Problem Statement

t-SNE (t-Distributed Stochastic Neighbor Embedding) is widely used for visualizing high-dimensional data in 2D/3D. Currently missing from aprender.

Use Cases:

• Visualize MNIST digits
• Explore embeddings (word vectors, image features)
• Cluster visualization
• Exploratory data analysis

Advantages:

• Preserves local structure better than PCA
• Reveals clusters visually
• Non-linear dimensionality reduction

Proposed Solution

Implement t-SNE following sklearn API with EXTREME TDD.

Algorithm

Core Idea: Preserve pairwise similarities in lower dimensions

Steps:

1. Compute pairwise similarities in high-D (Gaussian)
2. Initialize low-D embedding (random or PCA)
3. Compute pairwise similarities in low-D (Student's t)
4. Minimize KL divergence via gradient descent
5. Use early exaggeration for better separation

Implementation

Trait: Transformer

API Design:

pub struct TSNE {
    n_components: usize,  // Usually 2 or 3
    perplexity: f32,      // Balance local vs global structure (5-50)
    learning_rate: f32,
    n_iter: usize,
    embedding: Option<Matrix<f32>>,
}

impl Transformer for TSNE {
    fn fit(&mut self, x: &Matrix<f32>) -> Result<(), &'static str>;
    fn transform(&self, x: &Matrix<f32>) -> Result<Matrix<f32>, &'static str>;
}

Success Criteria

• ✅ t-SNE with gradient descent optimization
• ✅ Perplexity parameter
• ✅ Early exaggeration
• ✅ 10+ tests
• ✅ Zero clippy warnings
• ✅ Example: examples/tsne_mnist.rs (visualize digits)

Estimated Effort

Timeline: 5-7 days
Complexity: High (complex optimization, pairwise distances O(n²))