# Basics
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import warnings
# Machine Learning
from sklearn.datasets import make_blobs
from sklearn.decomposition import PCA
from sklearn.cluster import KMeans
from sklearn.mixture import GaussianMixture
from sklearn.ensemble import IsolationForestCS 307: Week 11
# Deal with pandas versus seaborn issues
warnings.simplefilter(action="ignore", category=FutureWarning)Dimension Reduction
X, _ = make_blobs(n_samples=500, n_features=50, cluster_std=5)Xarray([[ 10.17269451, 3.49621517, 0.93013758, ..., -8.11226321,
-6.21200063, 3.209094 ],
[ -2.72794725, -0.14436952, 9.0100893 , ..., -1.5114895 ,
-12.92370089, -3.19291496],
[ 1.6528662 , 4.43967606, 1.5429667 , ..., -5.91847788,
-2.26235952, -2.05393545],
...,
[ -6.17621516, 8.78322719, 3.90233933, ..., 2.36327881,
-14.64777359, -1.99756241],
[ 3.28858088, -2.29186493, -4.3438314 , ..., 1.41749562,
2.54734283, -17.40846237],
[ 12.01911868, 6.35893824, -2.74117713, ..., 2.52643442,
0.35434916, -4.55656682]])X.shape(500, 50)sns.scatterplot(x=X[:, 0], y=X[:, 1])
plt.xlabel("X1")
plt.ylabel("X2")
plt.grid(color="lightgrey", linestyle="-", linewidth=0.5)
plt.show()
pca = PCA(n_components=0.75)pca.fit(X)PCA(n_components=0.75)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
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PCA(n_components=0.75)
X_pca = pca.fit_transform(X)X_pcaarray([[ 31.89077094, -11.4244946 , 3.56788724, ..., 3.3458096 ,
-1.99002678, -7.63500724],
[ 37.73907407, -10.6243658 , -8.1071009 , ..., -1.21632252,
2.20330235, -1.43010385],
[ 33.47431956, -8.97845509, -7.80269135, ..., 3.71999293,
8.94516917, 0.60358975],
...,
[ -2.19161844, 41.27552166, 4.77198581, ..., 6.61928782,
4.1364567 , 4.67362872],
[-31.30842446, -15.69988365, -1.11601459, ..., 4.6702658 ,
-1.20841298, 5.69836199],
[ 26.74673295, -22.19718589, 7.19343428, ..., 4.83253565,
3.99521426, -3.16960512]])X_pca.shape(500, 20)sns.scatterplot(x=X_pca[:, 0], y=X_pca[:, 1])
plt.xlabel("PCA 1")
plt.ylabel("PCA 2")
plt.grid(color="lightgrey", linestyle="-", linewidth=0.5)
plt.show()
Clustering
X, _ = make_blobs(n_samples=500, n_features=2, cluster_std=1)sns.scatterplot(x=X[:, 0], y=X[:, 1])
plt.xlabel("X1")
plt.ylabel("X2")
plt.grid(color="lightgrey", linestyle="-", linewidth=0.5)
plt.show()
km = KMeans()km.fit(X)KMeans()In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
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KMeans()
clusters = km.fit_predict(X)clustersarray([1, 6, 0, 6, 1, 2, 7, 4, 0, 0, 3, 1, 6, 1, 2, 5, 4, 0, 4, 2, 2, 1,
6, 2, 0, 1, 7, 4, 3, 2, 7, 6, 4, 2, 7, 6, 3, 0, 5, 3, 5, 1, 3, 2,
4, 3, 2, 7, 2, 0, 2, 1, 2, 3, 3, 1, 0, 0, 5, 3, 2, 3, 0, 1, 0, 7,
1, 1, 1, 5, 7, 5, 1, 0, 4, 6, 0, 5, 4, 7, 7, 2, 0, 2, 4, 3, 3, 1,
1, 7, 6, 5, 2, 5, 1, 7, 4, 3, 0, 7, 7, 7, 2, 3, 3, 6, 3, 5, 7, 4,
5, 6, 4, 5, 5, 3, 3, 4, 7, 2, 0, 6, 4, 4, 3, 0, 1, 2, 3, 1, 5, 7,
2, 3, 1, 1, 1, 7, 0, 4, 6, 7, 5, 3, 2, 3, 0, 5, 5, 2, 3, 0, 2, 6,
5, 7, 2, 7, 2, 4, 2, 6, 3, 7, 4, 2, 3, 7, 6, 4, 6, 5, 5, 4, 1, 1,
3, 0, 4, 4, 4, 0, 5, 2, 1, 7, 2, 3, 3, 4, 4, 1, 3, 3, 2, 7, 1, 7,
1, 6, 2, 0, 4, 4, 5, 3, 7, 1, 3, 0, 4, 4, 2, 2, 0, 3, 6, 2, 7, 5,
3, 1, 3, 0, 0, 6, 7, 5, 7, 6, 3, 2, 3, 5, 0, 4, 2, 7, 6, 1, 3, 6,
0, 0, 2, 3, 5, 4, 0, 7, 7, 5, 2, 2, 1, 2, 3, 0, 5, 5, 7, 4, 2, 1,
3, 4, 3, 3, 7, 7, 6, 6, 7, 1, 6, 7, 5, 7, 2, 1, 6, 3, 3, 4, 1, 3,
2, 3, 1, 3, 1, 0, 2, 0, 3, 7, 1, 4, 3, 4, 7, 2, 3, 6, 7, 5, 4, 0,
3, 4, 4, 6, 1, 3, 1, 5, 4, 6, 4, 2, 2, 5, 5, 1, 1, 7, 1, 2, 3, 2,
5, 5, 5, 3, 1, 2, 3, 4, 3, 3, 3, 5, 3, 7, 2, 1, 0, 2, 6, 2, 4, 2,
3, 1, 7, 7, 2, 2, 4, 6, 3, 4, 3, 6, 4, 5, 2, 3, 7, 3, 6, 1, 2, 2,
6, 4, 5, 6, 3, 2, 0, 6, 1, 0, 7, 5, 2, 1, 5, 7, 7, 5, 1, 7, 7, 3,
5, 7, 7, 2, 4, 2, 2, 7, 3, 6, 6, 2, 3, 6, 7, 7, 2, 1, 1, 3, 2, 1,
6, 3, 5, 4, 6, 2, 2, 2, 1, 3, 4, 1, 7, 0, 2, 3, 3, 4, 7, 1, 6, 6,
5, 7, 1, 3, 0, 4, 0, 2, 5, 6, 6, 4, 3, 7, 3, 3, 5, 3, 6, 0, 7, 4,
5, 6, 2, 7, 3, 1, 0, 3, 4, 7, 3, 2, 3, 7, 3, 5, 2, 3, 0, 0, 7, 7,
5, 3, 2, 3, 3, 5, 1, 2, 4, 2, 4, 6, 0, 6, 1, 0], dtype=int32)sns.scatterplot(x=X[:, 0], y=X[:, 1], hue=pd.Categorical(clusters))
plt.xlabel("X1")
plt.ylabel("X2")
plt.grid(color="lightgrey", linestyle="-", linewidth=0.5)
plt.show()
km3 = KMeans(n_clusters=3)
km3.fit(X)
clusters = km3.fit_predict(X)
clustersarray([0, 0, 1, 0, 0, 2, 1, 0, 1, 1, 2, 0, 0, 0, 2, 1, 0, 1, 0, 2, 2, 0,
0, 2, 1, 0, 1, 0, 2, 2, 1, 0, 0, 2, 1, 0, 2, 1, 1, 2, 1, 0, 2, 2,
0, 2, 2, 1, 2, 1, 2, 0, 2, 2, 2, 0, 1, 1, 1, 2, 2, 2, 1, 0, 1, 1,
0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 2, 1, 2, 0, 2, 2, 0,
0, 1, 0, 1, 2, 1, 0, 1, 0, 2, 1, 1, 1, 1, 2, 2, 2, 0, 2, 1, 1, 0,
1, 0, 0, 1, 1, 2, 2, 0, 1, 2, 1, 0, 0, 0, 2, 1, 0, 2, 2, 0, 1, 1,
2, 2, 0, 0, 0, 1, 1, 0, 0, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 0,
1, 1, 2, 1, 2, 0, 2, 0, 2, 1, 0, 2, 2, 1, 0, 0, 0, 1, 1, 0, 0, 0,
2, 1, 0, 0, 0, 1, 1, 2, 0, 1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1, 0, 1,
0, 0, 2, 1, 0, 0, 1, 2, 1, 0, 2, 1, 0, 0, 2, 2, 1, 2, 0, 2, 1, 1,
2, 0, 2, 1, 1, 0, 1, 1, 1, 0, 2, 2, 2, 1, 1, 0, 2, 1, 0, 0, 2, 0,
1, 1, 2, 2, 1, 0, 1, 1, 1, 1, 2, 2, 0, 2, 2, 1, 1, 1, 1, 0, 2, 0,
2, 0, 2, 2, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 2, 2, 0, 0, 2,
2, 2, 0, 2, 0, 1, 2, 1, 2, 1, 0, 0, 2, 0, 1, 2, 2, 0, 1, 1, 0, 1,
2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 2, 1, 1, 0, 0, 1, 0, 2, 2, 2,
1, 1, 1, 2, 0, 2, 2, 0, 2, 2, 2, 1, 2, 1, 2, 0, 1, 2, 0, 2, 0, 2,
2, 0, 1, 1, 2, 2, 0, 0, 2, 0, 2, 0, 0, 1, 2, 2, 1, 2, 0, 0, 2, 2,
0, 0, 1, 0, 2, 2, 1, 0, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 0, 1, 1, 2,
1, 1, 1, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2, 0, 1, 1, 2, 0, 0, 2, 2, 0,
0, 2, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 1, 1, 2, 2, 2, 0, 1, 0, 0, 0,
1, 1, 0, 2, 1, 0, 1, 2, 1, 0, 0, 0, 2, 1, 2, 2, 1, 2, 0, 1, 1, 0,
1, 0, 2, 1, 2, 0, 1, 2, 0, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1,
1, 2, 2, 2, 2, 1, 0, 2, 0, 2, 0, 0, 1, 0, 0, 1], dtype=int32)sns.scatterplot(x=X[:, 0], y=X[:, 1], hue=pd.Categorical(clusters))
plt.xlabel("X1")
plt.ylabel("X2")
plt.grid(color="lightgrey", linestyle="-", linewidth=0.5)
plt.show()
Density Estimation
X, _ = make_blobs(n_samples=500, centers=2, n_features=1, cluster_std=[1.5, 3], random_state=42)plt.hist(X, bins=20, density=True)
plt.xlabel("X")
plt.ylabel("Frequency")
plt.grid(color="lightgrey", linestyle="-", linewidth=0.5)
plt.show()
gmm = GaussianMixture(n_components=2)
gmm.fit(X)
gmm.predict_proba(X)array([[1.26818553e-03, 9.98731814e-01],
[1.00000000e+00, 1.59175223e-28],
[1.00000000e+00, 1.61485806e-18],
[1.00000000e+00, 2.70107719e-14],
[6.31287489e-04, 9.99368713e-01],
[1.00000000e+00, 5.63768604e-14],
[7.88257983e-04, 9.99211742e-01],
[4.52189518e-03, 9.95478105e-01],
[4.74357664e-05, 9.99952564e-01],
[1.19807435e-02, 9.88019257e-01],
[1.00000000e+00, 8.41779417e-18],
[1.00000000e+00, 1.18563301e-29],
[1.00000000e+00, 4.54494624e-20],
[1.05555724e-04, 9.99894444e-01],
[1.00000000e+00, 1.90062307e-22],
[1.96286251e-04, 9.99803714e-01],
[5.58181276e-05, 9.99944182e-01],
[1.00000000e+00, 6.49582212e-26],
[1.00000000e+00, 2.63628609e-16],
[2.21543523e-04, 9.99778456e-01],
[9.55179254e-05, 9.99904482e-01],
[9.48250855e-05, 9.99905175e-01],
[1.68979346e-04, 9.99831021e-01],
[1.00000000e+00, 4.38461851e-21],
[1.00000000e+00, 1.21614544e-14],
[2.16133093e-04, 9.99783867e-01],
[1.14945843e-04, 9.99885054e-01],
[1.00000000e+00, 2.87834762e-11],
[6.94550430e-04, 9.99305450e-01],
[9.40203583e-05, 9.99905980e-01],
[1.00000000e+00, 7.45473466e-12],
[1.00000000e+00, 1.73398289e-26],
[7.20540939e-05, 9.99927946e-01],
[9.98087831e-01, 1.91216855e-03],
[1.00000000e+00, 4.57700753e-15],
[1.00000000e+00, 3.69664831e-12],
[1.07946092e-04, 9.99892054e-01],
[9.07375449e-05, 9.99909262e-01],
[2.21180099e-03, 9.97788199e-01],
[1.98794215e-03, 9.98012058e-01],
[9.99998822e-01, 1.17824044e-06],
[9.99806065e-01, 1.93935220e-04],
[5.33803182e-05, 9.99946620e-01],
[1.90729813e-04, 9.99809270e-01],
[1.00000000e+00, 1.98560827e-14],
[9.99670193e-01, 3.29807059e-04],
[1.00000000e+00, 1.83330866e-16],
[6.97710151e-05, 9.99930229e-01],
[2.18450465e-03, 9.97815495e-01],
[1.00000000e+00, 4.59073661e-16],
[1.00000000e+00, 1.36257041e-11],
[1.00000000e+00, 2.24358916e-10],
[9.99981364e-01, 1.86355051e-05],
[1.29303794e-04, 9.99870696e-01],
[1.40932039e-02, 9.85906796e-01],
[1.34047909e-03, 9.98659521e-01],
[2.45427492e-03, 9.97545725e-01],
[1.00000000e+00, 6.85066094e-14],
[9.99999999e-01, 1.38746472e-09],
[1.06157735e-04, 9.99893842e-01],
[1.16194304e-04, 9.99883806e-01],
[8.70624668e-05, 9.99912938e-01],
[2.66555774e-04, 9.99733444e-01],
[1.00000000e+00, 2.19292802e-15],
[3.76566336e-04, 9.99623434e-01],
[9.99999989e-01, 1.05915756e-08],
[3.95182315e-04, 9.99604818e-01],
[1.00000000e+00, 7.75341315e-15],
[7.74270917e-04, 9.99225729e-01],
[1.00000000e+00, 1.42783286e-15],
[1.00000000e+00, 8.53183191e-21],
[1.00199142e-03, 9.98998009e-01],
[5.88782630e-05, 9.99941122e-01],
[1.03408204e-02, 9.89659180e-01],
[8.65244834e-05, 9.99913476e-01],
[2.51354212e-01, 7.48645788e-01],
[1.00000000e+00, 1.30444456e-15],
[1.00000000e+00, 1.53974853e-14],
[1.50580459e-04, 9.99849420e-01],
[2.39282359e-03, 9.97607176e-01],
[9.99999770e-01, 2.30184013e-07],
[1.00000000e+00, 3.67309369e-18],
[4.59392199e-05, 9.99954061e-01],
[7.16004392e-05, 9.99928400e-01],
[1.00000000e+00, 2.82895224e-11],
[1.00000000e+00, 1.26476797e-13],
[2.20110122e-04, 9.99779890e-01],
[1.23332296e-04, 9.99876668e-01],
[1.59949423e-04, 9.99840051e-01],
[1.00000000e+00, 3.63535152e-11],
[9.66225392e-05, 9.99903377e-01],
[1.00000000e+00, 6.47500066e-26],
[6.61158392e-05, 9.99933884e-01],
[1.00000000e+00, 2.33203928e-11],
[9.99999447e-01, 5.52752427e-07],
[6.33802405e-05, 9.99936620e-01],
[9.99999959e-01, 4.09098750e-08],
[2.66116002e-04, 9.99733884e-01],
[1.00000000e+00, 5.21170655e-12],
[1.00000000e+00, 2.37779167e-47],
[1.14695370e-03, 9.98853046e-01],
[1.00000000e+00, 1.81324995e-15],
[9.99993954e-01, 6.04639611e-06],
[1.00000000e+00, 2.47868294e-19],
[1.00000000e+00, 4.94719252e-10],
[2.15973739e-04, 9.99784026e-01],
[1.00000000e+00, 8.27757703e-16],
[3.32441945e-03, 9.96675581e-01],
[9.99999986e-01, 1.43109584e-08],
[1.00000000e+00, 7.80164160e-14],
[1.00000000e+00, 1.34377649e-13],
[5.57826747e-04, 9.99442173e-01],
[5.50472254e-05, 9.99944953e-01],
[5.23116931e-05, 9.99947688e-01],
[4.66591820e-04, 9.99533408e-01],
[1.00000000e+00, 4.24668114e-22],
[4.59036253e-05, 9.99954096e-01],
[3.59804402e-03, 9.96401956e-01],
[1.00000000e+00, 1.24600645e-30],
[1.49958494e-04, 9.99850042e-01],
[1.00000000e+00, 8.13952370e-19],
[5.61148239e-02, 9.43885176e-01],
[9.99000530e-04, 9.99000999e-01],
[1.00000000e+00, 3.87751686e-35],
[6.21701903e-05, 9.99937830e-01],
[2.12055247e-04, 9.99787945e-01],
[2.87810461e-04, 9.99712190e-01],
[1.15207046e-04, 9.99884793e-01],
[1.46500040e-04, 9.99853500e-01],
[3.21273925e-03, 9.96787261e-01],
[9.78227505e-04, 9.99021772e-01],
[4.10710203e-04, 9.99589290e-01],
[2.86951089e-04, 9.99713049e-01],
[6.14626554e-05, 9.99938537e-01],
[5.53583959e-05, 9.99944642e-01],
[3.89111009e-03, 9.96108890e-01],
[5.85651313e-05, 9.99941435e-01],
[9.99996712e-01, 3.28792830e-06],
[1.00000000e+00, 1.14914187e-18],
[1.00000000e+00, 2.30945714e-29],
[2.00880365e-03, 9.97991196e-01],
[1.00000000e+00, 1.87482900e-22],
[1.00000000e+00, 1.26342155e-20],
[1.00000000e+00, 1.07288753e-15],
[3.69696186e-04, 9.99630304e-01],
[1.76598765e-02, 9.82340124e-01],
[1.38396805e-04, 9.99861603e-01],
[9.99977619e-01, 2.23811609e-05],
[9.99982310e-01, 1.76902201e-05],
[9.99999982e-01, 1.82280151e-08],
[1.00000000e+00, 7.93124767e-20],
[1.00000000e+00, 4.41358153e-23],
[1.01871393e-03, 9.98981286e-01],
[2.81147506e-03, 9.97188525e-01],
[1.11026044e-04, 9.99888974e-01],
[1.45172590e-04, 9.99854827e-01],
[2.18075414e-03, 9.97819246e-01],
[1.48615489e-04, 9.99851385e-01],
[9.07333841e-04, 9.99092666e-01],
[1.00000000e+00, 3.77781147e-29],
[9.99999971e-01, 2.91063461e-08],
[4.19457271e-03, 9.95805427e-01],
[8.46806802e-05, 9.99915319e-01],
[1.53001573e-03, 9.98469984e-01],
[1.00202120e-03, 9.98997979e-01],
[1.00000000e+00, 7.52173171e-22],
[5.62060753e-04, 9.99437939e-01],
[1.00000000e+00, 1.07678879e-19],
[5.23623539e-05, 9.99947638e-01],
[1.00000000e+00, 5.15217958e-30],
[9.99999998e-01, 1.67324739e-09],
[9.99999997e-01, 2.85700594e-09],
[1.00000000e+00, 2.34175937e-14],
[2.36730233e-03, 9.97632698e-01],
[2.93772631e-03, 9.97062274e-01],
[2.02481030e-02, 9.79751897e-01],
[9.99992400e-01, 7.60027084e-06],
[6.55546991e-04, 9.99344453e-01],
[2.88246863e-04, 9.99711753e-01],
[1.00000000e+00, 1.39749308e-10],
[1.67140329e-04, 9.99832860e-01],
[9.76915919e-05, 9.99902308e-01],
[1.00000000e+00, 6.37031067e-24],
[5.08384083e-04, 9.99491616e-01],
[8.21627098e-05, 9.99917837e-01],
[1.36138357e-04, 9.99863862e-01],
[1.69508641e-01, 8.30491359e-01],
[9.34908717e-05, 9.99906509e-01],
[1.00000000e+00, 1.96729960e-16],
[9.07538775e-01, 9.24612249e-02],
[1.00000000e+00, 1.24982879e-15],
[7.26312411e-05, 9.99927369e-01],
[2.45249113e-04, 9.99754751e-01],
[1.00000000e+00, 4.17016588e-11],
[1.00000000e+00, 1.69864806e-23],
[1.07059671e-03, 9.98929403e-01],
[5.14392542e-05, 9.99948561e-01],
[1.00000000e+00, 1.26284481e-28],
[1.45316829e-01, 8.54683171e-01],
[1.00000000e+00, 1.97410686e-13],
[6.24451503e-02, 9.37554850e-01],
[1.00000000e+00, 8.94975827e-27],
[1.00000000e+00, 4.26292171e-15],
[1.00000000e+00, 1.06498061e-14],
[3.38494058e-04, 9.99661506e-01],
[1.00000000e+00, 3.91611049e-25],
[1.00000000e+00, 1.21666893e-27],
[9.99999996e-01, 3.93509378e-09],
[5.54615318e-05, 9.99944538e-01],
[1.46546851e-02, 9.85345315e-01],
[1.00000000e+00, 4.20404100e-10],
[1.96051394e-03, 9.98039486e-01],
[5.35672664e-02, 9.46432734e-01],
[1.00000000e+00, 3.70643965e-27],
[5.10935293e-04, 9.99489065e-01],
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0.01504405, 0.1359983 , 0.06120944, 0.05800769, 0.10324914,
0.139401 , 0.10631277, 0.0661446 , 0.08490373, 0.05190301,
0.05361922, 0.11424735, 0.04615414, 0.06400462, 0.05730316,
0.13242062, 0.14002874, 0.05866495, 0.04917616, 0.14276069,
0.05519367, 0.0644829 , 0.14237554, 0.05782235, 0.06503186,
0.14216907, 0.08133261, 0.04896387, 0.021441 , 0.1305158 ,
0.0648879 , 0.02315582, 0.10103989, 0.06501846, 0.05290947,
0.06448741, 0.01144346, 0.06104912, 0.13432675, 0.13594296,
0.09423774, 0.12250632, 0.06614859, 0.08341821, 0.11099212,
0.05434346, 0.1211743 , 0.12786085, 0.04509381, 0.06277878,
0.05444506, 0.05900135, 0.13693505, 0.11325445, 0.14149424,
0.12306417, 0.05658937, 0.01521691, 0.04709487, 0.03188792,
0.09335299, 0.13630887, 0.05544855, 0.05630717, 0.0628946 ,
0.02376967, 0.02705523, 0.06570556, 0.0598789 , 0.0550126 ,
0.063374 , 0.04413456, 0.14090723, 0.05194098, 0.06344013,
0.04291318, 0.13811833, 0.13702523, 0.0364081 , 0.06524937,
0.00708012, 0.06536085, 0.13895114, 0.04958668, 0.13053022,
0.03032181, 0.01841401, 0.01031467, 0.06365824, 0.01876559,
0.01840517, 0.04085323, 0.06616104, 0.1350135 , 0.06595312,
0.04724824, 0.12554683, 0.14203591, 0.10530541, 0.02667144,
0.0121631 , 0.1317186 , 0.06157441, 0.06580962, 0.0590895 ,
0.12796298, 0.00487272, 0.05917033, 0.06259974, 0.04301246,
0.04212389, 0.06331014, 0.1373698 , 0.05744691, 0.06246497,
0.13857387, 0.05609004, 0.13901543, 0.07969418, 0.10910154,
0.13157661, 0.05039403, 0.14073353, 0.13976097, 0.14210578,
0.10878082, 0.06507112, 0.03174709, 0.05165878, 0.03520216,
0.04922782, 0.09008347, 0.05638423, 0.13514379, 0.03236899,
0.1296597 , 0.01318037, 0.04947638, 0.06567734, 0.12906014,
0.00809059, 0.06459945, 0.01851578, 0.04302933, 0.06617698,
0.0998146 , 0.03361572, 0.04696904, 0.01685546, 0.1416999 ,
0.01987535, 0.0080242 , 0.09839694, 0.12755756, 0.05853619,
0.01621363, 0.06486161, 0.1394685 , 0.14284633, 0.06423959,
0.0430993 , 0.02240914, 0.09414582, 0.04795443, 0.13716851,
0.13417064, 0.03689347, 0.06552443, 0.04250122, 0.06605351,
0.02330818, 0.13949016, 0.0060319 , 0.03433645, 0.06934779,
0.06607671, 0.13141272, 0.01572851, 0.06462334, 0.00655451,
0.10737192, 0.04821442, 0.06475601, 0.05319493, 0.06611443])plt.hist(X, bins=20, alpha=0.5, density=True)
x = np.linspace(X.min(), X.max(), 1000)
logprob = gmm.score_samples(x.reshape(-1, 1))
pdf = np.exp(logprob)
plt.plot(x, pdf, "-r", label="GMM")
plt.xlabel("X")
plt.ylabel("Density")
plt.legend()
plt.grid(color="lightgrey", linestyle="-", linewidth=0.5)
plt.show()
Outlier Detection
X, _ = make_blobs(n_samples=500, centers=3, n_features=2, cluster_std=1.5, random_state=42)
outliers = np.random.RandomState(42).uniform(low=-10, high=10, size=(25, 2))
X = np.vstack((X, outliers))sns.scatterplot(x=X[:, 0], y=X[:, 1])
plt.xlabel("X1")
plt.ylabel("X2")
plt.grid(color="lightgrey", linestyle="-", linewidth=0.5)
plt.show()
iso = IsolationForest()
iso.fit(X)IsolationForest()In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
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IsolationForest()
inout = iso.fit_predict(X)inoutarray([ 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1,
-1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1,
-1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1,
1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1,
1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1,
1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1,
1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1,
1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1,
1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1,
1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1,
1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1,
1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1,
1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1,
1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1,
1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1])sns.scatterplot(x=X[:, 0], y=X[:, 1], hue=pd.Categorical(inout))
plt.xlabel("X1")
plt.ylabel("X2")
plt.grid(color="lightgrey", linestyle="-", linewidth=0.5)
plt.show()