1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042
//! ## Kernel methods
//!
//! Kernel methods are a class of algorithms for pattern analysis, whose best known member is the
//! [support vector machine](https://en.wikipedia.org/wiki/Support_vector_machine). They owe their name to the kernel functions,
//! which maps the features to some higher-dimensional target space. Common examples for kernel
//! functions are the radial basis function (euclidean distance) or polynomial kernels.
//!
//! ## Current State
//!
//! linfa-kernel currently provides an implementation of kernel methods for RBF and polynomial kernels,
//! with sparse or dense representation. Further a k-neighbour approximation allows to reduce the kernel
//! matrix size.
//!
//! Low-rank kernel approximation are currently missing, but are on the roadmap. Examples for these are the
//! [Nyström approximation](https://www.jmlr.org/papers/volume6/drineas05a/drineas05a.pdf) or [Quasi Random Fourier Features](http://www-personal.umich.edu/~aniketde/processed_md/Stats608_Aniketde.pdf).
pub mod inner;
mod sparse;
pub use inner::{Inner, KernelInner};
use linfa_nn::CommonNearestNeighbour;
use linfa_nn::NearestNeighbour;
use ndarray::prelude::*;
use ndarray::Data;
#[cfg(feature = "serde")]
use serde_crate::{Deserialize, Serialize};
use sprs::{CsMat, CsMatView};
use std::ops::Mul;
use linfa::{
dataset::AsTargets, dataset::DatasetBase, dataset::FromTargetArray, dataset::Records,
traits::Transformer, Float,
};
/// Kernel representation, can be either dense or sparse
#[derive(Debug, Clone, PartialEq, Eq, Hash)]
pub enum KernelType {
Dense,
/// A sparse kernel requires to define a number of neighbours
/// between 1 and the total number of samples in input minus one.
Sparse(usize),
}
/// A generic kernel
#[cfg_attr(
feature = "serde",
derive(Serialize, Deserialize),
serde(crate = "serde_crate")
)]
#[derive(Debug, Clone, PartialEq)]
pub struct KernelBase<K1: Inner, K2: Inner>
where
K1::Elem: Float,
K2::Elem: Float,
{
#[cfg_attr(
feature = "serde",
serde(bound(
serialize = "KernelInner<K1, K2>: Serialize",
deserialize = "KernelInner<K1, K2>: Deserialize<'de>"
))
)]
pub inner: KernelInner<K1, K2>,
#[cfg_attr(
feature = "serde",
serde(bound(
serialize = "KernelMethod<K1::Elem>: Serialize",
deserialize = "KernelMethod<K1::Elem>: Deserialize<'de>"
))
)]
/// The inner product that will be used by the kernel
pub method: KernelMethod<K1::Elem>,
}
/// Type definition of Kernel that owns its inner matrix
pub type Kernel<F> = KernelBase<Array2<F>, CsMat<F>>;
/// Type definition of Kernel that borrows its inner matrix
pub type KernelView<'a, F> = KernelBase<ArrayView2<'a, F>, CsMatView<'a, F>>;
impl<F: Float, K1: Inner<Elem = F>, K2: Inner<Elem = F>> KernelBase<K1, K2> {
/// Whether the kernel is a linear kernel
///
/// ## Returns
///
/// - `true`: if the kernel is linear
/// - `false`: otherwise
pub fn is_linear(&self) -> bool {
self.method.is_linear()
}
/// Generates the default set of parameters for building a kernel.
/// Use this to initialize a set of parameters to be customized using `KernelParams`'s methods
pub fn params() -> KernelParams<F, CommonNearestNeighbour> {
Self::params_with_nn(CommonNearestNeighbour::KdTree)
}
/// Generate parameters with a specific nearest neighbour algorithm
pub fn params_with_nn<N: NearestNeighbour>(nn_algo: N) -> KernelParams<F, N> {
KernelParams {
kind: KernelType::Dense,
method: KernelMethod::Gaussian(F::cast(0.5)),
nn_algo,
}
}
/// Performs the matrix product between the kernel matrix
/// and the input
///
/// ## Parameters
///
/// - `rhs`: The matrix on the right-hand side of the multiplication
///
/// ## Returns
///
/// A new matrix containing the matrix product between the kernel
/// and `rhs`
///
/// ## Panics
///
/// If the shapes of kernel and `rhs` are not compatible for multiplication
pub fn dot(&self, rhs: &ArrayView2<F>) -> Array2<F> {
match &self.inner {
KernelInner::Dense(inn) => inn.dot(rhs),
KernelInner::Sparse(inn) => inn.dot(rhs),
}
}
/// Sums all elements in the same row of the kernel matrix
///
/// ## Returns
///
/// A new array with the sum of all the elements in each row
pub fn sum(&self) -> Array1<F> {
match &self.inner {
KernelInner::Dense(inn) => inn.sum(),
KernelInner::Sparse(inn) => inn.sum(),
}
}
/// Gives the size of the side of the square kernel matrix
pub fn size(&self) -> usize {
match &self.inner {
KernelInner::Dense(inn) => inn.size(),
KernelInner::Sparse(inn) => inn.size(),
}
}
/// Getter for a column of the kernel matrix
///
/// ## Params
///
/// - `i`: the index of the column
///
/// ## Returns
///
/// The i-th column of the kernel matrix, stored as a `Vec`
///
/// ## Panics
///
/// If `i` is out of bounds
pub fn column(&self, i: usize) -> Vec<F> {
match &self.inner {
KernelInner::Dense(inn) => inn.column(i),
KernelInner::Sparse(inn) => inn.column(i),
}
}
/// Getter for the data in the upper triangle of the kernel
/// matrix
///
/// ## Returns
///
/// A copy of all elements in the upper triangle of the kernel
/// matrix, stored in a `Vec`
pub fn to_upper_triangle(&self) -> Vec<F> {
match &self.inner {
KernelInner::Dense(inn) => inn.to_upper_triangle(),
KernelInner::Sparse(inn) => inn.to_upper_triangle(),
}
}
/// Getter for the elements in the diagonal of the kernel matrix
///
/// ## Returns
///
/// A new array containing the copy of all elements in the diagonal fo
/// the kernel matrix
pub fn diagonal(&self) -> Array1<F> {
match &self.inner {
KernelInner::Dense(inn) => inn.diagonal(),
KernelInner::Sparse(inn) => inn.diagonal(),
}
}
}
impl<'a, F: Float> Kernel<F> {
pub fn new<N: NearestNeighbour>(
dataset: ArrayView2<'a, F>,
params: &KernelParams<F, N>,
) -> Kernel<F> {
let inner = match params.kind {
KernelType::Dense => KernelInner::Dense(dense_from_fn(&dataset, ¶ms.method)),
KernelType::Sparse(k) => {
KernelInner::Sparse(sparse_from_fn(&dataset, k, ¶ms.method, ¶ms.nn_algo))
}
};
Kernel {
inner,
method: params.method.clone(),
}
}
/// Gives a KernelView which has a view on the original kernel's inner matrix
pub fn view(&'a self) -> KernelView<'a, F> {
KernelView {
inner: match &self.inner {
KernelInner::Dense(inn) => KernelInner::Dense(inn.view()),
KernelInner::Sparse(inn) => KernelInner::Sparse(inn.view()),
},
method: self.method.clone(),
}
}
}
impl<'a, F: Float> KernelView<'a, F> {
pub fn to_owned(&self) -> Kernel<F> {
Kernel {
inner: match &self.inner {
KernelInner::Dense(inn) => KernelInner::Dense(inn.to_owned()),
KernelInner::Sparse(inn) => KernelInner::Sparse(inn.to_owned()),
},
method: self.method.clone(),
}
}
}
impl<F: Float, K1: Inner<Elem = F>, K2: Inner<Elem = F>> Records for KernelBase<K1, K2> {
type Elem = F;
fn nsamples(&self) -> usize {
self.size()
}
fn nfeatures(&self) -> usize {
self.size()
}
}
/// The inner product definition used by a kernel.
///
/// There are three methods available:
///
/// - Gaussian(eps): `d(x, x') = exp(-norm(x - x')/eps) `
/// - Linear: `d(x, x') = <x, x'>`
/// - Polynomial(constant, degree): `d(x, x') = (<x, x'> + costant)^(degree)`
#[cfg_attr(
feature = "serde",
derive(Serialize, Deserialize),
serde(crate = "serde_crate")
)]
#[derive(Debug, Clone, PartialEq)]
pub enum KernelMethod<F> {
/// Gaussian(eps): exp(-norm(x - x')/eps)
Gaussian(F),
/// Euclidean inner product
Linear,
/// Polynomial(constant, degree): ` (<x, x'> + costant)^(degree)`
Polynomial(F, F),
}
impl<F: Float> KernelMethod<F> {
pub fn distance(&self, a: ArrayView1<F>, b: ArrayView1<F>) -> F {
match *self {
KernelMethod::Gaussian(eps) => {
let distance = a
.iter()
.zip(b.iter())
.map(|(x, y)| (*x - *y) * (*x - *y))
.sum::<F>();
(-distance / eps).exp()
}
KernelMethod::Linear => a.mul(&b).sum(),
KernelMethod::Polynomial(c, d) => (a.mul(&b).sum() + c).powf(d),
}
}
pub fn is_linear(&self) -> bool {
matches!(*self, KernelMethod::Linear)
}
}
/// Defines the set of parameters needed to build a kernel
#[derive(Debug, Clone, PartialEq)]
pub struct KernelParams<F, N = CommonNearestNeighbour> {
/// Whether to construct a dense or sparse kernel
kind: KernelType,
/// The inner product used by the kernel
method: KernelMethod<F>,
/// Nearest neighbour algorithm for calculating adjacency matrices
nn_algo: N,
}
impl<F, N> KernelParams<F, N> {
/// Setter for `method`, the inner product used by the kernel
pub fn method(mut self, method: KernelMethod<F>) -> Self {
self.method = method;
self
}
/// Setter for `kind`, whether to construct a dense or sparse kernel
pub fn kind(mut self, kind: KernelType) -> Self {
self.kind = kind;
self
}
/// Setter for `nn_algo`, nearest neighbour algorithm for calculating adjacency matrices
pub fn nn_algo(mut self, nn_algo: N) -> Self {
self.nn_algo = nn_algo;
self
}
}
impl<F: Float, N: NearestNeighbour> Transformer<&Array2<F>, Kernel<F>> for KernelParams<F, N> {
/// Builds a kernel from a view of the input data.
///
/// ## Parameters
///
/// - `x`: view of a matrix of records (#records, #features)
///
/// A kernel build from `x` according to the parameters on which
/// this method is called
///
/// ## Panics
///
/// If the kernel type is `Sparse` and the number of neighbors specified is
/// not between 1 and #records-1
fn transform(&self, x: &Array2<F>) -> Kernel<F> {
Kernel::new(x.view(), self)
}
}
impl<'a, F: Float, N: NearestNeighbour> Transformer<ArrayView2<'a, F>, Kernel<F>>
for KernelParams<F, N>
{
/// Builds a kernel from a view of the input data.
///
/// ## Parameters
///
/// - `x`: view of a matrix of records (#records, #features)
///
/// A kernel build from `x` according to the parameters on which
/// this method is called
///
/// ## Panics
///
/// If the kernel type is `Sparse` and the number of neighbors specified is
/// not between 1 and #records-1
fn transform(&self, x: ArrayView2<'a, F>) -> Kernel<F> {
Kernel::new(x, self)
}
}
impl<'a, F: Float, N: NearestNeighbour> Transformer<&ArrayView2<'a, F>, Kernel<F>>
for KernelParams<F, N>
{
/// Builds a kernel from a view of the input data.
///
/// ## Parameters
///
/// - `x`: view of a matrix of records (#records, #features)
///
/// A kernel build from `x` according to the parameters on which
/// this method is called
///
/// ## Panics
///
/// If the kernel type is `Sparse` and the number of neighbors specified is
/// not between 1 and #records-1
fn transform(&self, x: &ArrayView2<'a, F>) -> Kernel<F> {
Kernel::new(*x, self)
}
}
impl<'a, F: Float, T: AsTargets, N: NearestNeighbour>
Transformer<DatasetBase<Array2<F>, T>, DatasetBase<Kernel<F>, T>> for KernelParams<F, N>
{
/// Builds a new Dataset with the kernel as the records and the same targets as the input one.
///
/// It takes ownership of the original dataset.
///
/// ## Parameters
///
/// - `x`: A dataset with a matrix of records (#records, #features) and any targets
///
/// ## Returns
///
/// A new dataset with:
/// - records: a kernel build from `x.records()` according to the parameters on which
/// this method is called
/// - targets: same as `x.targets()`
///
/// ## Panics
///
/// If the kernel type is `Sparse` and the number of neighbors specified is
/// not between 1 and #records-1
fn transform(&self, x: DatasetBase<Array2<F>, T>) -> DatasetBase<Kernel<F>, T> {
let kernel = Kernel::new(x.records.view(), self);
DatasetBase::new(kernel, x.targets)
}
}
impl<'a, F: Float, L: 'a, T: AsTargets<Elem = L> + FromTargetArray<'a>, N: NearestNeighbour>
Transformer<&'a DatasetBase<Array2<F>, T>, DatasetBase<Kernel<F>, T::View>>
for KernelParams<F, N>
{
/// Builds a new Dataset with the kernel as the records and the same targets as the input one.
///
/// ## Parameters
///
/// - `x`: A dataset with a matrix of records (#records, #features) and any targets
///
/// ## Returns
///
/// A new dataset with:
/// - records: a kernel build from `x.records()` according to the parameters on which
/// this method is called
/// - targets: same as `x.targets()`
///
/// ## Panics
///
/// If the kernel type is `Sparse` and the number of neighbors specified is
/// not between 1 and #records-1
fn transform(&self, x: &'a DatasetBase<Array2<F>, T>) -> DatasetBase<Kernel<F>, T::View> {
let kernel = Kernel::new(x.records.view(), self);
DatasetBase::new(kernel, T::new_targets_view(x.as_targets()))
}
}
// lifetime 'b allows the kernel to borrow the underlying data
// for a possibly shorter time than 'a, useful in fold_fit
impl<
'a,
'b,
F: Float,
L: 'b,
T: AsTargets<Elem = L> + FromTargetArray<'b>,
N: NearestNeighbour,
> Transformer<&'b DatasetBase<ArrayView2<'a, F>, T>, DatasetBase<Kernel<F>, T::View>>
for KernelParams<F, N>
{
/// Builds a new Dataset with the kernel as the records and the same targets as the input one.
///
/// ## Parameters
///
/// - `x`: A dataset with a matrix of records (##records, ##features) and any targets
///
/// ## Returns
///
/// A new dataset with:
/// - records: a kernel build from `x.records()` according to the parameters on which
/// this method is called
/// - targets: a slice of `x.targets()`
///
/// ## Panics
///
/// If the kernel type is `Sparse` and the number of neighbors specified is
/// not between 1 and ##records-1
fn transform(
&self,
x: &'b DatasetBase<ArrayView2<'a, F>, T>,
) -> DatasetBase<Kernel<F>, T::View> {
let kernel = Kernel::new(x.records.view(), self);
DatasetBase::new(kernel, T::new_targets_view(x.as_targets()))
}
}
fn dense_from_fn<F: Float, D: Data<Elem = F>>(
dataset: &ArrayBase<D, Ix2>,
method: &KernelMethod<F>,
) -> Array2<F> {
let n_observations = dataset.len_of(Axis(0));
let mut similarity = Array2::eye(n_observations);
for i in 0..n_observations {
for j in 0..n_observations {
let a = dataset.row(i);
let b = dataset.row(j);
similarity[(i, j)] = method.distance(a, b);
}
}
similarity
}
fn sparse_from_fn<F: Float, D: Data<Elem = F>, N: NearestNeighbour>(
dataset: &ArrayBase<D, Ix2>,
k: usize,
method: &KernelMethod<F>,
nn_algo: &N,
) -> CsMat<F> {
// compute adjacency matrix between points in the input dataset:
// one point for each row
let mut data = sparse::adjacency_matrix(dataset, k, nn_algo);
// iterate through each row of the adjacency matrix where each
// row is represented by a vec containing a pair (col_index, value)
// for each non-zero element in the row
for (i, mut vec) in data.outer_iterator_mut().enumerate() {
// If there is a non-zero element in row i at index j
// then it means that points i and j in the input matrix are
// k-neighbours and their distance is stored in position (i,j)
for (j, val) in vec.iter_mut() {
let a = dataset.row(i);
let b = dataset.row(j);
*val = method.distance(a, b);
}
}
data
}
#[cfg(test)]
mod tests {
use super::*;
use linfa::Dataset;
use linfa_nn::{BallTree, KdTree};
use ndarray::{Array1, Array2};
use std::f64::consts;
#[test]
fn autotraits() {
fn has_autotraits<T: Send + Sync + Sized + Unpin>() {}
has_autotraits::<KernelType>();
has_autotraits::<KernelBase<ArrayView2<f64>, ArrayView2<f64>>>();
has_autotraits::<KernelMethod<f64>>();
has_autotraits::<KernelParams<f64, f64>>();
has_autotraits::<KernelView<f64>>();
has_autotraits::<KernelInner<ArrayView2<f64>, ArrayView2<f64>>>();
has_autotraits::<Kernel<f64>>();
}
#[test]
fn sparse_from_fn_test() {
// pts 0 & 1 pts 2 & 3 pts 4 & 5 pts 6 & 7
// |0.| |0.1| _ |1.| |1.1| _ |2.| |2.1| _ |3.| |3.1|
// |0.| |0.1| |1.| |1.1| |2.| |2.1| |3.| |3.1|
let input_mat = vec![
0., 0., 0.1, 0.1, 1., 1., 1.1, 1.1, 2., 2., 2.1, 2.1, 3., 3., 3.1, 3.1,
];
let input_arr = Array2::from_shape_vec((8, 2), input_mat).unwrap();
let adj_mat = sparse_from_fn(&input_arr, 1, &KernelMethod::Linear, &KdTree);
assert_eq!(adj_mat.nnz(), 16);
// 2*0^2
assert_eq!(*adj_mat.get(0, 0).unwrap() as usize, 0);
// 2*0.1^2
assert_eq!((*adj_mat.get(1, 1).unwrap() * 100.) as usize, 2);
// 2*1^2
assert_eq!(*adj_mat.get(2, 2).unwrap() as usize, 2);
// 2*1.1^2
assert_eq!((*adj_mat.get(3, 3).unwrap() * 100.) as usize, 242);
// 2 * 2^2
assert_eq!(*adj_mat.get(4, 4).unwrap() as usize, 8);
// 2 * 2.1^2
assert_eq!((*adj_mat.get(5, 5).unwrap() * 100.) as usize, 882);
// 2 * 3^2
assert_eq!(*adj_mat.get(6, 6).unwrap() as usize, 18);
// 2 * 3.1^2
assert_eq!((*adj_mat.get(7, 7).unwrap() * 100.) as usize, 1922);
// 2*(0 * 0.1)
assert_eq!(*adj_mat.get(0, 1).unwrap() as usize, 0);
assert_eq!(*adj_mat.get(1, 0).unwrap() as usize, 0);
// 2*(1 * 1.1)
assert_eq!((*adj_mat.get(2, 3).unwrap() * 10.) as usize, 22);
assert_eq!((*adj_mat.get(3, 2).unwrap() * 10.) as usize, 22);
// 2*(2 * 2.1)
assert_eq!((*adj_mat.get(4, 5).unwrap() * 10.) as usize, 84);
assert_eq!((*adj_mat.get(5, 4).unwrap() * 10.) as usize, 84);
// 2*(3 * 3.1)
assert_eq!((*adj_mat.get(6, 7).unwrap() * 10.) as usize, 186);
assert_eq!((*adj_mat.get(7, 6).unwrap() * 10.) as usize, 186);
}
#[test]
fn dense_from_fn_test() {
// pts 0 & 1 pts 2 & 3 pts 4 & 5 pts 6 & 7
// |0.| |0.1| _ |1.| |1.1| _ |2.| |2.1| _ |3.| |3.1|
// |0.| |0.1| |1.| |1.1| |2.| |2.1| |3.| |3.1|
let input_mat = vec![
0., 0., 0.1, 0.1, 1., 1., 1.1, 1.1, 2., 2., 2.1, 2.1, 3., 3., 3.1, 3.1,
];
let input_arr = Array2::from_shape_vec((8, 2), input_mat).unwrap();
let method: KernelMethod<f64> = KernelMethod::Linear;
let similarity_matrix = dense_from_fn(&input_arr, &method);
for i in 0..8 {
for j in 0..8 {
assert!(
(similarity_matrix.row(i)[j]
- method.distance(input_arr.row(i), input_arr.row(j)))
.abs()
<= f64::EPSILON
);
}
}
}
#[test]
fn gaussian_test() {
let gauss_1 = KernelMethod::Gaussian(1.);
let p1 = Array1::from_shape_vec(2, vec![0., 0.]).unwrap();
let p2 = Array1::from_shape_vec(2, vec![0., 0.]).unwrap();
let distance = gauss_1.distance(p1.view(), p2.view());
let expected = 1.;
assert!(((distance - expected) as f64).abs() <= f64::EPSILON);
let p1 = Array1::from_shape_vec(2, vec![1., 1.]).unwrap();
let p2 = Array1::from_shape_vec(2, vec![5., 5.]).unwrap();
let distance = gauss_1.distance(p1.view(), p2.view());
let expected = (consts::E).powf(-32.);
// this fails with e^-31 or e^-33 so f64::EPSILON still holds
assert!(((distance - expected) as f64).abs() <= f64::EPSILON);
let gauss_01 = KernelMethod::Gaussian(0.1);
let p1 = Array1::from_shape_vec(2, vec![0., 0.]).unwrap();
let p2 = Array1::from_shape_vec(2, vec![0., 0.]).unwrap();
let distance = gauss_01.distance(p1.view(), p2.view());
let expected = 1.;
assert!(((distance - expected) as f64).abs() <= f64::EPSILON);
let p1 = Array1::from_shape_vec(2, vec![1., 1.]).unwrap();
let p2 = Array1::from_shape_vec(2, vec![2., 2.]).unwrap();
let distance = gauss_01.distance(p1.view(), p2.view());
let expected = (consts::E).powf(-20.);
assert!(((distance - expected) as f64).abs() <= f64::EPSILON);
}
#[test]
fn poly2_test() {
let pol_0 = KernelMethod::Polynomial(0., 2.);
let p1 = Array1::from_shape_vec(2, vec![0., 0.]).unwrap();
let p2 = Array1::from_shape_vec(2, vec![0., 0.]).unwrap();
let distance = pol_0.distance(p1.view(), p2.view());
let expected = 0.;
assert!(((distance - expected) as f64).abs() <= f64::EPSILON);
let p1 = Array1::from_shape_vec(2, vec![1., 1.]).unwrap();
let p2 = Array1::from_shape_vec(2, vec![5., 5.]).unwrap();
let distance = pol_0.distance(p1.view(), p2.view());
let expected = 100.;
assert!(((distance - expected) as f64).abs() <= f64::EPSILON);
let pol_2 = KernelMethod::Polynomial(2., 2.);
let p1 = Array1::from_shape_vec(2, vec![0., 0.]).unwrap();
let p2 = Array1::from_shape_vec(2, vec![0., 0.]).unwrap();
let distance = pol_2.distance(p1.view(), p2.view());
let expected = 4.;
assert!(((distance - expected) as f64).abs() <= f64::EPSILON);
let p1 = Array1::from_shape_vec(2, vec![1., 1.]).unwrap();
let p2 = Array1::from_shape_vec(2, vec![2., 2.]).unwrap();
let distance = pol_2.distance(p1.view(), p2.view());
let expected = 36.;
assert!(((distance - expected) as f64).abs() <= f64::EPSILON);
}
#[test]
fn test_kernel_dot() {
let input_vec: Vec<f64> = (0..100).map(|v| v as f64 * 0.1).collect();
let vec_to_multiply: Vec<f64> = (0..100).map(|v| v as f64 * 0.3).collect();
let input_arr = Array2::from_shape_vec((10, 10), input_vec).unwrap();
let to_multiply = Array2::from_shape_vec((10, 10), vec_to_multiply).unwrap();
// dense kernel dot
let mul_mat = dense_from_fn(&input_arr, &KernelMethod::Linear).dot(&to_multiply);
let kernel = KernelView::params()
.kind(KernelType::Dense)
.method(KernelMethod::Linear)
.transform(input_arr.view());
let mul_ker = kernel.dot(&to_multiply.view());
assert!(matrices_almost_equal(mul_mat.view(), mul_ker.view()));
// sparse kernel dot
let mul_mat =
sparse_from_fn(&input_arr, 3, &KernelMethod::Linear, &KdTree).mul(&to_multiply.view());
let kernel = KernelView::params()
.kind(KernelType::Sparse(3))
.method(KernelMethod::Linear)
.transform(input_arr.view());
let mul_ker = kernel.dot(&to_multiply.view());
assert!(matrices_almost_equal(mul_mat.view(), mul_ker.view()));
}
#[test]
fn test_kernel_upper_triangle() {
// symmetric vec, kernel matrix is a "cross" of ones
let input_vec: Vec<f64> = (0..50).map(|v| v as f64 * 0.1).collect();
let input_arr_1 = Array2::from_shape_vec((5, 10), input_vec.clone()).unwrap();
let mut input_arr_2 = Array2::from_shape_vec((5, 10), input_vec).unwrap();
input_arr_2.invert_axis(Axis(0));
let input_arr =
ndarray::concatenate(Axis(0), &[input_arr_1.view(), input_arr_2.view()]).unwrap();
for kind in vec![KernelType::Dense, KernelType::Sparse(1)] {
let kernel = KernelView::params()
.kind(kind)
// Such a value for eps brings to zero the inner product
// between any two points that are not equal
.method(KernelMethod::Gaussian(1e-5))
.transform(input_arr.view());
let mut kernel_upper_triang = kernel.to_upper_triangle();
assert_eq!(kernel_upper_triang.len(), 45);
//so that i can use pop()
kernel_upper_triang.reverse();
for i in 0..9 {
for j in (i + 1)..10 {
if j == (9 - i) {
assert_eq!(kernel_upper_triang.pop().unwrap() as usize, 1);
} else {
assert_eq!(kernel_upper_triang.pop().unwrap() as usize, 0);
}
}
}
assert!(kernel_upper_triang.is_empty());
}
}
/* #[test]
fn test_kernel_weighted_sum() {
let input_vec: Vec<f64> = (0..100).map(|v| v as f64 * 0.1).collect();
let input_arr = Array2::from_shape_vec((10, 10), input_vec).unwrap();
let weights = [1., 2., 3., 4., 5., 6., 7., 8., 9., 10.];
for kind in vec![KernelType::Dense, KernelType::Sparse(1)] {
let kernel = KernelView::params()
.kind(kind)
// Such a value for eps brings to zero the inner product
// between any two points that are not equal
.method(KernelMethod::Gaussian(1e-5))
.transform(input_arr.view());
for (sample, w) in input_arr.outer_iter().zip(&weights) {
// with that kernel, only the input samples have non
// zero inner product with the samples used to generate the matrix.
// In particular, they have inner product equal to one only for the
// column corresponding to themselves
//let w_sum = kernel.weighted_sum(&weights, sample);
//assert!(values_almost_equal(&w_sum, w));
}
}
}*/
#[test]
fn test_kernel_sum() {
let input_vec: Vec<f64> = (0..100).map(|v| v as f64 * 0.1).collect();
let input_arr = Array2::from_shape_vec((10, 10), input_vec).unwrap();
let method = KernelMethod::Linear;
// dense kernel sum
let cols_sum = dense_from_fn(&input_arr, &method).sum_axis(Axis(1));
let kernel = KernelView::params()
.kind(KernelType::Dense)
.method(method.clone())
.transform(input_arr.view());
let kers_sum = kernel.sum();
assert!(arrays_almost_equal(cols_sum.view(), kers_sum.view()));
// sparse kernel sum
let cols_sum = sparse_from_fn(&input_arr, 3, &method, &BallTree)
.to_dense()
.sum_axis(Axis(1));
let kernel = KernelView::params()
.kind(KernelType::Sparse(3))
.method(method)
.transform(input_arr.view());
let kers_sum = kernel.sum();
assert!(arrays_almost_equal(cols_sum.view(), kers_sum.view()));
}
#[test]
fn test_kernel_diag() {
let input_vec: Vec<f64> = (0..100).map(|v| v as f64 * 0.1).collect();
let input_arr = Array2::from_shape_vec((10, 10), input_vec).unwrap();
let method = KernelMethod::Linear;
// dense kernel diag
let input_diagonal = dense_from_fn(&input_arr, &method).diag().into_owned();
let kernel = KernelView::params()
.kind(KernelType::Dense)
.method(method.clone())
.transform(input_arr.view());
let kers_diagonal = kernel.diagonal();
assert!(arrays_almost_equal(
input_diagonal.view(),
kers_diagonal.view()
));
// sparse kernel diag
let input_diagonal: Vec<_> = sparse_from_fn(&input_arr, 3, &method, &BallTree)
.outer_iterator()
.enumerate()
.map(|(i, row)| *row.get(i).unwrap())
.collect();
let input_diagonal = Array1::from_shape_vec(10, input_diagonal).unwrap();
let kernel = KernelView::params()
.kind(KernelType::Sparse(3))
.method(method)
.transform(input_arr.view());
let kers_diagonal = kernel.diagonal();
assert!(arrays_almost_equal(
input_diagonal.view(),
kers_diagonal.view()
));
}
// inspired from scikit learn's tests
#[test]
fn test_kernel_transform_from_array2() {
let input_vec: Vec<f64> = (0..100).map(|v| v as f64 * 0.1).collect();
let input = Array2::from_shape_vec((50, 2), input_vec).unwrap();
// checks that the transform for Array2 builds the right kernel
// according to its input params.
check_kernel_from_array2_type(&input, KernelType::Dense);
check_kernel_from_array2_type(&input, KernelType::Sparse(3));
// checks that the transform for ArrayView2 builds the right kernel
// according to its input params.
check_kernel_from_array_view_2_type(input.view(), KernelType::Dense);
check_kernel_from_array_view_2_type(input.view(), KernelType::Sparse(3));
}
// inspired from scikit learn's tests
#[test]
fn test_kernel_transform_from_dataset() {
let input_vec: Vec<f64> = (0..100).map(|v| v as f64 * 0.1).collect();
let input_arr = Array2::from_shape_vec((50, 2), input_vec).unwrap();
let input = Dataset::from(input_arr);
// checks that the transform for dataset builds the right kernel
// according to its input params.
check_kernel_from_dataset_type(&input, KernelType::Dense);
check_kernel_from_dataset_type(&input, KernelType::Sparse(3));
// checks that the transform for dataset view builds the right kernel
// according to its input params.
check_kernel_from_dataset_view_type(&input.view(), KernelType::Dense);
check_kernel_from_dataset_view_type(&input.view(), KernelType::Sparse(3));
}
fn check_kernel_from_dataset_type<'a, L: 'a, T: AsTargets<Elem = L> + FromTargetArray<'a>>(
input: &'a DatasetBase<Array2<f64>, T>,
k_type: KernelType,
) {
let methods = vec![
KernelMethod::Linear,
KernelMethod::Gaussian(0.1),
KernelMethod::Polynomial(1., 2.),
];
for method in methods {
let kernel_ref = Kernel::new(
input.records().view(),
&Kernel::params_with_nn(KdTree)
.method(method.clone())
.kind(k_type.clone()),
);
let kernel_tr = Kernel::params()
.kind(k_type.clone())
.method(method.clone())
.transform(input);
match (&kernel_ref.inner, &kernel_tr.records().inner) {
(KernelInner::Dense(m1), KernelInner::Dense(m2)) => {
assert!(kernels_almost_equal(m1, m2))
}
(KernelInner::Sparse(m1), KernelInner::Sparse(m2)) => {
assert!(kernels_almost_equal(m1, m2))
}
_ => panic!("Kernel inners must match!"),
};
}
}
fn check_kernel_from_dataset_view_type<
'a,
L: 'a,
T: AsTargets<Elem = L> + FromTargetArray<'a>,
>(
input: &'a DatasetBase<ArrayView2<'a, f64>, T>,
k_type: KernelType,
) {
let methods = vec![
KernelMethod::Linear,
KernelMethod::Gaussian(0.1),
KernelMethod::Polynomial(1., 2.),
];
for method in methods {
let kernel_ref = Kernel::new(
*input.records(),
&Kernel::params_with_nn(KdTree)
.method(method.clone())
.kind(k_type.clone()),
);
let kernel_tr = Kernel::params()
.kind(k_type.clone())
.method(method.clone())
.transform(input);
match (&kernel_ref.inner, &kernel_tr.records().inner) {
(KernelInner::Dense(m1), KernelInner::Dense(m2)) => {
assert!(kernels_almost_equal(m1, m2))
}
(KernelInner::Sparse(m1), KernelInner::Sparse(m2)) => {
assert!(kernels_almost_equal(m1, m2))
}
_ => panic!("Kernel inners must match!"),
};
}
}
/// Test method for checking each KernelMethod can operate on `&Array2<f64>` using type and `view()`
fn check_kernel_from_array2_type(input: &Array2<f64>, k_type: KernelType) {
let methods = vec![
KernelMethod::Linear,
KernelMethod::Gaussian(0.1),
KernelMethod::Polynomial(1., 2.),
];
for method in methods {
let kernel_ref = Kernel::new(
input.view(),
&Kernel::params_with_nn(KdTree)
.method(method.clone())
.kind(k_type.clone()),
);
let kernel_tr = Kernel::params()
.kind(k_type.clone())
.method(method.clone())
.transform(input.view());
match (&kernel_ref.inner, &kernel_tr.inner) {
(KernelInner::Dense(m1), KernelInner::Dense(m2)) => {
assert!(kernels_almost_equal(m1, m2))
}
(KernelInner::Sparse(m1), KernelInner::Sparse(m2)) => {
assert!(kernels_almost_equal(m1, m2))
}
_ => panic!("Kernel inners must match!"),
};
}
}
/// Test method for checking each KernelMethod can operate on `ArrayView2<f64>` type
fn check_kernel_from_array_view_2_type(input: ArrayView2<f64>, k_type: KernelType) {
let methods = vec![
KernelMethod::Linear,
KernelMethod::Gaussian(0.1),
KernelMethod::Polynomial(1., 2.),
];
for method in methods {
let kernel_ref = Kernel::new(
input,
&Kernel::params_with_nn(KdTree)
.method(method.clone())
.kind(k_type.clone()),
);
let kernel_tr = Kernel::params()
.kind(k_type.clone())
.method(method.clone())
.transform(input);
match (&kernel_ref.inner, &kernel_tr.inner) {
(KernelInner::Dense(m1), KernelInner::Dense(m2)) => {
assert!(kernels_almost_equal(m1, m2))
}
(KernelInner::Sparse(m1), KernelInner::Sparse(m2)) => {
assert!(kernels_almost_equal(m1, m2))
}
_ => panic!("Kernel inners must match!"),
};
}
}
/// Determines if two matrices:`ArrayView2<f64>` are equivalent within f64::EPSILON
fn matrices_almost_equal(reference: ArrayView2<f64>, transformed: ArrayView2<f64>) -> bool {
for (ref_row, tr_row) in reference
.axis_iter(Axis(0))
.zip(transformed.axis_iter(Axis(0)))
{
if !arrays_almost_equal(ref_row, tr_row) {
return false;
}
}
true
}
/// Determines if two arrays:`ArrayView1<64>` are equivalent within f64::EPSILON
fn arrays_almost_equal(reference: ArrayView1<f64>, transformed: ArrayView1<f64>) -> bool {
for (ref_item, tr_item) in reference.iter().zip(transformed.iter()) {
if !values_almost_equal(ref_item, tr_item) {
return false;
}
}
true
}
/// Determines if two kernels are equivalent for all matched elements are equivalent within f64::EPSILON
fn kernels_almost_equal<K: Inner<Elem = f64>>(reference: &K, transformed: &K) -> bool {
for i in 0..reference.size() {
if !vecs_almost_equal(reference.column(i), transformed.column(i)) {
return false;
}
}
true
}
/// Determines if all matched elements within a pair of vectors are equivalent within f64::EPSILON
fn vecs_almost_equal(reference: Vec<f64>, transformed: Vec<f64>) -> bool {
for (ref_item, tr_item) in reference.iter().zip(transformed.iter()) {
if !values_almost_equal(ref_item, tr_item) {
return false;
}
}
true
}
/// Determines if two values are equal within an absolute difference of f64::EPSILON
fn values_almost_equal(v1: &f64, v2: &f64) -> bool {
(v1 - v2).abs() <= f64::EPSILON
}
}