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feat: adds PCA

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This commit is contained in:
Volodymyr Orlov
2020-03-06 09:13:54 -08:00
parent 619560a1cd
commit 7b3fa982be
9 changed files with 1422 additions and 20 deletions
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src/decomposition/pca.rs
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use crate::linalg::{Matrix};
#[derive(Debug)]
pub struct PCA<M: Matrix> {
eigenvectors: M,
eigenvalues: Vec<f64>,
projection: M,
mu: Vec<f64>,
pmu: Vec<f64>
}
#[derive(Debug, Clone)]
pub struct PCAParameters {
use_correlation_matrix: bool
}
impl Default for PCAParameters {
fn default() -> Self {
PCAParameters {
use_correlation_matrix: false
}
}
}
impl<M: Matrix> PCA<M> {
pub fn new(data: &M, n_components: usize, parameters: PCAParameters) -> PCA<M> {
let (m, n) = data.shape();
let mu = data.column_mean();
let mut x = data.clone();
for c in 0..n {
for r in 0..m {
x.sub_element_mut(r, c, mu[c]);
}
}
let mut eigenvalues;
let mut eigenvectors;
if m > n && !parameters.use_correlation_matrix{
let svd = x.svd();
eigenvalues = svd.s;
for i in 0..eigenvalues.len() {
eigenvalues[i] *= eigenvalues[i];
}
eigenvectors = svd.V;
} else {
let mut cov = M::zeros(n, n);
for k in 0..m {
for i in 0..n {
for j in 0..=i {
cov.add_element_mut(i, j, x.get(k, i) * x.get(k, j));
}
}
}
for i in 0..n {
for j in 0..=i {
cov.div_element_mut(i, j, m as f64);
cov.set(j, i, cov.get(i, j));
}
}
if parameters.use_correlation_matrix {
let mut sd = vec![0f64; n];
for i in 0..n {
sd[i] = cov.get(i, i).sqrt();
}
for i in 0..n {
for j in 0..=i {
cov.div_element_mut(i, j, sd[i] * sd[j]);
cov.set(j, i, cov.get(i, j));
}
}
let evd = cov.evd(true);
eigenvalues = evd.d;
eigenvectors = evd.V;
for i in 0..n {
for j in 0..n {
eigenvectors.div_element_mut(i, j, sd[i]);
}
}
} else {
let evd = cov.evd(true);
eigenvalues = evd.d;
eigenvectors = evd.V;
}
}
let mut projection = M::zeros(n_components, n);
for i in 0..n {
for j in 0..n_components {
projection.set(j, i, eigenvectors.get(i, j));
}
}
let mut pmu = vec![0f64; n_components];
for k in 0..n {
for i in 0..n_components {
pmu[i] += projection.get(i, k) * mu[k];
}
}
PCA {
eigenvectors: eigenvectors,
eigenvalues: eigenvalues,
projection: projection.transpose(),
mu: mu,
pmu: pmu
}
}
pub fn transform(&self, x: &M) -> M {
let (nrows, ncols) = x.shape();
let (_, n_components) = self.projection.shape();
if ncols != self.mu.len() {
panic!("Invalid input vector size: {}, expected: {}", ncols, self.mu.len());
}
let mut x_transformed = x.dot(&self.projection);
for r in 0..nrows {
for c in 0..n_components {
x_transformed.sub_element_mut(r, c, self.pmu[c]);
}
}
x_transformed
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::linalg::naive::dense_matrix::DenseMatrix;
fn us_arrests_data() -> DenseMatrix {
DenseMatrix::from_array(&[
&[13.2, 236.0, 58.0, 21.2],
&[10.0, 263.0, 48.0, 44.5],
&[8.1, 294.0, 80.0, 31.0],
&[8.8, 190.0, 50.0, 19.5],
&[9.0, 276.0, 91.0, 40.6],
&[7.9, 204.0, 78.0, 38.7],
&[3.3, 110.0, 77.0, 11.1],
&[5.9, 238.0, 72.0, 15.8],
&[15.4, 335.0, 80.0, 31.9],
&[17.4, 211.0, 60.0, 25.8],
&[5.3, 46.0, 83.0, 20.2],
&[2.6, 120.0, 54.0, 14.2],
&[10.4, 249.0, 83.0, 24.0],
&[7.2, 113.0, 65.0, 21.0],
&[2.2, 56.0, 57.0, 11.3],
&[6.0, 115.0, 66.0, 18.0],
&[9.7, 109.0, 52.0, 16.3],
&[15.4, 249.0, 66.0, 22.2],
&[2.1, 83.0, 51.0, 7.8],
&[11.3, 300.0, 67.0, 27.8],
&[4.4, 149.0, 85.0, 16.3],
&[12.1, 255.0, 74.0, 35.1],
&[2.7, 72.0, 66.0, 14.9],
&[16.1, 259.0, 44.0, 17.1],
&[9.0, 178.0, 70.0, 28.2],
&[6.0, 109.0, 53.0, 16.4],
&[4.3, 102.0, 62.0, 16.5],
&[12.2, 252.0, 81.0, 46.0],
&[2.1, 57.0, 56.0, 9.5],
&[7.4, 159.0, 89.0, 18.8],
&[11.4, 285.0, 70.0, 32.1],
&[11.1, 254.0, 86.0, 26.1],
&[13.0, 337.0, 45.0, 16.1],
&[0.8, 45.0, 44.0, 7.3],
&[7.3, 120.0, 75.0, 21.4],
&[6.6, 151.0, 68.0, 20.0],
&[4.9, 159.0, 67.0, 29.3],
&[6.3, 106.0, 72.0, 14.9],
&[3.4, 174.0, 87.0, 8.3],
&[14.4, 279.0, 48.0, 22.5],
&[3.8, 86.0, 45.0, 12.8],
&[13.2, 188.0, 59.0, 26.9],
&[12.7, 201.0, 80.0, 25.5],
&[3.2, 120.0, 80.0, 22.9],
&[2.2, 48.0, 32.0, 11.2],
&[8.5, 156.0, 63.0, 20.7],
&[4.0, 145.0, 73.0, 26.2],
&[5.7, 81.0, 39.0, 9.3],
&[2.6, 53.0, 66.0, 10.8],
&[6.8, 161.0, 60.0, 15.6]])
}
#[test]
fn decompose_covariance() {
let us_arrests = us_arrests_data();
let expected_eigenvectors = DenseMatrix::from_array(&[
&[-0.0417043206282872, -0.0448216562696701, -0.0798906594208108, -0.994921731246978],
&[-0.995221281426497, -0.058760027857223, 0.0675697350838043, 0.0389382976351601],
&[-0.0463357461197108, 0.97685747990989, 0.200546287353866, -0.0581691430589319],
&[-0.075155500585547, 0.200718066450337, -0.974080592182491, 0.0723250196376097]
]);
let expected_projection = DenseMatrix::from_array(&[
&[-64.8022, -11.448, 2.4949, -2.4079],
&[-92.8275, -17.9829, -20.1266, 4.094],
&[-124.0682, 8.8304, 1.6874, 4.3537],
&[-18.34, -16.7039, -0.2102, 0.521],
&[-107.423, 22.5201, -6.7459, 2.8118],
&[-34.976, 13.7196, -12.2794, 1.7215],
&[60.8873, 12.9325, 8.4207, 0.6999],
&[-66.731, 1.3538, 11.281, 3.728],
&[-165.2444, 6.2747, 2.9979, -1.2477],
&[-40.5352, -7.2902, -3.6095, -7.3437],
&[123.5361, 24.2912, -3.7244, -3.4728],
&[51.797, -9.4692, 1.5201, 3.3478],
&[-78.9921, 12.8971, 5.8833, -0.3676],
&[57.551, 2.8463, -3.7382, -1.6494],
&[115.5868, -3.3421, 0.654, 0.8695],
&[55.7897, 3.1572, -0.3844, -0.6528],
&[62.3832, -10.6733, -2.2371, -3.8762],
&[-78.2776, -4.2949, 3.8279, -4.4836],
&[89.261, -11.4878, 4.6924, 2.1162],
&[-129.3301, -5.007, 2.3472, 1.9283],
&[21.2663, 19.4502, 7.5071, 1.0348],
&[-85.4515, 5.9046, -6.4643, -0.499],
&[98.9548, 5.2096, -0.0066, 0.7319],
&[-86.8564, -27.4284, 5.0034, -3.8798],
&[-7.9863, 5.2756, -5.5006, -0.6794],
&[62.4836, -9.5105, -1.8384, -0.2459],
&[69.0965, -0.2112, -0.468, 0.6566],
&[-83.6136, 15.1022, -15.8887, -0.3342],
&[114.7774, -4.7346, 2.2824, 0.9359],
&[10.8157, 23.1373, 6.3102, -1.6124],
&[-114.8682, -0.3365, -2.2613, 1.3812],
&[-84.2942, 15.924, 4.7213, -0.892],
&[-164.3255, -31.0966, 11.6962, 2.1112],
&[127.4956, -16.135, 1.3118, 2.301],
&[50.0868, 12.2793, -1.6573, -2.0291],
&[19.6937, 3.3701, 0.4531, 0.1803],
&[11.1502, 3.8661, -8.13, 2.914],
&[64.6891, 8.9115, 3.2065, -1.8749],
&[-3.064, 18.374, 17.47, 2.3083],
&[-107.2811, -23.5361, 2.0328, -1.2517],
&[86.1067, -16.5979, -1.3144, 1.2523],
&[-17.5063, -6.5066, -6.1001, -3.9229],
&[-31.2911, 12.985, 0.3934, -4.242],
&[49.9134, 17.6485, -1.7882, 1.8677],
&[124.7145, -27.3136, -4.8028, 2.005],
&[14.8174, -1.7526, -1.0454, -1.1738],
&[25.0758, 9.968, -4.7811, 2.6911],
&[91.5446, -22.9529, 0.402, -0.7369],
&[118.1763, 5.5076, 2.7113, -0.205],
&[10.4345, -5.9245, 3.7944, 0.5179]
]);
let expected_eigenvalues: Vec<f64> = vec![343544.6277001563, 9897.625949808047, 2063.519887011604, 302.04806302399646];
let pca = PCA::new(&us_arrests, 4, Default::default());
assert!(pca.eigenvectors.abs().approximate_eq(&expected_eigenvectors.abs(), 1e-4));
for i in 0..pca.eigenvalues.len() {
assert_eq!(pca.eigenvalues[i].abs(), expected_eigenvalues[i].abs());
}
let us_arrests_t = pca.transform(&us_arrests);
assert!(us_arrests_t.abs().approximate_eq(&expected_projection.abs(), 1e-4));
}
#[test]
fn decompose_correlation() {
let us_arrests = us_arrests_data();
let expected_eigenvectors = DenseMatrix::from_array(&[
&[0.124288601688222, -0.0969866877028367, 0.0791404742697482, -0.150572299008293],
&[0.00706888610512014, -0.00227861130898090, 0.00325028101296307, 0.00901099154845273],
&[0.0194141494466002, 0.060910660326921, 0.0263806464184195, -0.0093429458365566],
&[0.0586084532558777, 0.0180450999787168, -0.0881962972508558, -0.0096011588898465]
]);
let expected_projection = DenseMatrix::from_array(&[
&[0.9856, -1.1334, 0.4443, -0.1563],
&[1.9501, -1.0732, -2.04, 0.4386],
&[1.7632, 0.746, -0.0548, 0.8347],
&[-0.1414, -1.1198, -0.1146, 0.1828],
&[2.524, 1.5429, -0.5986, 0.342],
&[1.5146, 0.9876, -1.095, -0.0015],
&[-1.3586, 1.0889, 0.6433, 0.1185],
&[0.0477, 0.3254, 0.7186, 0.882],
&[3.013, -0.0392, 0.5768, 0.0963],
&[1.6393, -1.2789, 0.3425, -1.0768],
&[-0.9127, 1.5705, -0.0508, -0.9028],
&[-1.6398, -0.211, -0.2598, 0.4991],
&[1.3789, 0.6818, 0.6775, 0.122],
&[-0.5055, 0.1516, -0.2281, -0.4247],
&[-2.2536, 0.1041, -0.1646, -0.0176],
&[-0.7969, 0.2702, -0.0256, -0.2065],
&[-0.7509, -0.9584, 0.0284, -0.6706],
&[1.5648, -0.8711, 0.7835, -0.4547],
&[-2.3968, -0.3764, 0.0657, 0.3305],
&[1.7634, -0.4277, 0.1573, 0.5591],
&[-0.4862, 1.4745, 0.6095, 0.1796],
&[2.1084, 0.1554, -0.3849, -0.1024],
&[-1.6927, 0.6323, -0.1531, -0.0673],
&[0.9965, -2.3938, 0.7408, -0.2155],
&[0.6968, 0.2634, -0.3774, -0.2258],
&[-1.1855, -0.5369, -0.2469, -0.1237],
&[-1.2656, 0.194, -0.1756, -0.0159],
&[2.8744, 0.7756, -1.1634, -0.3145],
&[-2.3839, 0.0181, -0.0369, 0.0331],
&[0.1816, 1.4495, 0.7645, -0.2434],
&[1.98, -0.1428, -0.1837, 0.3395],
&[1.6826, 0.8232, 0.6431, 0.0135],
&[1.1234, -2.228, 0.8636, 0.9544],
&[-2.9922, -0.5991, -0.3013, 0.254],
&[-0.226, 0.7422, 0.0311, -0.4739],
&[-0.3118, 0.2879, 0.0153, -0.0103],
&[0.0591, 0.5414, -0.9398, 0.2378],
&[-0.8884, 0.5711, 0.4006, -0.3591],
&[-0.8638, 1.492, 1.3699, 0.6136],
&[1.3207, -1.9334, 0.3005, 0.1315],
&[-1.9878, -0.8233, -0.3893, 0.1096],
&[0.9997, -0.8603, -0.1881, -0.6529],
&[1.3551, 0.4125, 0.4921, -0.6432],
&[-0.5506, 1.4715, -0.2937, 0.0823],
&[-2.8014, -1.4023, -0.8413, 0.1449],
&[-0.0963, -0.1997, -0.0117, -0.2114],
&[-0.2169, 0.9701, -0.6249, 0.2208],
&[-2.1086, -1.4248, -0.1048, -0.1319],
&[-2.0797, 0.6113, 0.1389, -0.1841],
&[-0.6294, -0.321, 0.2407, 0.1667]
]);
let expected_eigenvalues: Vec<f64> = vec![2.480241579149493, 0.9897651525398419, 0.35656318058083064, 0.1734300877298357];
let pca = PCA::new(&us_arrests, 4, PCAParameters{use_correlation_matrix: true});
assert!(pca.eigenvectors.abs().approximate_eq(&expected_eigenvectors.abs(), 1e-4));
for i in 0..pca.eigenvalues.len() {
assert_eq!(pca.eigenvalues[i].abs(), expected_eigenvalues[i].abs());
}
let us_arrests_t = pca.transform(&us_arrests);
assert!(us_arrests_t.abs().approximate_eq(&expected_projection.abs(), 1e-4));
}
}