April 2020
Intermediate to advanced
344 pages
8h 22m
Japanese
Content preview from Pythonではじめる教師なし学習 ―機械学習の可能性を広げるラベルなしデータの利用
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3.4
特異値分解
81
3.4
特異値分解
データの背後にある構造を学習する方法として、元の特徴量行列のランクよりも小さなランクを持つ
行列を作り、小さなランクの行列のベクトルの一部の線形結合として元の行列が再構成できるようにす
る方法がある。この方法は、特異値分解（
SVD
：
Singular Value Decomposition
）と呼ばれている。
SVD
は小さいランクの行列を作る際に、元の行列の最も多くの情報を持つベクトル（すなわち最も大
きい特異値を持つもの）を維持する。小さいランクの行列は、元の特徴量空間の最も重要な要素を捉え
ている。
この手法は
PCA
とよく似ている。
PCA
は共分散行列の固有値分解を用いて次元削減を行う。
SVG
では、名前の通り特異値分解を用いる。実際、
PCA
の実装では
SVD
を内部的に用いる場合がある。だ
が、この議論は本書の範囲を超える。
SVD
の使い方を見てみよう。
# Singular Value Decomposition
from sklearn.decomposition import TruncatedSVD
n_components = 200
algorithm = 'randomized'
n_iter = 5
random_state = 2018
svd = TruncatedSVD(n_components=n_components, algorithm=algorithm, \
n_iter=n_iter, random_state=random_state) ...
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