
|
let x_f64: Vec<_> = x.iter().map(|e| e.to_f64().unwrap()).collect();
|
|
let k_v = self
|
|
.parameters
|
|
.kernel
|
|
.as_ref()
|
|
.expect("Kernel should be defined at this point, use with_kernel() on parameters")
|
|
.apply(&x_f64, &x_f64)
|
|
.unwrap();
|
|
|
|
self.sv.insert(
|
|
0,
|
|
SupportVector::<TX>::new(
|
|
i,
|
|
x.to_vec(),
|
|
TX::from(y).unwrap(),
|
|
g,
|
|
self.parameters.c.to_f64().unwrap(),
|
|
k_v,
|
|
),
|
|
);
|
|
|
|
if y > TY::zero() {
|
|
self.smo(None, Some(0), TX::zero(), cache);
|
|
} else {
|
|
self.smo(Some(0), None, TX::zero(), cache);
|
|
}
|
|
|
|
true
|
|
}
|
|
|
|
fn reprocess(&mut self, tol: TX, cache: &mut Cache<TX, TY, X, Y>) -> bool {
|
|
let status = self.smo(None, None, tol, cache);
|
|
self.clean(cache);
|
|
status
|
|
}
|
|
|
|
fn finish(&mut self, cache: &mut Cache<TX, TY, X, Y>) {
|
|
let mut max_iter = self.sv.len();
|
|
|
|
while self.smo(None, None, self.parameters.tol, cache) && max_iter > 0 {
|
|
max_iter -= 1;
|
|
}
|
|
|
|
self.clean(cache);
|
|
}
|
|
|
|
fn find_min_max_gradient(&mut self) {
|
|
if !self.recalculate_minmax_grad {
|
|
return;
|
|
}
|
|
|
|
self.gmin = <TX as Bounded>::max_value();
|
|
self.gmax = <TX as Bounded>::min_value();
|
|
|
|
for i in 0..self.sv.len() {
|
|
let v = &self.sv[i];
|
|
let g = v.grad;
|
|
let a = v.alpha;
|
|
if g < self.gmin.to_f64().unwrap() && a > v.cmin {
|
|
self.gmin = TX::from(g).unwrap();
|
|
self.svmin = i;
|
|
}
|
|
if g > self.gmax.to_f64().unwrap() && a < v.cmax {
|
|
self.gmax = TX::from(g).unwrap();
|
|
self.svmax = i;
|
|
}
|
|
}
|
|
|
|
self.recalculate_minmax_grad = false
|
|
}
|
|
|
|
fn clean(&mut self, cache: &mut Cache<TX, TY, X, Y>) {
|
|
self.find_min_max_gradient();
|
|
|
|
let gmax = self.gmax;
|
|
let gmin = self.gmin;
|
|
|
|
let mut idxs_to_drop: HashSet<usize> = HashSet::new();
|
|
|
|
self.sv.retain(|v| {
|
|
if v.alpha == 0f64
|
|
&& ((TX::from(v.grad).unwrap() >= gmax && TX::zero() >= TX::from(v.cmax).unwrap())
|
|
|| (TX::from(v.grad).unwrap() <= gmin
|
|
&& TX::zero() <= TX::from(v.cmin).unwrap()))
|
|
{
|
|
idxs_to_drop.insert(v.index);
|
|
return false;
|
|
};
|
|
true
|
|
});
|
|
|
|
cache.drop(idxs_to_drop);
|
|
self.recalculate_minmax_grad = true;
|
|
}
|
|
|
|
fn permutate(&self, n: usize) -> Vec<usize> {
|
|
let mut rng = get_rng_impl(self.parameters.seed);
|
|
let mut range: Vec<usize> = (0..n).collect();
|
|
range.shuffle(&mut rng);
|
|
range
|
|
}
|
|
|
|
fn select_pair(
|
|
&mut self,
|
|
idx_1: Option<usize>,
|
|
idx_2: Option<usize>,
|
|
cache: &mut Cache<TX, TY, X, Y>,
|
|
) -> Option<(usize, usize, f64)> {
|
|
match (idx_1, idx_2) {
|
|
(None, None) => {
|
|
if self.gmax > -self.gmin {
|
|
self.select_pair(None, Some(self.svmax), cache)
|
|
} else {
|
|
self.select_pair(Some(self.svmin), None, cache)
|
|
}
|
|
}
|
|
(Some(idx_1), None) => {
|
|
let sv1 = &self.sv[idx_1];
|
|
let mut idx_2 = None;
|
|
let mut k_v_12 = None;
|
|
let km = sv1.k;
|
|
let gm = sv1.grad;
|
|
let mut best = 0f64;
|
|
let xi: Vec<_> = sv1.x.iter().map(|e| e.to_f64().unwrap()).collect();
|
|
for i in 0..self.sv.len() {
|
|
let v = &self.sv[i];
|
|
let xj: Vec<_> = v.x.iter().map(|e| e.to_f64().unwrap()).collect();
|
|
let z = v.grad - gm;
|
|
let k = cache.get(
|
|
sv1,
|
|
v,
|
|
self.parameters
|
|
.kernel
|
|
.as_ref()
|
|
.unwrap()
|
|
.apply(&xi, &xj)
|
|
.unwrap(),
|
|
);
|
|
let mut curv = km + v.k - 2f64 * k;
|
|
if curv <= 0f64 {
|
|
curv = self.tau.to_f64().unwrap();
|
|
}
|
|
let mu = z / curv;
|
|
if (mu > 0f64 && v.alpha < v.cmax) || (mu < 0f64 && v.alpha > v.cmin) {
|
|
let gain = z * mu;
|
|
if gain > best {
|
|
best = gain;
|
|
idx_2 = Some(i);
|
|
k_v_12 = Some(k);
|
|
}
|
|
}
|
|
}
|
|
|
|
let xi: Vec<_> = self.sv[idx_1]
|
|
.x
|
|
.iter()
|
|
.map(|e| e.to_f64().unwrap())
|
|
.collect::<Vec<_>>();
|
|
|
|
idx_2.map(|idx_2| {
|
|
(
|
|
idx_1,
|
|
idx_2,
|
|
k_v_12.unwrap_or_else(|| {
|
|
self.parameters
|
|
.kernel
|
|
.as_ref()
|
|
.unwrap()
|
|
.apply(
|
|
&xi,
|
|
&self.sv[idx_2]
|
|
.x
|
|
.iter()
|
|
.map(|e| e.to_f64().unwrap())
|
|
.collect::<Vec<_>>(),
|
|
)
|
|
.unwrap()
|
|
}),
|
|
)
|
|
})
|
|
}
|
|
(None, Some(idx_2)) => {
|
|
let mut idx_1 = None;
|
|
let sv2 = &self.sv[idx_2];
|
|
let mut k_v_12 = None;
|
|
let km = sv2.k;
|
|
let gm = sv2.grad;
|
|
let mut best = 0f64;
|
|
|
|
let xi: Vec<_> = sv2.x.iter().map(|e| e.to_f64().unwrap()).collect();
|
|
for i in 0..self.sv.len() {
|
|
let v = &self.sv[i];
|
|
let xj: Vec<_> = v.x.iter().map(|e| e.to_f64().unwrap()).collect();
|
|
let z = gm - v.grad;
|
|
let k = cache.get(
|
|
sv2,
|
|
v,
|
|
self.parameters
|
|
.kernel
|
|
.as_ref()
|
|
.unwrap()
|
|
.apply(&xi, &xj)
|
|
.unwrap(),
|
|
);
|
|
let mut curv = km + v.k - 2f64 * k;
|
|
if curv <= 0f64 {
|
|
curv = self.tau.to_f64().unwrap();
|
|
}
|
|
|
|
let mu = z / curv;
|
|
if (mu > 0f64 && v.alpha > v.cmin) || (mu < 0f64 && v.alpha < v.cmax) {
|
|
let gain = z * mu;
|
|
if gain > best {
|
|
best = gain;
|
|
idx_1 = Some(i);
|
|
k_v_12 = Some(k);
|
|
}
|
|
}
|
|
}
|
|
|
|
let xj: Vec<_> = self.sv[idx_2]
|
|
.x
|
|
.iter()
|
|
.map(|e| e.to_f64().unwrap())
|
|
.collect();
|
|
|
|
idx_1.map(|idx_1| {
|
|
(
|
|
idx_1,
|
|
idx_2,
|
|
k_v_12.unwrap_or_else(|| {
|
|
self.parameters
|
|
.kernel
|
|
.as_ref()
|
|
.unwrap()
|
|
.apply(
|
|
&self.sv[idx_1]
|
|
.x
|
|
.iter()
|
|
.map(|e| e.to_f64().unwrap())
|
|
.collect::<Vec<_>>(),
|
|
&xj,
|
|
)
|
|
.unwrap()
|
|
}),
|
|
)
|
|
})
|
|
}
|
|
(Some(idx_1), Some(idx_2)) => Some((
|
|
idx_1,
|
|
idx_2,
|
|
self.parameters
|
|
.kernel
|
|
.as_ref()
|
|
.unwrap()
|
|
.apply(
|
|
&self.sv[idx_1]
|
|
.x
|
|
.iter()
|
|
.map(|e| e.to_f64().unwrap())
|
|
.collect::<Vec<_>>(),
|
|
&self.sv[idx_2]
|
|
.x
|
|
.iter()
|
|
.map(|e| e.to_f64().unwrap())
|
|
.collect::<Vec<_>>(),
|
|
)
|
|
.unwrap(),
|
|
)),
|
|
}
|
|
}
|
|
|
|
fn smo(
|
|
&mut self,
|
|
idx_1: Option<usize>,
|
|
idx_2: Option<usize>,
|
|
tol: TX,
|
|
cache: &mut Cache<TX, TY, X, Y>,
|
|
) -> bool {
|
|
match self.select_pair(idx_1, idx_2, cache) {
|
|
Some((idx_1, idx_2, k_v_12)) => {
|
|
let mut curv = self.sv[idx_1].k + self.sv[idx_2].k - 2f64 * k_v_12;
|
|
if curv <= 0f64 {
|
|
curv = self.tau.to_f64().unwrap();
|
|
}
|
|
|
|
let mut step = (self.sv[idx_2].grad - self.sv[idx_1].grad) / curv;
|
|
|
|
if step >= 0f64 {
|
|
let mut ostep = self.sv[idx_1].alpha - self.sv[idx_1].cmin;
|
|
if ostep < step {
|
|
step = ostep;
|
|
}
|
|
ostep = self.sv[idx_2].cmax - self.sv[idx_2].alpha;
|
|
if ostep < step {
|
|
step = ostep;
|
|
}
|
|
} else {
|
|
let mut ostep = self.sv[idx_2].cmin - self.sv[idx_2].alpha;
|
|
if ostep > step {
|
|
step = ostep;
|
|
}
|
|
ostep = self.sv[idx_1].alpha - self.sv[idx_1].cmax;
|
|
if ostep > step {
|
|
step = ostep;
|
|
}
|
|
}
|
|
|
|
self.update(idx_1, idx_2, TX::from(step).unwrap(), cache);
|
|
|
|
self.gmax - self.gmin > tol
|
|
}
|
|
None => false,
|
|
}
|
|
}
|
|
|
|
fn update(&mut self, v1: usize, v2: usize, step: TX, cache: &mut Cache<TX, TY, X, Y>) {
|
|
self.sv[v1].alpha -= step.to_f64().unwrap();
|
|
self.sv[v2].alpha += step.to_f64().unwrap();
|
|
|
|
let xi_v1: Vec<_> = self.sv[v1].x.iter().map(|e| e.to_f64().unwrap()).collect();
|
|
let xi_v2: Vec<_> = self.sv[v2].x.iter().map(|e| e.to_f64().unwrap()).collect();
|
|
for i in 0..self.sv.len() {
|
|
let xj: Vec<_> = self.sv[i].x.iter().map(|e| e.to_f64().unwrap()).collect();
|
|
let k2 = cache.get(
|
|
&self.sv[v2],
|
|
&self.sv[i],
|
|
self.parameters
|
|
.kernel
|
|
.as_ref()
|
|
.unwrap()
|
|
.apply(&xi_v2, &xj)
|
|
.unwrap(),
|
|
);
|
|
let k1 = cache.get(
|
|
&self.sv[v1],
|
|
&self.sv[i],
|
|
self.parameters
|
|
.kernel
|
|
.as_ref()
|
|
.unwrap()
|
|
.apply(&xi_v1, &xj)
|
|
.unwrap(),
|
|
);
|
|
self.sv[i].grad -= step.to_f64().unwrap() * (k2 - k1);
|
|
}
|
|
|
|
self.recalculate_minmax_grad = true;
|
|
self.find_min_max_gradient();
|
|
}
|
|
}
|
|
|
|
#[cfg(test)]
|
|
mod tests {
|
|
use num::ToPrimitive;
|
|
|
|
use super::*;
|
|
use crate::linalg::basic::matrix::DenseMatrix;
|
|
use crate::metrics::accuracy;
|
|
use crate::svm::Kernels;
|
|
|
|
#[cfg_attr(
|
|
all(target_arch = "wasm32", not(target_os = "wasi")),
|
|
wasm_bindgen_test::wasm_bindgen_test
|
|
)]
|
|
#[test]
|
|
fn svc_fit_predict() {
|
|
let x = DenseMatrix::from_2d_array(&[
|
|
&[5.1, 3.5, 1.4, 0.2],
|
|
&[4.9, 3.0, 1.4, 0.2],
|
|
&[4.7, 3.2, 1.3, 0.2],
|
|
&[4.6, 3.1, 1.5, 0.2],
|
|
&[5.0, 3.6, 1.4, 0.2],
|
|
&[5.4, 3.9, 1.7, 0.4],
|
|
&[4.6, 3.4, 1.4, 0.3],
|
|
&[5.0, 3.4, 1.5, 0.2],
|
|
&[4.4, 2.9, 1.4, 0.2],
|
|
&[4.9, 3.1, 1.5, 0.1],
|
|
&[7.0, 3.2, 4.7, 1.4],
|
|
&[6.4, 3.2, 4.5, 1.5],
|
|
&[6.9, 3.1, 4.9, 1.5],
|
|
&[5.5, 2.3, 4.0, 1.3],
|
|
&[6.5, 2.8, 4.6, 1.5],
|
|
&[5.7, 2.8, 4.5, 1.3],
|
|
&[6.3, 3.3, 4.7, 1.6],
|
|
&[4.9, 2.4, 3.3, 1.0],
|
|
&[6.6, 2.9, 4.6, 1.3],
|
|
&[5.2, 2.7, 3.9, 1.4],
|
|
])
|
|
.unwrap();
|
|
|
|
let y: Vec<i32> = vec![
|
|
-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
|
];
|
|
|
|
let knl = Kernels::linear();
|
|
let params = SVCParameters::default()
|
|
.with_c(200.0)
|
|
.with_kernel(knl)
|
|
.with_seed(Some(100));
|
|
|
|
let y_hat = SVC::fit(&x, &y, ¶ms)
|
|
.and_then(|lr| lr.predict(&x))
|
|
.unwrap();
|
|
let acc = accuracy(&y, &(y_hat.iter().map(|e| e.to_i32().unwrap()).collect()));
|
|
|
|
assert!(acc >= 0.9, "accuracy ({acc}) is not larger or equal to 0.9");
|
|
}
|
|
|
|
#[cfg_attr(
|
|
all(target_arch = "wasm32", not(target_os = "wasi")),
|
|
wasm_bindgen_test::wasm_bindgen_test
|
|
)]
|
|
#[test]
|
|
fn svc_fit_decision_function() {
|
|
let x = DenseMatrix::from_2d_array(&[&[4.0, 0.0], &[0.0, 4.0], &[8.0, 0.0], &[0.0, 8.0]])
|
|
.unwrap();
|
|
|
|
let x2 = DenseMatrix::from_2d_array(&[
|
|
&[3.0, 3.0],
|
|
&[4.0, 4.0],
|
|
&[6.0, 6.0],
|
|
&[10.0, 10.0],
|
|
&[1.0, 1.0],
|
|
&[0.0, 0.0],
|
|
])
|
|
.unwrap();
|
|
|
|
let y: Vec<i32> = vec![-1, -1, 1, 1];
|
|
|
|
let y_hat = SVC::fit(
|
|
&x,
|
|
&y,
|
|
&SVCParameters::default()
|
|
.with_c(200.0)
|
|
.with_kernel(Kernels::linear()),
|
|
)
|
|
.and_then(|lr| lr.decision_function(&x2))
|
|
.unwrap();
|
|
|
|
// x can be classified by a straight line through [6.0, 0.0] and [0.0, 6.0],
|
|
// so the score should increase as points get further away from that line
|
|
assert!(y_hat[1] < y_hat[2]);
|
|
assert!(y_hat[2] < y_hat[3]);
|
|
|
|
// for negative scores the score should decrease
|
|
assert!(y_hat[4] > y_hat[5]);
|
|
|
|
// y_hat[0] is on the line, so its score should be close to 0
|
|
assert!(num::Float::abs(y_hat[0]) <= 0.1);
|
|
}
|
|
|
|
#[cfg_attr(
|
|
all(target_arch = "wasm32", not(target_os = "wasi")),
|
|
wasm_bindgen_test::wasm_bindgen_test
|
|
)]
|
|
#[test]
|
|
fn svc_fit_predict_rbf() {
|
|
let x = DenseMatrix::from_2d_array(&[
|
|
&[5.1, 3.5, 1.4, 0.2],
|
|
&[4.9, 3.0, 1.4, 0.2],
|
|
&[4.7, 3.2, 1.3, 0.2],
|
|
&[4.6, 3.1, 1.5, 0.2],
|
|
&[5.0, 3.6, 1.4, 0.2],
|
|
&[5.4, 3.9, 1.7, 0.4],
|
|
&[4.6, 3.4, 1.4, 0.3],
|
|
&[5.0, 3.4, 1.5, 0.2],
|
|
&[4.4, 2.9, 1.4, 0.2],
|
|
&[4.9, 3.1, 1.5, 0.1],
|
|
&[7.0, 3.2, 4.7, 1.4],
|
|
&[6.4, 3.2, 4.5, 1.5],
|
|
&[6.9, 3.1, 4.9, 1.5],
|
|
&[5.5, 2.3, 4.0, 1.3],
|
|
&[6.5, 2.8, 4.6, 1.5],
|
|
&[5.7, 2.8, 4.5, 1.3],
|
|
&[6.3, 3.3, 4.7, 1.6],
|
|
&[4.9, 2.4, 3.3, 1.0],
|
|
&[6.6, 2.9, 4.6, 1.3],
|
|
&[5.2, 2.7, 3.9, 1.4],
|
|
])
|
|
.unwrap();
|
|
|
|
let y: Vec<i32> = vec![
|
|
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
|
];
|
|
|
|
let y_hat = SVC::fit(
|
|
&x,
|
|
&y,
|
|
&SVCParameters::default()
|
|
.with_c(1.0)
|
|
.with_kernel(Kernels::rbf().with_gamma(0.7)),
|
|
)
|
|
.and_then(|lr| lr.predict(&x))
|
|
.unwrap();
|
|
|
|
let acc = accuracy(&y, &(y_hat.iter().map(|e| e.to_i32().unwrap()).collect()));
|
|
|
|
assert!(acc >= 0.9, "accuracy ({acc}) is not larger or equal to 0.9");
|
|
}
|
|
|
|
#[cfg_attr(
|
|
all(target_arch = "wasm32", not(target_os = "wasi")),
|
|
wasm_bindgen_test::wasm_bindgen_test
|
|
)]
|
|
#[test]
|
|
#[cfg(all(feature = "serde", not(target_arch = "wasm32")))]
|
|
fn svc_serde() {
|
|
let x = DenseMatrix::from_2d_array(&[
|
|
&[5.1, 3.5, 1.4, 0.2],
|
|
&[4.9, 3.0, 1.4, 0.2],
|
|
&[4.7, 3.2, 1.3, 0.2],
|
|
&[4.6, 3.1, 1.5, 0.2],
|
|
&[5.0, 3.6, 1.4, 0.2],
|
|
&[5.4, 3.9, 1.7, 0.4],
|
|
&[4.6, 3.4, 1.4, 0.3],
|
|
&[5.0, 3.4, 1.5, 0.2],
|
|
&[4.4, 2.9, 1.4, 0.2],
|
|
&[4.9, 3.1, 1.5, 0.1],
|
|
&[7.0, 3.2, 4.7, 1.4],
|
|
&[6.4, 3.2, 4.5, 1.5],
|
|
&[6.9, 3.1, 4.9, 1.5],
|
|
&[5.5, 2.3, 4.0, 1.3],
|
|
&[6.5, 2.8, 4.6, 1.5],
|
|
&[5.7, 2.8, 4.5, 1.3],
|
|
&[6.3, 3.3, 4.7, 1.6],
|
|
&[4.9, 2.4, 3.3, 1.0],
|
|
&[6.6, 2.9, 4.6, 1.3],
|
|
&[5.2, 2.7, 3.9, 1.4],
|
|
])
|
|
.unwrap();
|
|
|
|
let y: Vec<i32> = vec![
|
|
-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
|
];
|
|
|
|
let knl = Kernels::linear();
|
|
let params = SVCParameters::default().with_kernel(knl);
|
|
let svc = SVC::fit(&x, &y, ¶ms).unwrap();
|
|
|
|
// serialization
|
|
let deserialized_svc: SVC<f64, i32, _, _> =
|
|
serde_json::from_str(&serde_json::to_string(&svc).unwrap()).unwrap();
|
|
|
|
assert_eq!(svc, deserialized_svc);
|
|
}
|
|
}
|