Machine Learning Academy · レッスン

t-SNE：可視化のための近傍関係の保持

異なるperplexity設定でMNISTの埋め込みにt-SNEを適用し、t-SNE上の距離は後続のモデリングにおいて意味を持たないことを理解します。

「t-SNE：可視化のための近傍関係の保持」はCoddyKit上の無料Machine Learning Academyレッスンです。これはレッスン3/4です。下記で完全なレッスンを無料で読むことができます。その後、ブラウザ内の組み込みコードエディタと24時間対応のAIチューターでハンズオン演習できます。これはMachine Learning Academy学習パスの一部であり、ウェブとCoddyKitアプリ全体で進捗が同期されます。 Machine Learning Academyコースには全4レッスンが含まれています。

このレッスンの一部はまだ翻訳されておらず、英語で表示されています。

Beyond PCA: Non-Linear Visualisation

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.

The Core Idea: Similarity Distributions

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.

The Perplexity Parameter

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.

Running t-SNE in scikit-learn

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).

from sklearn.manifold import TSNE
from sklearn.datasets import load_digits
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA

X, y = load_digits(return_X_y=True)
X_scaled = StandardScaler().fit_transform(X)

# Pre-reduce with PCA for speed
X_pca = PCA(n_components=30).fit_transform(X_scaled)

# t-SNE to 2D
tsne = TSNE(n_components=2, perplexity=30, n_iter=1000, random_state=42)
X_tsne = tsne.fit_transform(X_pca)

print('t-SNE shape:', X_tsne.shape)

Visualising t-SNE Embeddings

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.

import matplotlib.pyplot as plt

fig, ax = plt.subplots(figsize=(8, 6))
scatter = ax.scatter(X_tsne[:, 0], X_tsne[:, 1], c=y, cmap='tab10', s=8, alpha=0.7)
fig.colorbar(scatter, ax=ax, label='Digit')
ax.set_title('MNIST digits — t-SNE (perplexity=30)')
ax.set_xlabel('t-SNE 1')
ax.set_ylabel('t-SNE 2')
plt.tight_layout()
plt.show()

Effect of Perplexity on the Embedding

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.

import matplotlib.pyplot as plt
from sklearn.manifold import TSNE

perplexities = [5, 15, 30, 50]
fig, axes = plt.subplots(1, 4, figsize=(16, 4))

for ax, perp in zip(axes, perplexities):
    tsne = TSNE(n_components=2, perplexity=perp, n_iter=800, random_state=0)
    X_emb = tsne.fit_transform(X_pca[:300])  # subset for speed
    ax.scatter(X_emb[:, 0], X_emb[:, 1], c=y[:300], cmap='tab10', s=10)
    ax.set_title(f'Perplexity={perp}')
    ax.axis('off')
plt.tight_layout()
plt.show()

t-SNE Distances Are Not Meaningful

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.

t-SNE Is Stochastic and Non-Deterministic

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: A Modern Alternative to t-SNE

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.

# pip install umap-learn
import umap

reducer = umap.UMAP(n_components=2, n_neighbors=15, min_dist=0.1, random_state=42)
X_umap = reducer.fit_transform(X_pca)

import matplotlib.pyplot as plt
plt.scatter(X_umap[:, 0], X_umap[:, 1], c=y, cmap='tab10', s=8)
plt.title('MNIST — UMAP embedding')
plt.colorbar(label='Digit')
plt.show()

When to Use t-SNE vs PCA

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.

Complete t-SNE Visualisation Pipeline

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.

from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
from sklearn.manifold import TSNE
from sklearn.datasets import load_digits
import matplotlib.pyplot as plt

X, y = load_digits(return_X_y=True)

# Step 1: scale
X_s = StandardScaler().fit_transform(X)

# Step 2: PCA pre-reduction
X_pca = PCA(n_components=30, random_state=0).fit_transform(X_s)

# Step 3: t-SNE
X_tsne = TSNE(n_components=2, perplexity=30, random_state=0).fit_transform(X_pca)

# Step 4: plot
plt.scatter(X_tsne[:, 0], X_tsne[:, 1], c=y, cmap='tab10', s=10)
plt.title('Digits t-SNE')
plt.colorbar(label='Digit')
plt.show()

Quick Check

Test your understanding of t-SNE from this lesson.

Lesson Recap

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.

よくある質問

「t-SNE：可視化のための近傍関係の保持」レッスンは無料ですか？

はい。「t-SNE：可視化のための近傍関係の保持」の完全なテキストはこのウェブで無料で読めます。インタラクティブに演習し（組み込みコードエディタと24時間対応のAIチューター）、Machine Learning Academyコースの残りをアンロックするには、CoddyKit PROにアップグレードしてください。 Machine Learning Academyコースには全4レッスンが含まれています。

「t-SNE：可視化のための近傍関係の保持」で何を学びますか？

異なるperplexity設定でMNISTの埋め込みにt-SNEを適用し、t-SNE上の距離は後続のモデリングにおいて意味を持たないことを理解します。ブラウザで直接実行するハンズオンコードでMachine Learning Academyを演習し、24時間対応のAIチューターがレッスンを進める中での質問に答えます。

Machine Learning Academyを始めるのに経験は必要ですか？

事前経験は必要ありません。CoddyKitのMachine Learning Academyは初級者から上級者向けに構成されているため、ここから始めるか最初から始めて、自分のペースで進むことができます。これはレッスン3/4です。

「t-SNE：可視化のための近傍関係の保持」レッスンにはどのくらい時間がかかりますか？

ほとんどのCoddyKitレッスンは約5～10分かかります。各レッスンはコンパクトでインタラクティブなので、着実に進歩し、ウェブとアプリ全体で正確に前回の場所から再開できます。

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