Chapter 7 无监督方法
7.1 聚类
7.1.1 K均值聚类：
K均值聚类是一种常见的聚类方法，它将数据分为预定义数量的簇，其中每个数据点属于与其最近的簇。
from sklearn.cluster import KMeans
from sklearn.datasets import make_blobs
# 生成模拟数据
X, _ = make_blobs(n_samples=300, centers=4, random_state=0, cluster_std=1.0)
# 创建K均值聚类模型
kmeans = KMeans(n_clusters=4)
# 训练模型
kmeans.fit(X)
# 获取簇的标签## KMeans(n_clusters=4)## 簇的标签:## [3 2 0 2 0 1 3 0 2 2 3 2 0 2 1 0 0 1 3 3 1 1 0 3 3 3 1 0 3 0 2 2 0 2 2 2 2
## 2 3 1 0 3 2 0 3 3 2 3 2 1 3 1 2 1 0 3 2 3 2 1 2 0 2 3 3 3 2 1 2 3 0 0 2 3
## 3 2 3 0 1 2 1 0 1 1 2 0 1 0 2 2 0 1 2 3 3 0 1 1 2 3 2 1 2 1 0 1 1 0 2 0 3
## 3 1 2 1 1 2 1 1 0 0 1 0 1 1 1 1 3 1 3 2 3 3 1 2 3 3 2 3 2 2 3 0 3 0 3 2 0
## 2 2 2 0 0 0 1 3 2 3 1 0 2 0 0 1 0 3 1 0 1 0 0 2 1 0 0 2 1 1 0 3 1 0 3 3 0
## 0 0 0 1 2 3 3 0 0 3 3 3 0 3 2 0 3 1 3 0 3 3 2 0 2 0 3 0 0 2 3 3 1 1 0 2 1
## 1 3 1 3 3 2 2 0 0 2 0 1 3 0 1 3 2 3 1 0 1 2 2 2 2 3 3 0 0 3 1 0 3 3 0 1 1
## 2 0 0 3 1 2 3 0 2 0 1 1 3 3 1 1 1 1 0 2 2 1 1 0 1 1 1 2 0 2 0 1 1 2 2 2 1
## 1 0 2 3]7.1.2 层次聚类：
层次聚类是一种聚类方法，它通过构建树状结构将数据分层次地分成簇，可以使用不同的链接准则（如单链接、完全链接、平均链接等）。
from sklearn.cluster import AgglomerativeClustering
from sklearn.datasets import make_blobs
# 生成模拟数据
X, _ = make_blobs(n_samples=300, centers=4, random_state=0, cluster_std=1.0)
# 创建层次聚类模型
agg_clustering = AgglomerativeClustering(n_clusters=4)
# 训练模型
agg_clustering.fit(X)
# 获取簇的标签## AgglomerativeClustering(n_clusters=4)## 簇的标签:## [0 1 0 1 0 2 3 0 1 1 3 1 0 1 2 0 0 2 0 3 2 2 0 3 3 0 2 0 3 0 1 1 0 1 1 1 1
## 1 3 2 0 3 1 0 3 0 1 3 1 2 3 2 1 2 0 0 1 3 1 2 1 0 1 0 3 0 1 2 1 3 0 0 1 3
## 3 1 3 0 2 1 2 0 2 2 1 0 2 0 1 1 0 2 1 3 0 0 2 2 0 3 1 2 1 2 0 2 2 0 1 0 3
## 3 2 1 2 2 1 2 0 0 0 2 0 2 0 2 2 3 2 3 1 3 3 2 1 3 3 1 0 1 1 0 0 0 0 3 1 0
## 1 1 1 0 0 0 2 0 1 3 2 0 1 0 0 0 0 3 3 0 2 0 0 1 2 0 0 1 2 2 0 0 2 0 3 3 0
## 0 0 0 2 1 0 0 0 0 3 3 3 0 3 1 0 0 2 3 0 0 3 1 0 1 0 3 0 0 1 0 0 2 2 0 1 2
## 2 3 2 3 0 1 1 0 0 1 0 2 0 0 2 0 1 3 2 0 2 1 1 1 1 3 0 0 0 3 2 0 3 0 0 2 2
## 1 0 0 3 2 1 0 0 1 0 2 2 3 3 2 2 2 2 0 1 1 2 2 0 2 2 2 1 0 1 0 2 2 1 1 1 2
## 2 0 1 3]7.1.3 DBSCAN（基于密度的聚类）：
DBSCAN是一种基于密度的聚类方法，它能够自动发现不规则形状的簇，并适用于噪声数据。
from sklearn.cluster import DBSCAN
from sklearn.datasets import make_moons
# 生成半月形数据
X, _ = make_moons(n_samples=200, noise=0.05)
# 创建DBSCAN模型
dbscan = DBSCAN(eps=0.3, min_samples=5)
# 训练模型
dbscan.fit(X)
# 获取簇的标签## DBSCAN(eps=0.3)## 簇的标签:## [0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1
## 1 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0
## 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 1
## 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0
## 0 1 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 1
## 1 0 0 1 1 0 0 1 0 0 0 1 1 1 1]7.1.4 谱聚类：
谱聚类是一种基于图论的聚类方法，它通过将数据点表示为图中的节点，并通过图的拉普拉斯特征来划分簇。
from sklearn.cluster import SpectralClustering
from sklearn.datasets import make_blobs
# 生成模拟数据
X, _ = make_blobs(n_samples=300, centers=4, random_state=0, cluster_std=1.0)
# 创建谱聚类模型
spectral = SpectralClustering(n_clusters=4, eigen_solver='arpack', affinity="nearest_neighbors")
# 训练模型
spectral.fit(X)
# 获取簇的标签## SpectralClustering(affinity='nearest_neighbors', eigen_solver='arpack',
## n_clusters=4)## 簇的标签:## [2 3 2 3 2 1 0 2 3 3 0 3 2 3 1 2 2 1 0 0 1 1 2 0 0 0 1 2 0 2 3 3 2 3 3 3 3
## 3 0 1 2 0 3 2 0 0 3 0 3 1 0 1 3 1 2 0 3 0 3 1 3 2 3 0 0 0 3 1 3 0 2 2 3 0
## 0 3 0 2 1 3 1 2 1 1 3 2 1 2 3 3 2 1 3 0 0 2 1 1 3 0 3 1 3 1 2 1 1 2 3 2 0
## 0 1 3 1 1 3 1 2 2 2 1 2 1 1 1 1 0 1 0 3 0 0 1 3 0 0 3 2 3 3 0 2 0 2 0 3 2
## 3 3 3 2 2 2 1 0 3 0 1 2 3 2 2 1 2 0 1 2 1 2 2 3 1 2 2 3 1 1 2 0 1 2 0 0 2
## 2 2 2 1 3 2 0 2 2 0 0 0 2 0 3 2 2 1 0 2 0 0 3 2 3 2 0 2 2 3 0 0 1 1 2 3 1
## 1 0 1 0 2 3 3 2 2 3 2 1 0 2 1 0 3 0 1 2 1 3 3 3 3 0 0 2 2 0 1 2 0 0 2 1 1
## 3 2 2 0 1 3 0 2 3 2 1 1 0 0 1 1 1 1 2 3 3 1 1 2 1 1 1 3 2 3 2 1 1 3 3 3 1
## 1 2 3 0]7.2 降维
Scikit-Learn（Sklearn）提供了多种降维方法，包括主成分分析（PCA）、线性判别分析（LDA）、t-分布随机邻域嵌入（t-SNE）和多维尺度分析（MDS）等。
7.2.1 主成分分析（PCA）：
PCA是一种常见的线性降维方法，通过线性变换将高维数据映射到低维空间，保留尽可能多的方差。
from sklearn.decomposition import PCA
from sklearn.datasets import load_iris
# 加载鸢尾花数据集
iris = load_iris()
X = iris.data
# 创建PCA模型，将数据降维到2维
pca = PCA(n_components=2)
# 训练模型
X_reduced = pca.fit_transform(X)
print("降维后的数据:")## 降维后的数据:## [[-2.68412563 0.31939725]
## [-2.71414169 -0.17700123]
## [-2.88899057 -0.14494943]
## [-2.74534286 -0.31829898]
## [-2.72871654 0.32675451]
## [-2.28085963 0.74133045]
## [-2.82053775 -0.08946138]
## [-2.62614497 0.16338496]
## [-2.88638273 -0.57831175]
## [-2.6727558 -0.11377425]
## [-2.50694709 0.6450689 ]
## [-2.61275523 0.01472994]
## [-2.78610927 -0.235112 ]
## [-3.22380374 -0.51139459]
## [-2.64475039 1.17876464]
## [-2.38603903 1.33806233]
## [-2.62352788 0.81067951]
## [-2.64829671 0.31184914]
## [-2.19982032 0.87283904]
## [-2.5879864 0.51356031]
## [-2.31025622 0.39134594]
## [-2.54370523 0.43299606]
## [-3.21593942 0.13346807]
## [-2.30273318 0.09870885]
## [-2.35575405 -0.03728186]
## [-2.50666891 -0.14601688]
## [-2.46882007 0.13095149]
## [-2.56231991 0.36771886]
## [-2.63953472 0.31203998]
## [-2.63198939 -0.19696122]
## [-2.58739848 -0.20431849]
## [-2.4099325 0.41092426]
## [-2.64886233 0.81336382]
## [-2.59873675 1.09314576]
## [-2.63692688 -0.12132235]
## [-2.86624165 0.06936447]
## [-2.62523805 0.59937002]
## [-2.80068412 0.26864374]
## [-2.98050204 -0.48795834]
## [-2.59000631 0.22904384]
## [-2.77010243 0.26352753]
## [-2.84936871 -0.94096057]
## [-2.99740655 -0.34192606]
## [-2.40561449 0.18887143]
## [-2.20948924 0.43666314]
## [-2.71445143 -0.2502082 ]
## [-2.53814826 0.50377114]
## [-2.83946217 -0.22794557]
## [-2.54308575 0.57941002]
## [-2.70335978 0.10770608]
## [ 1.28482569 0.68516047]
## [ 0.93248853 0.31833364]
## [ 1.46430232 0.50426282]
## [ 0.18331772 -0.82795901]
## [ 1.08810326 0.07459068]
## [ 0.64166908 -0.41824687]
## [ 1.09506066 0.28346827]
## [-0.74912267 -1.00489096]
## [ 1.04413183 0.2283619 ]
## [-0.0087454 -0.72308191]
## [-0.50784088 -1.26597119]
## [ 0.51169856 -0.10398124]
## [ 0.26497651 -0.55003646]
## [ 0.98493451 -0.12481785]
## [-0.17392537 -0.25485421]
## [ 0.92786078 0.46717949]
## [ 0.66028376 -0.35296967]
## [ 0.23610499 -0.33361077]
## [ 0.94473373 -0.54314555]
## [ 0.04522698 -0.58383438]
## [ 1.11628318 -0.08461685]
## [ 0.35788842 -0.06892503]
## [ 1.29818388 -0.32778731]
## [ 0.92172892 -0.18273779]
## [ 0.71485333 0.14905594]
## [ 0.90017437 0.32850447]
## [ 1.33202444 0.24444088]
## [ 1.55780216 0.26749545]
## [ 0.81329065 -0.1633503 ]
## [-0.30558378 -0.36826219]
## [-0.06812649 -0.70517213]
## [-0.18962247 -0.68028676]
## [ 0.13642871 -0.31403244]
## [ 1.38002644 -0.42095429]
## [ 0.58800644 -0.48428742]
## [ 0.80685831 0.19418231]
## [ 1.22069088 0.40761959]
## [ 0.81509524 -0.37203706]
## [ 0.24595768 -0.2685244 ]
## [ 0.16641322 -0.68192672]
## [ 0.46480029 -0.67071154]
## [ 0.8908152 -0.03446444]
## [ 0.23054802 -0.40438585]
## [-0.70453176 -1.01224823]
## [ 0.35698149 -0.50491009]
## [ 0.33193448 -0.21265468]
## [ 0.37621565 -0.29321893]
## [ 0.64257601 0.01773819]
## [-0.90646986 -0.75609337]
## [ 0.29900084 -0.34889781]
## [ 2.53119273 -0.00984911]
## [ 1.41523588 -0.57491635]
## [ 2.61667602 0.34390315]
## [ 1.97153105 -0.1797279 ]
## [ 2.35000592 -0.04026095]
## [ 3.39703874 0.55083667]
## [ 0.52123224 -1.19275873]
## [ 2.93258707 0.3555 ]
## [ 2.32122882 -0.2438315 ]
## [ 2.91675097 0.78279195]
## [ 1.66177415 0.24222841]
## [ 1.80340195 -0.21563762]
## [ 2.1655918 0.21627559]
## [ 1.34616358 -0.77681835]
## [ 1.58592822 -0.53964071]
## [ 1.90445637 0.11925069]
## [ 1.94968906 0.04194326]
## [ 3.48705536 1.17573933]
## [ 3.79564542 0.25732297]
## [ 1.30079171 -0.76114964]
## [ 2.42781791 0.37819601]
## [ 1.19900111 -0.60609153]
## [ 3.49992004 0.4606741 ]
## [ 1.38876613 -0.20439933]
## [ 2.2754305 0.33499061]
## [ 2.61409047 0.56090136]
## [ 1.25850816 -0.17970479]
## [ 1.29113206 -0.11666865]
## [ 2.12360872 -0.20972948]
## [ 2.38800302 0.4646398 ]
## [ 2.84167278 0.37526917]
## [ 3.23067366 1.37416509]
## [ 2.15943764 -0.21727758]
## [ 1.44416124 -0.14341341]
## [ 1.78129481 -0.49990168]
## [ 3.07649993 0.68808568]
## [ 2.14424331 0.1400642 ]
## [ 1.90509815 0.04930053]
## [ 1.16932634 -0.16499026]
## [ 2.10761114 0.37228787]
## [ 2.31415471 0.18365128]
## [ 1.9222678 0.40920347]
## [ 1.41523588 -0.57491635]
## [ 2.56301338 0.2778626 ]
## [ 2.41874618 0.3047982 ]
## [ 1.94410979 0.1875323 ]
## [ 1.52716661 -0.37531698]
## [ 1.76434572 0.07885885]
## [ 1.90094161 0.11662796]
## [ 1.39018886 -0.28266094]]7.2.2 线性判别分析（LDA）：
LDA是一种监督学习的降维方法，它在降维的同时最大化类间差异，通常用于分类问题。
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
from sklearn.datasets import load_iris
# 加载鸢尾花数据集
iris = load_iris()
X = iris.data
y = iris.target
# 创建LDA模型，将数据降维到2维
lda = LinearDiscriminantAnalysis(n_components=2)
# 训练模型
X_reduced = lda.fit_transform(X, y)
print("降维后的数据:")## 降维后的数据:## [[ 8.06179978e+00 3.00420621e-01]
## [ 7.12868772e+00 -7.86660426e-01]
## [ 7.48982797e+00 -2.65384488e-01]
## [ 6.81320057e+00 -6.70631068e-01]
## [ 8.13230933e+00 5.14462530e-01]
## [ 7.70194674e+00 1.46172097e+00]
## [ 7.21261762e+00 3.55836209e-01]
## [ 7.60529355e+00 -1.16338380e-02]
## [ 6.56055159e+00 -1.01516362e+00]
## [ 7.34305989e+00 -9.47319209e-01]
## [ 8.39738652e+00 6.47363392e-01]
## [ 7.21929685e+00 -1.09646389e-01]
## [ 7.32679599e+00 -1.07298943e+00]
## [ 7.57247066e+00 -8.05464137e-01]
## [ 9.84984300e+00 1.58593698e+00]
## [ 9.15823890e+00 2.73759647e+00]
## [ 8.58243141e+00 1.83448945e+00]
## [ 7.78075375e+00 5.84339407e-01]
## [ 8.07835876e+00 9.68580703e-01]
## [ 8.02097451e+00 1.14050366e+00]
## [ 7.49680227e+00 -1.88377220e-01]
## [ 7.58648117e+00 1.20797032e+00]
## [ 8.68104293e+00 8.77590154e-01]
## [ 6.25140358e+00 4.39696367e-01]
## [ 6.55893336e+00 -3.89222752e-01]
## [ 6.77138315e+00 -9.70634453e-01]
## [ 6.82308032e+00 4.63011612e-01]
## [ 7.92461638e+00 2.09638715e-01]
## [ 7.99129024e+00 8.63787128e-02]
## [ 6.82946447e+00 -5.44960851e-01]
## [ 6.75895493e+00 -7.59002759e-01]
## [ 7.37495254e+00 5.65844592e-01]
## [ 9.12634625e+00 1.22443267e+00]
## [ 9.46768199e+00 1.82522635e+00]
## [ 7.06201386e+00 -6.63400423e-01]
## [ 7.95876243e+00 -1.64961722e-01]
## [ 8.61367201e+00 4.03253602e-01]
## [ 8.33041759e+00 2.28133530e-01]
## [ 6.93412007e+00 -7.05519379e-01]
## [ 7.68823131e+00 -9.22362309e-03]
## [ 7.91793715e+00 6.75121313e-01]
## [ 5.66188065e+00 -1.93435524e+00]
## [ 7.24101468e+00 -2.72615132e-01]
## [ 6.41443556e+00 1.24730131e+00]
## [ 6.85944381e+00 1.05165396e+00]
## [ 6.76470393e+00 -5.05151855e-01]
## [ 8.08189937e+00 7.63392750e-01]
## [ 7.18676904e+00 -3.60986823e-01]
## [ 8.31444876e+00 6.44953177e-01]
## [ 7.67196741e+00 -1.34893840e-01]
## [-1.45927545e+00 2.85437643e-02]
## [-1.79770574e+00 4.84385502e-01]
## [-2.41694888e+00 -9.27840307e-02]
## [-2.26247349e+00 -1.58725251e+00]
## [-2.54867836e+00 -4.72204898e-01]
## [-2.42996725e+00 -9.66132066e-01]
## [-2.44848456e+00 7.95961954e-01]
## [-2.22666513e-01 -1.58467318e+00]
## [-1.75020123e+00 -8.21180130e-01]
## [-1.95842242e+00 -3.51563753e-01]
## [-1.19376031e+00 -2.63445570e+00]
## [-1.85892567e+00 3.19006544e-01]
## [-1.15809388e+00 -2.64340991e+00]
## [-2.66605725e+00 -6.42504540e-01]
## [-3.78367218e-01 8.66389312e-02]
## [-1.20117255e+00 8.44373592e-02]
## [-2.76810246e+00 3.21995363e-02]
## [-7.76854039e-01 -1.65916185e+00]
## [-3.49805433e+00 -1.68495616e+00]
## [-1.09042788e+00 -1.62658350e+00]
## [-3.71589615e+00 1.04451442e+00]
## [-9.97610366e-01 -4.90530602e-01]
## [-3.83525931e+00 -1.40595806e+00]
## [-2.25741249e+00 -1.42679423e+00]
## [-1.25571326e+00 -5.46424197e-01]
## [-1.43755762e+00 -1.34424979e-01]
## [-2.45906137e+00 -9.35277280e-01]
## [-3.51848495e+00 1.60588866e-01]
## [-2.58979871e+00 -1.74611728e-01]
## [ 3.07487884e-01 -1.31887146e+00]
## [-1.10669179e+00 -1.75225371e+00]
## [-6.05524589e-01 -1.94298038e+00]
## [-8.98703769e-01 -9.04940034e-01]
## [-4.49846635e+00 -8.82749915e-01]
## [-2.93397799e+00 2.73791065e-02]
## [-2.10360821e+00 1.19156767e+00]
## [-2.14258208e+00 8.87797815e-02]
## [-2.47945603e+00 -1.94073927e+00]
## [-1.32552574e+00 -1.62869550e-01]
## [-1.95557887e+00 -1.15434826e+00]
## [-2.40157020e+00 -1.59458341e+00]
## [-2.29248878e+00 -3.32860296e-01]
## [-1.27227224e+00 -1.21458428e+00]
## [-2.93176055e-01 -1.79871509e+00]
## [-2.00598883e+00 -9.05418042e-01]
## [-1.18166311e+00 -5.37570242e-01]
## [-1.61615645e+00 -4.70103580e-01]
## [-1.42158879e+00 -5.51244626e-01]
## [ 4.75973788e-01 -7.99905482e-01]
## [-1.54948259e+00 -5.93363582e-01]
## [-7.83947399e+00 2.13973345e+00]
## [-5.50747997e+00 -3.58139892e-02]
## [-6.29200850e+00 4.67175777e-01]
## [-5.60545633e+00 -3.40738058e-01]
## [-6.85055995e+00 8.29825394e-01]
## [-7.41816784e+00 -1.73117995e-01]
## [-4.67799541e+00 -4.99095015e-01]
## [-6.31692685e+00 -9.68980756e-01]
## [-6.32773684e+00 -1.38328993e+00]
## [-6.85281335e+00 2.71758963e+00]
## [-4.44072512e+00 1.34723692e+00]
## [-5.45009572e+00 -2.07736942e-01]
## [-5.66033713e+00 8.32713617e-01]
## [-5.95823722e+00 -9.40175447e-02]
## [-6.75926282e+00 1.60023206e+00]
## [-5.80704331e+00 2.01019882e+00]
## [-5.06601233e+00 -2.62733839e-02]
## [-6.60881882e+00 1.75163587e+00]
## [-9.17147486e+00 -7.48255067e-01]
## [-4.76453569e+00 -2.15573720e+00]
## [-6.27283915e+00 1.64948141e+00]
## [-5.36071189e+00 6.46120732e-01]
## [-7.58119982e+00 -9.80722934e-01]
## [-4.37150279e+00 -1.21297458e-01]
## [-5.72317531e+00 1.29327553e+00]
## [-5.27915920e+00 -4.24582377e-02]
## [-4.08087208e+00 1.85936572e-01]
## [-4.07703640e+00 5.23238483e-01]
## [-6.51910397e+00 2.96976389e-01]
## [-4.58371942e+00 -8.56815813e-01]
## [-6.22824009e+00 -7.12719638e-01]
## [-5.22048773e+00 1.46819509e+00]
## [-6.80015000e+00 5.80895175e-01]
## [-3.81515972e+00 -9.42985932e-01]
## [-5.10748966e+00 -2.13059000e+00]
## [-6.79671631e+00 8.63090395e-01]
## [-6.52449599e+00 2.44503527e+00]
## [-4.99550279e+00 1.87768525e-01]
## [-3.93985300e+00 6.14020389e-01]
## [-5.20383090e+00 1.14476808e+00]
## [-6.65308685e+00 1.80531976e+00]
## [-5.10555946e+00 1.99218201e+00]
## [-5.50747997e+00 -3.58139892e-02]
## [-6.79601924e+00 1.46068695e+00]
## [-6.84735943e+00 2.42895067e+00]
## [-5.64500346e+00 1.67771734e+00]
## [-5.17956460e+00 -3.63475041e-01]
## [-4.96774090e+00 8.21140550e-01]
## [-5.88614539e+00 2.34509051e+00]
## [-4.68315426e+00 3.32033811e-01]]7.2.3 多维尺度分析（MDS）：
MDS是一种距离度量的降维方法，它试图在低维空间中保持数据点之间的距离关系。
from sklearn.manifold import MDS
from sklearn.datasets import load_iris
# 加载鸢尾花数据集
iris = load_iris()
X = iris.data
# 创建MDS模型，将数据降维到2维
mds = MDS(n_components=2)
# 训练模型
X_reduced = mds.fit_transform(X)
print("降维后的数据:")## 降维后的数据:## [[ 2.21493806 1.56217939]
## [ 2.49838014 1.10287551]
## [ 2.61874174 1.25449374]
## [ 2.58278832 1.00804328]
## [ 2.24596805 1.60849812]
## [ 1.63420577 1.76735088]
## [ 2.54589824 1.29123899]
## [ 2.2380282 1.39501926]
## [ 2.82250689 0.86264598]
## [ 2.42293458 1.15205048]
## [ 1.88361653 1.78104739]
## [ 2.29587818 1.26172236]
## [ 2.587974 1.08660399]
## [ 3.08692761 1.09068784]
## [ 1.74415403 2.33552187]
## [ 1.43597459 2.35197647]
## [ 1.89619249 2.00952465]
## [ 2.18325475 1.54578571]
## [ 1.49952171 1.83692885]
## [ 2.0236492 1.72292355]
## [ 1.83008783 1.45398861]
## [ 2.0193518 1.62705907]
## [ 2.7776783 1.69103698]
## [ 1.97229094 1.18967335]
## [ 2.1096466 1.04198191]
## [ 2.30308522 1.01131513]
## [ 2.1067539 1.29884887]
## [ 2.08496426 1.54241903]
## [ 2.18042156 1.5306755 ]
## [ 2.41872618 1.06684872]
## [ 2.38153582 1.03956875]
## [ 1.90041588 1.53691655]
## [ 1.98089043 2.00851255]
## [ 1.75264661 2.22452415]
## [ 2.38751445 1.13720282]
## [ 2.50861915 1.43506322]
## [ 1.98960887 1.85738546]
## [ 2.34409928 1.5993994 ]
## [ 2.86521364 0.98757605]
## [ 2.17670458 1.4323303 ]
## [ 2.31650207 1.56458354]
## [ 3.01272842 0.44001755]
## [ 2.82491888 1.12296046]
## [ 2.00620076 1.33295392]
## [ 1.67607979 1.51049146]
## [ 2.52777042 1.04146628]
## [ 1.97332751 1.69789467]
## [ 2.62059539 1.15687624]
## [ 1.95152672 1.73824026]
## [ 2.33489203 1.38165898]
## [-1.49589323 0.10832104]
## [-0.97464306 -0.15167731]
## [-1.56492402 -0.13793114]
## [ 0.25895092 -0.79924461]
## [-1.03957724 -0.32218333]
## [-0.3520002 -0.66821403]
## [-1.10081448 -0.29937134]
## [ 1.14685902 -0.51259291]
## [-1.09280496 -0.1160219 ]
## [ 0.40038967 -0.69288939]
## [ 1.07718996 -0.87745191]
## [-0.39474224 -0.33152812]
## [ 0.20241771 -0.86082334]
## [-0.80732185 -0.54887631]
## [ 0.26198891 -0.08207754]
## [-1.07492667 0.07261712]
## [-0.36477337 -0.73650175]
## [-0.04447532 -0.33278004]
## [-0.47000889 -1.07201094]
## [ 0.24993886 -0.49607067]
## [-0.85889808 -0.83301636]
## [-0.31074303 -0.12452513]
## [-1.05471024 -0.71820737]
## [-0.72599856 -0.5367 ]
## [-0.73569458 -0.07883377]
## [-0.9909382 -0.01707652]
## [-1.38748727 -0.15627628]
## [-1.51856419 -0.43577495]
## [-0.62710623 -0.53515573]
## [ 0.4588692 -0.14784975]
## [ 0.41249826 -0.55485446]
## [ 0.51630368 -0.49170472]
## [ 0.03056565 -0.28743678]
## [-1.00017658 -1.02676465]
## [-0.2049495 -0.90202194]
## [-0.81699949 -0.16675016]
## [-1.29181916 -0.15010509]
## [-0.65600032 -0.32646214]
## [-0.0949578 -0.3225071 ]
## [ 0.18225328 -0.64020644]
## [-0.06769147 -0.81639118]
## [-0.76203694 -0.44987582]
## [ 0.00497144 -0.43077573]
## [ 1.11221625 -0.54373983]
## [-0.07336693 -0.58762878]
## [-0.18989463 -0.32190738]
## [-0.18882237 -0.42887293]
## [-0.58754584 -0.21528147]
## [ 1.17631482 -0.23131518]
## [-0.0972932 -0.42960566]
## [-2.1237449 -1.64665366]
## [-0.94880662 -1.24080969]
## [-2.49811599 -0.86813504]
## [-1.62726082 -1.14769922]
## [-2.04220904 -1.21722256]
## [-3.31159784 -1.05393405]
## [ 0.17755187 -1.44020491]
## [-2.85742976 -0.9597933 ]
## [-1.94938728 -1.37533653]
## [-2.96943328 -0.72624427]
## [-1.58602412 -0.6277047 ]
## [-1.49097129 -1.00566805]
## [-2.02388492 -0.81227744]
## [-0.78931756 -1.3940889 ]
## [-1.03964147 -1.55094484]
## [-1.72856464 -0.99398756]
## [-1.73968111 -0.879427 ]
## [-3.6653959 -0.52750496]
## [-3.55551349 -1.50100433]
## [-0.70361443 -1.36419053]
## [-2.30496422 -0.91677447]
## [-0.70598124 -1.27253819]
## [-3.40985364 -1.16554119]
## [-1.15409045 -0.78085312]
## [-2.15055346 -0.89441774]
## [-2.61972942 -0.60680272]
## [-1.03020632 -0.74173423]
## [-1.0568331 -0.79844499]
## [-1.77504469 -1.19399926]
## [-2.43433081 -0.43176833]
## [-2.80866661 -0.74995722]
## [-3.51754372 -0.24123269]
## [-1.80294283 -1.23672919]
## [-1.23485318 -0.7182038 ]
## [-1.25273004 -1.48643705]
## [-3.11705297 -0.67394425]
## [-1.82136834 -1.45391363]
## [-1.69033354 -0.91073282]
## [-0.91865621 -0.79544208]
## [-2.04607638 -0.66006853]
## [-2.12554761 -1.04965446]
## [-1.96560986 -0.44065068]
## [-0.94880662 -1.24080969]
## [-2.36411804 -1.10360043]
## [-2.24445629 -1.16883995]
## [-1.86718566 -0.68961676]
## [-1.18745167 -1.02729761]
## [-1.59770886 -0.77371442]
## [-1.59959451 -1.35354741]
## [-1.04412492 -1.05155794]]这些示例提供了Sklearn中不同降维方法的详细示例，包括参数设置。不同的降维方法适用于不同的数据和问题，你可以根据你的需求选择合适的降维方法。
7.3 离群点检测
7.3.1 1. Isolation Forest:
Isolation Forest 是一种基于树的方法，它通过构建随机树来检测离群点。该方法在一系列随机分割中测量观测的离群程度。
from sklearn.ensemble import IsolationForest
from sklearn.datasets import make_blobs
# 生成模拟数据
X, _ = make_blobs(n_samples=300, centers=1, cluster_std=0.3, random_state=0)
# 创建Isolation Forest模型
clf = IsolationForest(contamination=0.05, random_state=0)
# 训练模型并预测离群点
y_pred = clf.fit_predict(X)
print("离群点预测结果:")## 离群点预测结果:## [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1
## 1 1 1 1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 -1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1 1 -1 1 -1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 -1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1 1]7.3.2 One-Class SVM:
One-Class SVM 是一种支持向量机方法，用于将数据点分为正常点和离群点。它通过寻找包围大多数数据点的边界来检测离群点。
from sklearn.svm import OneClassSVM
from sklearn.datasets import make_blobs
# 生成模拟数据
X, _ = make_blobs(n_samples=300, centers=1, cluster_std=0.3, random_state=0)
# 创建One-Class SVM模型
clf = OneClassSVM(nu=0.05)
# 训练模型并预测离群点
y_pred = clf.fit_predict(X)
print("离群点预测结果:")## 离群点预测结果:## [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 1
## 1 1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1
## 1 1 1 1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 -1 1 1 1 1 1 1
## 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 -1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1 1]7.3.3 Local Outlier Factor (LOF):
LOF 是一种基于局部密度的方法，它使用每个数据点的邻近数据点来计算该点的离群分数。
from sklearn.neighbors import LocalOutlierFactor
from sklearn.datasets import make_blobs
# 生成模拟数据
X, _ = make_blobs(n_samples=300, centers=1, cluster_std=0.3, random_state=0)
# 创建LOF模型
clf = LocalOutlierFactor(n_neighbors=20, contamination=0.05)
# 训练模型并预测离群点
y_pred = clf.fit_predict(X)
print("离群点预测结果:")## 离群点预测结果:## [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 1
## 1 1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1
## -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 -1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 -1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 -1 1 1 1 1 1 1
## 1 1 1 1 1 -1 1 1 1 1 1 1]