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//! t-SNE: t-Distributed Stochastic Neighbor Embedding
//! (van der Maaten & Hinton 2008).
//!
//! Nonlinear dimensionality reduction for visualization.
//! Maps high-dimensional data to 2D (or 3D) preserving
//! local structure.
//!
//! Algorithm:
//! 1. Compute pairwise affinities in high-D (Gaussian kernel)
//! 2. Compute pairwise affinities in low-D (Student-t kernel)
//! 3. Minimize KL divergence via gradient descent
//!
//! This simplified implementation uses:
//! - Fixed perplexity for bandwidth
//! - Momentum-based gradient descent
//! - Early exaggeration
use crate::GreenersError;
use ndarray::Array2;
use std::fmt;
/// Result of t-SNE.
#[derive(Debug)]
pub struct TsneResult {
/// 2D embedding (n x 2)
pub embedding: Array2<f64>,
/// Final KL divergence
pub kl_divergence: f64,
/// Number of iterations
pub n_iter: usize,
/// Perplexity
pub perplexity: f64,
/// Learning rate
pub learning_rate: f64,
/// Number of observations
pub n_obs: usize,
/// Number of original features
pub n_features: usize,
/// Number of output dimensions
pub n_components: usize,
/// Iterations array (for plotting)
pub costs: Vec<f64>,
}
impl fmt::Display for TsneResult {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
writeln!(f, "\n{:=^78}", " t-SNE ")?;
writeln!(f, "van der Maaten & Hinton (2008)")?;
writeln!(f, "t-Distributed Stochastic Neighbor Embedding")?;
writeln!(f, "{:<20} {:>12}", "Observations:", self.n_obs)?;
writeln!(f, "{:<20} {:>12}", "Input features:", self.n_features)?;
writeln!(f, "{:<20} {:>12}", "Output dims:", self.n_components)?;
writeln!(f, "{:<20} {:>12.2}", "Perplexity:", self.perplexity)?;
writeln!(f, "{:<20} {:>12.2}", "Learning rate:", self.learning_rate)?;
writeln!(f, "{:<20} {:>12}", "Iterations:", self.n_iter)?;
writeln!(
f,
"{:<20} {:>12.6}",
"Final KL divergence:", self.kl_divergence
)?;
// Embedding (first 10 points)
writeln!(f, "\n{:-^78}", "")?;
writeln!(f, " 2D embedding (first 10 points):")?;
writeln!(f, " {:<6} {:>12} {:>12}", "Obs", "Dim 1", "Dim 2")?;
writeln!(f, "{:-^78}", "")?;
let n_show = 10.min(self.n_obs);
for i in 0..n_show {
writeln!(
f,
" {:<6} {:>12.4} {:>12.4}",
i + 1,
self.embedding[(i, 0)],
self.embedding[(i, 1)]
)?;
}
// Cost history (every 50 iterations)
if !self.costs.is_empty() {
writeln!(f, "\n KL divergence history:")?;
writeln!(f, " {:<10} {:>12}", "Iter", "KL")?;
writeln!(f, "{:-^78}", "")?;
for (i, cost) in self.costs.iter().enumerate() {
if i % 50 == 0 || i == self.costs.len() - 1 {
writeln!(f, " {:<10} {:>12.6}", i + 1, cost)?;
}
}
}
write!(f, "{:=^78}", "")
}
}
pub struct TSNE;
impl TSNE {
/// Run t-SNE dimensionality reduction.
///
/// # Arguments
/// * `x` - High-dimensional data (n x d)
/// * `perplexity` - Target perplexity (default 30.0)
/// * `n_components` - Output dimensions (default 2)
/// * `max_iter` - Max iterations (default 500)
/// * `learning_rate` - Gradient descent learning rate (default 200.0)
pub fn fit(
x: &Array2<f64>,
perplexity: Option<f64>,
n_components: Option<usize>,
max_iter: Option<usize>,
learning_rate: Option<f64>,
) -> Result<TsneResult, GreenersError> {
let n = x.nrows();
let d = x.ncols();
if n < 5 {
return Err(GreenersError::InvalidOperation(
"TSNE: need at least 5 observations".into(),
));
}
let perp = perplexity.unwrap_or(30.0).min(n as f64 / 3.0).max(5.0);
let n_comp = n_components.unwrap_or(2);
let max_iterations = max_iter.unwrap_or(500);
let lr = learning_rate.unwrap_or(200.0);
// Step 1: Compute pairwise distances in high-D
let mut h_dists = Array2::zeros((n, n));
for i in 0..n {
for j in i..n {
let dist: f64 = (0..d)
.map(|f| (x[(i, f)] - x[(j, f)]).powi(2))
.sum::<f64>()
.sqrt();
h_dists[(i, j)] = dist;
h_dists[(j, i)] = dist;
}
}
// Step 2: Compute high-D affinities P (symmetric Gaussian)
let mut p = Array2::zeros((n, n));
let target_entropy = (perp * 2.0_f64.ln()).max(1e-10);
for i in 0..n {
// Binary search for sigma_i
let mut sigma = 1.0;
let mut sigma_min = 0.1;
let mut sigma_max = 100.0;
for _ in 0..50 {
let mut sum_p = 0.0;
let mut entropy = 0.0;
for j in 0..n {
if i == j {
continue;
}
let p_ij = (-h_dists[(i, j)].powi(2) / (2.0 * sigma * sigma)).exp();
p[(i, j)] = p_ij;
sum_p += p_ij;
}
if sum_p < 1e-15 {
sigma = (sigma_min + sigma_max) / 2.0;
continue;
}
for j in 0..n {
if i != j {
p[(i, j)] /= sum_p;
if p[(i, j)] > 1e-15 {
entropy -= p[(i, j)] * p[(i, j)].ln();
}
}
}
if entropy > target_entropy {
sigma_max = sigma;
sigma = (sigma_min + sigma) / 2.0;
} else {
sigma_min = sigma;
sigma = (sigma + sigma_max) / 2.0;
}
}
}
// Symmetrize P
for i in 0..n {
for j in 0..n {
p[(i, j)] = (p[(i, j)] + p[(j, i)]) / (2.0 * n as f64);
}
}
// Clamp P to avoid log(0)
for i in 0..n {
for j in 0..n {
p[(i, j)] = p[(i, j)].max(1e-12);
}
}
// Step 3: Initialize low-D embedding randomly
let mut y = Array2::zeros((n, n_comp));
for i in 0..n {
for j in 0..n_comp {
y[(i, j)] = (Self::rand_normal() * 1e-4).clamp(-1e-4, 1e-4);
}
}
// Gradient descent with momentum
let mut prev_grad = Array2::<f64>::zeros((n, n_comp));
let mut costs = Vec::new();
let mut kl = 0.0;
let mut momentum = 0.5;
let early_exaggeration = 4.0;
let exaggeration_end = 100;
for iter in 0..max_iterations {
let exaggeration = if iter < exaggeration_end {
early_exaggeration
} else {
1.0
};
// Compute low-D affinities Q (Student-t)
let mut q = Array2::zeros((n, n));
let mut sum_q = 0.0;
for i in 0..n {
for j in 0..n {
if i == j {
continue;
}
let dist: f64 = (0..n_comp)
.map(|f| (y[(i, f)] - y[(j, f)]).powi(2))
.sum::<f64>();
let q_ij = 1.0 / (1.0 + dist);
q[(i, j)] = q_ij;
sum_q += q_ij;
}
}
sum_q = sum_q.max(1e-12);
for i in 0..n {
for j in 0..n {
q[(i, j)] /= sum_q;
q[(i, j)] = q[(i, j)].max(1e-12);
}
}
// KL divergence
kl = 0.0;
for i in 0..n {
for j in 0..n {
if i != j {
kl += p[(i, j)] * (p[(i, j)] / q[(i, j)]).ln();
}
}
}
costs.push(kl);
// Gradient
let mut grad = Array2::zeros((n, n_comp));
for i in 0..n {
for j in 0..n {
if i == j {
continue;
}
let pq = exaggeration * p[(i, j)] - q[(i, j)];
let dist: f64 = (0..n_comp)
.map(|f| (y[(i, f)] - y[(j, f)]).powi(2))
.sum::<f64>();
let factor = pq * 4.0 / (1.0 + dist);
for f in 0..n_comp {
grad[(i, f)] += factor * (y[(i, f)] - y[(j, f)]);
}
}
// Scale gradient
for f in 0..n_comp {
grad[(i, f)] *= -lr;
}
}
// Update with momentum
for i in 0..n {
for f in 0..n_comp {
y[(i, f)] += grad[(i, f)] + momentum * prev_grad[(i, f)];
prev_grad[(i, f)] = grad[(i, f)];
}
}
// Re-center
for f in 0..n_comp {
let mean: f64 = (0..n).map(|i| y[(i, f)]).sum::<f64>() / n as f64;
for i in 0..n {
y[(i, f)] -= mean;
}
}
// Update momentum
if iter == 250 {
momentum = 0.8;
}
// Check convergence
if iter > 100 && (costs[iter] - costs[iter - 1]).abs() < 1e-7 {
break;
}
}
Ok(TsneResult {
embedding: y,
kl_divergence: kl,
n_iter: costs.len(),
perplexity: perp,
learning_rate: lr,
n_obs: n,
n_features: d,
n_components: n_comp,
costs,
})
}
fn rand_normal() -> f64 {
let u1 = Self::rand_uniform().max(1e-10);
let u2 = Self::rand_uniform();
(-2.0 * u1.ln()).sqrt() * (2.0 * std::f64::consts::PI * u2).cos()
}
fn rand_uniform() -> f64 {
use std::cell::Cell;
thread_local! {
static STATE: Cell<u64> = const { Cell::new(7766554433) };
}
STATE.with(|s| {
let mut state = s.get();
state = state
.wrapping_mul(6364136223846793005)
.wrapping_add(1442695040888963407);
s.set(state);
((state >> 11) as f64) / (1u64 << 53) as f64
})
}
}