t-SNE: 시각화를 위한 이웃 구조 보존

PCA projects data linearly and preserves global variance, but can fail to show local cluster structure. t-SNE (t-distributed Stochastic Neighbour Embedding) is a non-linear dimensionality reduction technique designed specifically for 2D and 3D visualisation. It prioritises preserving local neighbourhoods: points that are close in high-dimensional space should also be close in the 2D plot.

t-SNE defines a probability distribution over pairs of points in high-dimensional space: nearby points have high similarity. It then defines a similar distribution in the low-dimensional embedding. The algorithm minimises the KL divergence between the two distributions using gradient descent, nudging points in 2D until the neighbourhood structure matches the high-D structure.

Perplexity is t-SNE's most important hyperparameter. It loosely controls how many neighbours each point considers when building the high-D similarity distribution — typically between 5 and 50. Low perplexity focuses on very local structure (many small clusters); high perplexity captures more global structure (broader, more spread-out clusters). The same dataset can look very different under different perplexity values.

Use sklearn.manifold.TSNE. Key parameters: n_components (almost always 2), perplexity, n_iter (default 1000), and random_state. t-SNE is computationally expensive — O(n² log n) — so reduce the dataset with PCA first for large inputs (e.g., PCA to 50 dimensions, then t-SNE to 2D).

Plot the 2D t-SNE coordinates with class colour to reveal cluster structure. On MNIST digits with appropriate perplexity, you typically see well-separated digit clusters, with similar-looking digits (e.g., 3 and 8) placed close together. This confirms that t-SNE captures semantically meaningful groupings.

It is essential to try multiple perplexity values and compare the plots. A perplexity that is too low creates many small disconnected blobs even within the same true cluster. A perplexity that is too high smears clusters together. A good practice is to test perplexity in [5, 15, 30, 50] and choose the embedding where known cluster structure appears most clearly.

A critical warning: distances between clusters in t-SNE are not interpretable. A cluster appearing far from another does not mean they are globally distant; the algorithm optimises local neighbourhood preservation, not global distances. You cannot compare cluster sizes or inter-cluster distances across different runs or perplexity settings. Use t-SNE for exploration only, not for quantitative analysis.

Every t-SNE run with a different random_state produces a different layout — the embedding can rotate, reflect, or rearrange clusters. Always set random_state for reproducibility. Also, t-SNE does not have a transform method for out-of-sample points: you must refit on the entire dataset each time, which makes it unsuitable as a preprocessing step for a production model.

UMAP (Uniform Manifold Approximation and Projection) is a newer technique that is faster than t-SNE, preserves both local and more global structure, and supports transform for new points. It is not in scikit-learn but is installed via pip install umap-learn. For large datasets or production pipelines, UMAP is generally preferred over t-SNE.

Use PCA for: preprocessing before modelling, compression, anomaly detection via reconstruction error, or when you need a deterministic, reversible transform. Use t-SNE for: exploring cluster structure in high-dimensional data, generating visualisations for presentations, or confirming that a dataset has meaningful groupings before applying a clustering or classification algorithm.

Here is the recommended pipeline for t-SNE on any high-dimensional dataset: scale, reduce with PCA to ~50 dimensions, then apply t-SNE to 2D, and plot with class labels.

In this lesson you learned: t-SNE preserves local neighbourhoods by minimising KL divergence between high-D and low-D similarity distributions, perplexity controls the effective number of neighbours and should be tuned between 5 and 50, and t-SNE distances between clusters are not quantitatively meaningful — use it for exploration only. Next up we embed PCA inside a scikit-learn Pipeline as a preprocessing step for classifiers.