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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82
3
章 次元削減
図3-8 SVDを用いた場合の観測点の分離
3.5
ランダム射影
別の線形次元削減手法であるランダム射影（
random projection
）を見てみよう。これはJohnson-
Lindenstrauss の補題に基づくものだ。
Johnson-Lindenstrauss
の補題とは、高次元空間をはるかに低
次元な空間に埋め込んだ場合、点間の距離がほぼ保存されるというものだ。言い換えると、高次元空
間から低次元空間に移しても元の特徴量の構造は保存されるということだ。
3.5.1
ガウス型ランダム射影
ランダム射影には
2
つの方 法 が ある。標 準 的なのはガウス型ランダム射影（
Gaussian random
projection
）と 呼 ば れ る も の で 、 も う 一 方 は スパースランダム射影（
sparse random projection
）と 呼 ば
れるものだ。
ガウス型ランダム射影では、削減した特徴量空間で維持したい成分の数か、ハイパーパラメータ
eps
を指定できる。
eps
は、
Johnson-Lindenstrauss
の補題に基づいて埋め込みの質を制御するパラ
メータで、これを小さくすると、生成される次元数が大きくなる。ここではこのハイパーパラメータを
指定する。
# Gaussian Random Projection
from sklearn.random_projection import GaussianRandomProjection
n_components ...
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